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BISOR 
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II I HAVE TO DECIDE: 
II. WHO, WHAT, WHY, 
. WHERE, WHEN AND HOW 
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THINGS 
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t·71 2 9' 

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ASSISTANT SECRETARY OF DEFENSE 
WASHINGTON, D.C. 20301 

COMPTROLLER 

FOREWORD 
This text was developed as a guide to assist DoD Managers in their role as decision makers. Systems analysis is widely used to improve the quality of high impact decisions, for problems of force-mix or weapon system acquisition, but thousands of decisions are made daily by managers 
at the operating level without the benefit of a systematic consideration of the problem. These daily decisions total billions of dollars. All of us must learn to analyze our problems, to develop alternative courses of action for their solution, and to determine the costs and benefits of each alternative. We must constantly be aware of the importance of analysis in our daily managerial tasks and we must make the use of analysis a habit. 
I am convinced that the opportunity for significant savings exists at 
each managerial level and that this opportunity can be successfully exploited by the proper use of analysis. Our nation faces a critical period, beset by problems of shrinking resources, inflationary erosion, 
and rising personnel costs. The requirement for a strong defensive force has not changed, only its application has. Our department must simply 
do more with less. Each DoD decision maker should be cognizant of his responsibility to exploit every opportunity to ease this crisis. This 
text was developed for that very task, i.e., to help stretch our resources by improved analysis. 
There will be no new reporting system concerning the use of analysis, no one is going to be looking over your shoulder to insure the use of this text. Rather, I rely on your judgement and professional pride to motivate you to employ this text in a routine fashion. I suggest you make the use of analysiS your criterion of a job well done, of a decision founded on reason rather than emotion. 
Terence E. McClary 
Assistant Secretary of Defense 


ANALYSIS FOR MANAGERS OF PEOPLE AND THINGS 
Page FOREWORD TABLE OF CONTENTS iii ACKNOWLEDGEMENTS iv 
PART I THE NEED FOR ANALYSIS 
1. Managers Need Information; Not Just Numbers 3 
2. What Analysis Is, And Is Not 5 
3. Analysis By Whom And For Whom 9 
4. Government Activities Are Different; Or Are They? 11 
PART II SOME TECHNIQUES OF ANALYSIS 
1. The Right Places For The Right Numbers 15 
2. It's Only Arithmetic 21 
-

3. The Cost, The Whole Cost And Nothing But The Cost 29 
4. Accomplishment: What Are We Getting For Our Money? 35 
5. How To Get The Most For Our Money 43 
6. Getting Information From Our Numbers 57 
7. Use a Checklist: Do It Right 67 
PART III SOME USES OF ANALYSIS: CASE HISTORIES 
1. Monitoring Pharmacy Store Operations 71 
2. Budgeting For Pilot Training 79 
3. Measuring Productivity at Personnel Offices 89 
iii 
ACKNOWLEDGEMENTS 
The Office of the Assistant Secretary of Defense (Comptroller) expresses its gratitude to the individuals whose efforts made this text possible. 
• 
Authors-	Dr. lvon W. Ulrey, Professor of Economics, Navy Management 

Systems Center, Naval Postgraduate School Dr. Ann P. Ulrey, Economist; Consultant, Division of Research and Statistics, Board of Governors of the Federal Reserve System 

• 	
Illustrators -Robert B. Logan, Chief, Graphics and Presentations Branch Alex Della-Valle, Presentations Branch, OASD (C) 

• 	
Coordinator -Meyer Tartasky, Deputy Comptroller for Systems Policy, OASD (C) 


iv 
PART I 
THE NEED FOR ANALYSIS 

I ' 
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I .
II : 
I I I ·. 

I ! . :. 
!!: 
It
I li 
I II 
I 
I-1 
---------·-··---
·-------------
MANAGERS NEED 
INFORMATION: 
NOT JUST NUMBERS 

Data are not information 
My old boss just wanted You want your to stay with in his budget numbers to speak Eng I ish 
: i : 
I : 
Damn all those numbers: What do they say? I 
l. Managers Need Information-Not Just Numbers 
T
his book is about numbers-specifically those which relate accomplishments to their costs. It explains how managers can use cost and output data to obtain information which will help them make better use of resources-people and things. If you have management responsibilities at any level, and if your activity is one for which cost and output data are being or can be collected, these pages are directed to you. They will explain how the right numbers, properly used, can help you make better decisions in your job as manager. 
Analysis begins with a record keeping system which supplies adequate cost and output data for your activity. But simply collecting numbers is not analysis. First, they must be the right numbers. You must be able to identify quantitatively what got done over a specific period of time (accomplishment or output) and to match this with the resources consumed (costs) over the same period of time. The costs must include all those resources and only those resources used in turning out this output; and the product or service must be all the output but only the output associated with those costs. Furthermore, many analytic uses require numbers which are comparable over time and over a considerable range of outputs. 
Even when cost and output data meet these requirements, they do not-in themselves-help managers of operating activities make better decisions. Data are not information. They do not become information until they are organized in such a way that you can make comparisons (between planned output and actual output, for instance, or between two facilities engaged in similar work) and can identify relationships, such as that between costs and output over a range of operating levels. 
This book is about those comparisons and relationships. It shows-with examples-how significant information can be developed from appropriate data and how that information can be useful to managers in a broad range of situations which call for operating decisions. It is concerned with some of the conceptual problems faced in collecting and interpreting cost and output data-particularly by managers in governme~t activities. It is concerned also with recognizing the limitations of available data-and the uses to which imperfect numbers can and cannot be put. 
It does not set out to teach the specific statistical techniques that may be applied in developing information from numbers. Much of the analysis described in the pages which follow will not require a formal application of statistical procedures. And where it does, many managers-particularly those at installations with computer facilities-will call on a statistician. If you choose to work directly with the numbers yourself, any standard statistical text will detail the techniques which are not hard to learn. 
Whatever cost and output numbers are now being collected for your activity, reading this book may have three results. First, you will find ways in which you can use at least some of the available numbers to help solve management problems. Next, you are likely to learn that numbers currently being collected are inadequate or misleading in ways that make them less useful than they might be. For instance, data on operating costs may not be matched with equally reliable data on what got done over the same period of time, or cost figures may include items that are not relevant to your management decisions. You may well find that rather simple changes in record keeping procedures could make the numbers much more useful analytically. In any event, you will learn the kinds of analysis for which your numbers are suitable and the kinds for which they are not. And when you understand these limitations you will be able to protect yourself against the misuse of these numbers by others. And finally, you may uncover some numbers which are neither used nor useful and should no longer be collected. 
If none of these possibilities intrigue yon, you need not read further: this book is not for you. But if they do, the purpose of the following pages is to explain how numbers-specifically, cost and output data-appropriately arranged and analyzed, can lead to better use of resources-people and things. 
3 

I -2 

. II i i , I I 
I , i 
• I
WHAT ANALYSIS IS.
I 
AND IS NOT
I I 
1 
It's a process; not a system 
\ i 
J ; 
Here's what __ we have to do ( 
---L 
Here's what each 
waywill cost There are several 
ways to do it 

2. What Analysis Is, and Is Not 
T 
he essential ingredients of management decisions are people and things. Managers in all kinds of jobs, whether business or government, civilian or defense, and at all levels, have to make decisions about the best ways of combining people (clerks, production workers, technicians or scientists) and things (office supplies, machinery, sacks of flour, or missile systems) to turn out whatever happens to be the end product of their activity. They must make such decisions whether that product is something as tangible as engines repaired or as elusive as the capability of a weapons system, and in order to make the best possible decisions, they utilize whatever evidence is available to them. 
In every day language, analysis is simply a rational way of approaching problems which require decisions. All of us engage in analysis; we try to find out what went wrong with a golf stroke or why the car is making unfamiliar noises. In the case of management decisions, analysis is concerned with choices: alternative ways of acquiring and using resources (people and things) in various combinations to accomplish various objectives. 
Many of these choices-particularly for ongoing activities with a readily definable outputinvolve changes up or down from existing levels of production or expenditure. We start from where we are and consider the impact of a change from that starting point: most obviously, of course, changes in next year's budget or workload, but also such other changes as those in specifications for the job to be done, in service or quality of an end product, in wage rates or the cost of supplies, in the way work is distributed among two or more installations, in any factor likely to have an impact on the activity's cost or output. Since decisions at the operating level are of this type, the focus of this book will be directed primarily toward analysis dealing with problems in this category. 
There are other highly important but less frequent decisions which involve major acquisitions. These may range from a choice at the highest level among alternative weapons systems through the pros and cons of building a new hospital or undertaking the major remodeling of an old one to selection of new equipment at an office-management level. Such decisions also rest on a comparison of the relative costs and benefits of each alternative being considered, though the information supplied by record systems based on operating experience often does not furnish direct precedents for making these comparisons, necessitating use of various estimating procedures. 
As practiced in the Department of Defense, economic analysis has tended to concentrate on large scale procurement programs and projects. For decisions of this sort, preparation of a formal analysis is required, and for these situations a detailed procedure has been prescribed. (See Economic Analysis Handbook prepared by Defense Economic Analysis Council, Department of Defense.) Indeed, the term "economic analysis" is sometimes reserved specifically to describe this process of choosing among major investment alternatives, while the range of decisions which involve changes in an ongoing activity may be labelled "program evaluation" 
i.e. ways to improve existing operations. No such distinction is made here since analytic techniques can be applied to any problem for which you find them useful and at any level of decision making. 
The tendency for policy makers to focus on large scale procurement projects rather than operating level decisions is understandable. When a single decision involves many millions of dollars, the potential savings from making a better decision will be dramatically large. In other areas, the spending of Operation and Maintenance funds, for instance, individual management decisions are unlikely to produce such dramatic results. But collectively, the potential savings are fully as great. 
The Operation and Maintenance budget constitutes about 25 percent of the Department of Defense's total budget authority-$23.1 billion proposed for Fiscal Year 1974 as compared with an $18.8 billion total for Procurement. Among the major programs itemized in the Department of Defense Financial Summary, support activities such as Training, Medical, Other General Personnel Activities call for $18.2 billion; Central Supply and Maintenance for $8.4 billion; Intelligence and Communication, $6 billion; Airlift and Sealift, $0.8 billion; Administration and Associated Activities, $1.7 billion. In each of these areas, a generalized improvement in 

5 


management decisions could produce huge savings. 
The cost of operating a military food service center may involve a relatively modest $100,000 annually, but food services cost the Department of Defense over $3 billion each year. Motor pools, hospitals, basic training facilities, and the like, all provide similar examples. Each is a relatively small operation, but collectively such routine ongoing activities become the largest resource user the Department has. Moreover, because many of these activities lend themselves to cost and output measurement, analysis can contribute more easily to such improvement. 
As this book will demonstrate, analysis, at its lowest level, may consist simply of collecting the right numbers and organizing them to display information useful to you as a manager. Most often, analysis will involve using simple arithmetic with a pencil and ruler to obtain more information from your data and, if time permits, of applying elementary statistics to make that information more precise. 
These various uses of cost and output numbers will be presented and explained in Part II. Section 1 of that Part demonstrates the value of data formats which highlight directly the relationship of actual to planned output and actual to planned costs and display trends in those relationships over time. Section 2 shows how data collected over a range of output levels can be used to establish the relationship of operating costs to different levels of output and illustrates ways in which knowledge of this relationship can be used. I 
Sections 3 and 4 are concerned with problems-conceptual and practical-in measuring cost and output to obtain data which will be useful for analysis. 
Section 5 deals with the use of cost and output data to select the least costly way of combining resources (people and things) to achieve a particular level of output and also ways of identifying the most efficient scale for facilities which provide a particular end product or service. 
6 

As a practical matter, actual cost and output C numbers collected by an operating activity will always be imperfect. Section 6 considers the use of such data-what adjustments can or must be made to make comparisons valid and what statistical techniques can make it possible to identify significant relationships even when working with imprecise data. 
With this background, Section 7 returns to the problems of data collection-of making sure that record keeping systems supply cost and output numbers appropriate for alalysis. It summarizes, in the form of a check list, the most significant criteria for such systems. 
Finally, in Part III, the techniques discussed in Part II are applied to real instead of hypothetical cost and output data collected by actual operating activities. These case histories illustrate the use of analysis in several situations which required management decisions. 
The importance of cost and output information of the sort described in these pages extends beyond the operating level where the numbers are collected. Both the numbers and the management decisions made at that level become an integral part of the decision making process at successively higher levels. Cost and output numbers-organized so as to display C useful information-become part of the data -· that top level managers and analysts consider in estimating the costs and benefits which can be expected from the various defense options open to them. Moreover, these top level decision makers need to be confident that their estimates represent the lowest possible costs associated with each alternative under consideration. And each component in those estimates represents output-an end product at some level. 
Analysis should not be an occasional major 
undertaking but a way of life-a continuing process in which you, as a manager, can obtain information from numbers and apply that information as an aid to judgment. Analysis can be helpful at all levels of decision-making from improving day-to-day operations to long range planning, programming and budgeting. 
c 


I -3 

: i 
ANALYSIS BY WHOM 
AND FOR WHOM 

We all do it -more or less 
Let•s keep this series up-to-date ~~ 

Now it•s numbers for 
better management 

That will mean fewer quick and dirty answers 
ACCOUN~Ni: 

3. Analysis by Whom and for Whom 
T
he heading at the top of this page reflects a conventional way of looking at analysis as something that someone (the analyst) does to data. His activity is supposed to yield suggested conclusions (analysis). These can then be turned over to someone else (the user) who will, hopefully, find them helpful in arriving at some (unspecified) management decision. 
If you have read this far, you already realize that this view is partial and seriously misleading. Analysis is not an act performed by a technical specialist called an analyst; it is a process of using numbers to improve decision making. It includes several stages which take place over time and call for active participation by the resource manager, the statistical analyst and everyone involved in collecting, verifying and organizing the data on which the analysis is based. 
If the end product is to be helpful in solving a management problem, analysis must begin with a clear formulation of the problem for which a solution is sought. Only the decision maker qimself (in conventional terms the "user" of the 
completed analysis) can provide this perspective. 
The problem may be a continuing one such as performance evaluation; it may be recurrent like the need to prepare budget estimates which take account of prospective changes in workload, responsibilities or performance standards; it may pose specific choices: where to allocate additional work among two or more facilities (or where to cut back); whether to expand (or consolidate) existing facilities, set up new ones, decentralize or shut down old ones; whether to acquire more highly automated equipment, hire additional workers, or rely on some combination of the two. 
AB a broad generalization, the contribution of quantitative analysis to solving any of these problems lies in identifying the relationship between cost and output under varying conditions and providing comparisons. These may include comparisons over time, comparisons among two or more facilities, comparisons over a range of operating levels or among facilities of differing size, comparisons of operations carried out with differing combinations of resources (people and equipment). Part II will describe in some detail ways of making a number of these comparisons, and a technical specialist (the analyst) can apply any statistical techniques which are required. But the manager must decide which comparisons will be relevant and helpful in solving his particular problem. 
Similarly, an analyst can tell him what numbers are needed to apply the analytic techniques they select, but the manager must know what data are currently being collected for his operation, decide whether additional numbers should be obtained, and work with those involved in collecting and processing data to set up new or modified record keeping procedures where these are needed. 
Even more important, he must understand the data-what goes into the cost figures he receives, how output is measured, what time spans are covered by cost and output figures respectively, changes over time which affect the comparability of supposedly similar items. Such factors may preclude using certain data for some purposes and in any case will affect his interpretation of the results. 
Once the procedures for acquiring and analyzing suitable data have been set up, it will often be possible to continue them routinely at a clerical level and to program many of the statistical operations for computer processing. The manager will then be able to turn more of his attention to interpreting the results. But no matter how carefully designed an information system may be, he should never accept a continuing flow of numbers without scrutiny. A 
computer may be programmed to flag variations in data or statistical ratios which exceed some predetermined limit, but it cannot explain why such variations occur. 
Someone familiar with the actual conditions under which a facility or agency operates will have to decide whether particular changes affect the validity of key comparisons-those made over time, for instance, or among different installations. The "user" of analysis must play a continuing role in identifying such changes and in seeing that appropriate adjustments are made either in the statistics themselves or in the way he interprets them. This is part of the decision maker's responsibility for exercising judgment. 

9 


c 
I-4 
-·---·
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GOVERNMENT ACTIVITIES
ARE DIFFERENT~
OR ARE THEY? 

Needs unlimited; resources scarce 
We're doing a good job; but how can we provel 
We don't have a profitWe count different costs and loss statement Iike 
industry does 
.: TitHNICIAN . 
c 
4. Government Activities Are Different-Or Are They? 
W
hether managers of operating activities work for government or business, they need the same types of information in deciding how to make the best use of resources. The same cost/output relationships are significant to both. In this basic sense, government activities are not different from business. 
But you, as a maker of management decisions at some level within a government agency, face special problems in obtaining good cost and output data which your opposite number in industry may take for granted. On ·the other hand, you are likely to find that having the right numbers and being able to present them convincingly is even more important to youespecially in estimating and justifying your budget needs-than it is for your counterpart in the private economy. 
Government activities face specific challenges in measuring both cost and output. On the cost side, these arise from record keeping procedures and particularly from the time at which expenditures have traditionally been recorded. Output measurement, on the other hand, poses problems because of the way in which services performed by government are customarily provided to the public. 
Traditionally, government activities have kept detailed records of costs, principally to make sure that obligations to spend money do not exceed authorizations to obligate and that expenditures do not exceed what has been budgeted. Departmental officials-and the Congress-have needed, and always will need, records for purposes of control. The traditional records perform this essential function of holding commitments and expenditures within specified limits; they keep resource managers accurate and honest, but that is all they do; and that is no longer enough. 
Resources (people or things) are not consumed at the time they are ordered, or at the time they are delivered, or at the time they are paid for. Consequently, cost records geared to orders placed, deliveries received, or disbursements made cannot be matched, timewise, with the particular output for which those resources were actually used. Traditional government accounting records have not supplied the numbers needed to do this. 
Managers in private business on the other 
hand can obtain the numbers they need from 
their accounting records. Since business offers 
its output-goods or services-for sale in the 
market, managers must know whether the selling 
prices of specific items cover, exceed, or fall 
short of their cost (that is, the resources 
consumed in producing them). To associate 
specific costs with specific output, resources are 
treated as "costs," not when they are ordered, 
delivered, or paid for, but when they are used. 
Accrual accounting, as this method of record 
keeping is called, allows business managers to 
measure the resources consumed during a speci
fied period of time and match them with results 1(sales) during the same period. 
Similarly, business managers need to match 
each price on their sales list with the cost of 
turning out the particular item to which it 
applies. This requirement has given business 
accountants an incentive to distinguish those 
cost elements which are relevant to particular 
types of output and to allocate joint expendi
tures among their several end products. 
Historically, the records kept for govern
mental operations, detailed as they have been 
in other respects, have not filled either of these 
needs. This gap in information was recognized in 
the 1966 Department of Defense Instruction 
(DoD I 7000.1) which required establishment of 
Resource Management Systems for a variety of 
operations within the Department. In recent 
years much attention has been focused on 
collecting cost data in a form which does permit 
direct cost/output comparisons. For many oper
ations, numbers suitable for at least some such 
comparisons are becoming available. 
But cost data provide only half of the 
numbers needed for cost/output comparisons. 
Such comparisons cannot be made unless you 
are also able to measure what got done during 
the same time period. Both business and govern
ment use resources in order to fill "needs"-that 
is, they tum out products or services that people 
want. But output measurement is more difficult 
for government activities because most govern
ment services, instead of being sold in the 
market, are furnished directly to the public and 
paid for out of government funds. The manager 
of a business which offers its product for sale 
has an immediate measure of output in sales and 
11 


associated revenues. As the table below shows, chooses to spend on the output of other, quite c 
the resultant figure on profit or loss even gives him a first approximation to measuring his performance: 
BUSINESS GOVERNMENT 
• 	
Measure of what got done Sales Output 
(Revenues) 


• 
Cost of what got done Cost Cost 

• 
Measure of performance Profit (Loss) Needs met 


Moreover, these "measures" which are generated by business through the very process of doing business are expressed in a common denominator: dollars. The dollar amounts can be related directly to cost data; they can also be compared with sales and revenues for a range of price lines (similar items made to different quality specifications), and they can even be compared with amounts the buying public different business activities. 
The market does not provide the manager of a government activity with these direct dollar comparisons. For equivalent information on physical output units, he must look to a records system instead of sales records. He will not find any equivalent for the market's direct indication of dollar value. When tax money is spent to meet a public need, the public cannot record its satisfaction or dissatisfaction directly by generating profits or losses. Instead, the value of any government activity's proposed output-relative to other uses for the same money-is judged at successively higher levels of budget review. 
This is a process which culminates in Congressional decisions to commence, to continue, to increase, or to cut current appropriations. And at every level of review, an activity's budget will be in jeopardy if its managers cannot show, quantitatively, what has been accomplished for past expenditures and what can be expected from expenditures proposed for the future. 

12 


PART II 
SOME TECHNIQUES OF ANALYSIS 

ll-1 
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' I
I . l 	: i 
II 
THE RIGHT PLACES FOR 
I I I THE RIGHT NUMBERS 

Formats show relationships 
I 
With this format I 
can keep track of 
where we are 
I 
How often do 
you want it? 	That•s why we set 
it up that way 

c~ 

1. The Right Places for the Right Numbers 
D
ata are not information; they become information only when you, the U<Ser, are able to make comparisons or identify relationships which are significant in managing your activity. Even the most accurate cost and output numbers will not-by themselves-tell you how this month's performance compares with last month's or how actual accomplishment matches what you (and others) were expecting. 
Data become information when they are so arranged that you can make these comparisons, or others which are relevant to your current problems. The arrangement need not involve statistical techniques. It may involve nothing more than -finding the right places for numbers that are already being collected regularly. 
Suppose output data are available and you are interested in comparing your activity's performance this month with last month and the month before that. You might set down the monthly figure side by side: 
Table 1 
Comments: 
This tells you that actual output has increased each month over the three month period-a fact of some significance. But it does not tell you in a truly meaningful way that this month was "better" than last month and the month before. 
By providing a data format with additional slots to display each month's planned results alongside actual output, the amount of information immediately increases. Suppose, for instance that a constant level of output, say 100 units, had been expected each month. (See Table 2). From the numbers in this display, you see not only that output increased each month but also that actual performance, originally below expectations, first approached and then reached the planned level. 
On the other hand, displaying these same actual outputs alongside planned amounts might 
Table 2 
Planned Output 100 100 100 100 
Actual Output 90 95 100 
Difference -10 -5 0 
%Actual of 
Planned 90 95 100 
Comments: 
have revealed that the monthly increases did not in fact represent improved performance. Suppose the figures for planned output had called for substantial increases in the amount of work to be turned out each month: 
Table 3 
Planned Output 100 110 120 130 
%Actual of 
Planned 90 86 83 
Comments: 
Although the monthly rise in output is identical with that recorded in Table 2, Table 3 would reveal at a glance that your. activity, far from improving its performance during the three month period, was really falling farther and farther behind its target: only 83 percent of expectations this month, whereas comparable percentages for the two previous months had been 90 and 86 percent respectively. 
Output data can yield this information without any application of statistical techniques, simply through arranging the numbers to display directly comparisons over time and of planned results with actual. These comparisons constitute an .elementary but exceedingly valuable type of analysis. 
Still more revealing is the information that becomes available when both cost and output data for the same activity are arranged in 
15 

identical formats and set side by side. Suppose output has appeared to be consistently on c 
c 

cost and output numbers for your activity over the last three months were as follows: 
Table 4a 
COST 
(Thousands of dollars) 
Month 'Before -eas~ Last Month -_ This Month Next Month! i 
Planned 100 100 100 
(Cumulative) (100) (200) (300) 

Actual 100 100 100 
(Cumulative) (100) (200) (300) 

Difference 0 0 0 
%Actual of 
Planned 100 100 100 

Comments: 
Table 4b 
OUTPUT 
(Number of end products) 
Planned 100 100 100 
(Cumulative) (100) (200) (300) 

Actual 100 95 90 
(Cumulative) (100) (195) (285) 

%Actual of 
Planned 100 95 90 

Comments: 
Examining the cost record by itself, you would conclude that operations were proceeding according to plan-for each month, expenses actually incurred were equal to those expected for that time period. But the record for output tells a different story; actual end products matched expectations only in the first month, then fell short by increasing amounts. The comparison becomes even more unfavorable when the two sets of data are considered side by side, since output fell below expectations by increasing amounts while these monthly reductions were not matched by any corresponding reduction in costs. Here is a situation which you, as a manager, would clearly wish to know about promptly. Conversely, of course, unplanned deviations in expenditures might alert you to the need for investigating a situation in which target. 
An adequate data format should display both cost and output figures; either record, by itself, may be highly misleading. This requirement is significant because data on an activity's costs are more often already being collected, more complete or easier to obtain than comparable figures on output. In many situations where output is difficult to measure, cost data are used as indicators of accomplishment. 
For some purposes, such an indicator may be useful-or at least "better than nothing." But for many types of analysis, it is more likely to be "worse than nothing." When you use cost data to keep track of accomplishment, you are assuming that every change in the amount of resources used by your activity results in an exactly proportional change in the work turned out. For most kinds of work, this assumption is not warranted. Not only are the changes often likely to be disproportionate, but such divergences are themselves extremely significant information for supervisors, managers, budget officers and all those concerned with longer range planning. Much of a manager's job consists of understanding when and why disproportionate variations occur and deciding what-if anything--should be done about them. 
This is the reason why, in most government activities, increasing emphasis is now being placed on measuring output directly rather than relying on cost records as an indirect indicator of accomplishment. If yours is an on-going activity with a readily recognizable end product, statistics are very likely being collected on the number of objects turned out or services performed over given time periods: meals served, engines reworked, recruits trained, forms processed or whatever. There are problems and pitfalls in collecting such numbers, some of which will be discussed in more detail in Section 4 of this Part. These problems become more difficult for activities with complex end products or missions which are not readily countable. 
Finding ways to measure output statistically is well worth the effort; much of the analysis described later depends on establishing mathematical relationships between costs and output over a range of outputs. But even if such numbers are not yet available for your activity, you can use the technique described above for 
16 

monitoring performance over time. As explained here, this involves making two independent sets of comparisons for the same time period-one between actual costs and planned costs, the other between actual accomplishments and planned accomplishments-and then matching the two trends to discover whether they parallel each other or diverge. Even an array of plans in the form of a written list with items crossed off as they are accomplished could furnish some basis for this comparison. The essential requirement is to keep the method for assessing accomplishment independent of cost records so that the two trends can legitimately be compared with each other. 
Since the purpose of such comparisons is to alert you-as manager-whenever actual operations diverge from expectations, developing trends may become apparent more quickly if you can see the numbers transformed into lines on a chart. 
Consider the figures for cost and output from Table 4 above. These could be plotted in several ways. One way is to plot actual numbers against planned numbers. (See Figure 1.) 
" 

17 

A glance at the two charts quickly indicates that actual costs have matched planned costs exactly but that output, over the same time span, has been falling farther and farther below expectations. 
These facts might also be combined in a single chart by showing the percentage relationship of actual cost to expected cost for each month as one line and the relationship of actual to expected output as the other. In this chart the divergence between trends for cost and output data is highlighted even more directly. Figure 2.) 
If an activity's level of operations often fluctuates considerably from month to month, another graphic technique is likely to be useful. It involves plotting the cumulative totals for each month and the preceeding months, revealing at a glance whether monthly departures from expected norms have tended to build up over time or to cancel out. Using the data presented in the same table (Table 4), for instance, the cumulative impact of the downtrend in output relative to expectations is immediately apparent. (Figure 3.) 
100 
95 
90 

,-~-------------~-------------J 
Commoou, -
Another type of graphic presentation likely to be useful in an activity where the workload fluctuates around the norm from month to month can relieve managers of much routine supervision. This technique, sometimes referred to as "management by exception," can be used when the supervisor knows, from experience, the approximate range-say 10% above or below the planned level-within which monthly results can normally be expected to fluctuate. 
Suppose this is the case in your activity and that, over a three month period, the ratios of actual to planned output and of actual to planned costs have varied as shown below: 
I 
0 
Planned Cost 
0 0 
Actual Cost 
Cost 0 
0 0 
Ratio-Actual/ 0 
Planned 
Comments: 
--' 
~ Planned Output 
Output ~ Actual Output 
0 Ratio-Actual/
0 0 Planned 
Comments: 
.,._. "'·· 
Table 5 
; 
Md"nth Before-~ ' Last i · Las~'Moi\th · Thi~ M()r,th ! 
100 120 110 95 125 130 
95 104 118 
100 120 110 90 130 85 
90 108 78 
Figu're 3 
" '~J 
COST OUTPUT 
(Cumulative Totals) 
300 300 
200 200 
100 lOb 
0 0 

~---~---~-----~~-----·-----·---~--------··--·---·---~------~--· ---~--·-----------
18 


Using these numbers, monthly actual-toplanned ratios for both cost and output can be plotted above and below a centerline (actual equals 100 percent planned), showing each month's percentage deviation from expected costs and output. (See Figure 4.) The two broken lines on the chart mark off deviations of 10 percent above and below expectations. On the basis of experience, these form a band of allowable variations. When a monthly deviation from planned performance falls outside this range, the chart alerts the manager to the need for more than routine supervision. As plotted above, deviations flagged in the third month would require investigation and possible corrective action. 
The choice of specific limits in such a chart is, of course, a product of judgment as well as experience. To tighten control, the permissible deviation limits may be narrowed; unnecessarily rigid controls, on the other hand, may be relaxed by widening the range within which variations will not be treated as "out of line." The technique provides a basis for better control over an activity and can, at the same time, relieve the manager of routine work. This is an example of co'st and output numbers used, as they should be, to aid experience rather than to replace it. 
\ 
-T---
L
\ 
\ 
\ 
G) 
19 

( 
ll-2 
I I 
II , i :, 
I I ' . 
IT'S ONLY ARITHMETIC I .
'I : II I\ I I .
Really ? 
\ j ;
\ ~~~~~~=~ 
These comparisons help a lot 
Do you want the 
underlying data? Remember, the numbers 

are not very precise 
( 
2. It's Only Arithmetic 
K
eeping good cost and output records for an operating activity could pay its way in more efficient management even if the numbers were used only for monitoring current operations as described in the preceeding section. But they can do much more. Over time they will provide the data base needed for relating costs to output and for doing so over a rang(; of outputs. This section and most of those which follow will deal with techniques for analyzing that relationship and drawing conclusions which are significant 
for a wide variety of management decisions. 
If you are sure that cost and output numbers 
for a particular month really match, timewise 
and otherwise (a requirement which will be 
explained in detail in Section 3), these two 
numbers can be related graphically. The graph 
will show output-measured in physical units
along the horizontal axis while cost-measured 
in dollars-is plotted along the vertical axis. For 

instance, if your activity turned out 100 units of 
output and used $100 worth of resources in 
doing so, both cost and output observations 
would appear as a single point on this graph: 
·, :·. ','

Figu,re ~ 

i 
I I 
! 
I I 
Barring a future change in circumstances, that point gives you a fix on what it costs to turn out 100 units of output over the space of a month; this is the only information it supplies. It does not tell you what total costs would be if your activity's workload changed sharply-doubled or tripled or was cut in half. But the graph provides a means of visualizing your expectations about what would happen to costs as output rose or fell. If, for instance, you were to assume that the change in costs would be proportional-that your facility, with its present capacity, could cope with a doubled workload by doubling current expenditures-additional 
points could be plotted to reflect this expected cost/output relationship and joined by a solid line like that in Figure 2: 
Suppose your activity were then required, in 
fact, to turn out a larger amount of work, say 200 units. The cost/output point associated with that actual peak load might or might not lie 
along the expected cost/output line. If the actual observation was above the line (as shown by the dotted line in Figure 2) it would show that the cost increases associated with increases in output exceeded expectations. In this example when output was pushed from 100 to 200, costs were expected to rise to $200 on the vertical axis; but in fact they rose to $300. 
This divergence of actual from expected costs might be interpreted as were the deviations discussed in the last section: that is, it might suggest possible operating problems to be investigated. On the other hand, it might indicate that your expectations had been unrealistic. 

21 



Analysis can help determine whether or not cost/output relationships-for this particular activity and over this range of outputs-are what you have assumed. 
In order to predict how much impact a proposed change in your activity's output will have on costs, cost/output observations must be 
available for each of several different levels of output. These may be drawn from the activity's own records over time or they may be data for similar facilities operating at different output levels. In some cases-if, for instance, there have been sharp month to month fluctuations in the amount of service a facility has been called on to furnish-records kept over a relatively short span of time may supply you with data showing the actual costs which have been associated with a variety of different outputs as illustrated below: 
Table 1 
AUGUST  
Output  
(Units)  4,000  5,000  2,000  3,000  
Costs  
(Dollars)  36'000  46'000  19,000  27,000  
Comments:  

For purposes of analysis, the only difference among the four pairs of cost/output observations in Table 1 should be the differences in number of units turned out. In practice, since each pair represents a separate time period, a number of other circumstances may have changed: the price of materials may have risen, for instance, weather conditions may have disrupted operations or other factors may have affected comparability. Section 6 discusses ways of coping with this problem. 
But if the four pairs of numbers are comparable, you could determine from these data with some degree of confidence how the cost of performing the service (engines repaired, meals served, vehicles serviced, X-rays taken, recruits trained, etc.) was related to operating levels within the 2000-5000 unit/month range. (You would also be able, though with less confidence, to make better cost estimates if the monthly workload were to move outside that range.) Moreover, determining cost/output relationships over the relevant range of outputs would involve 
nothing more than simple arithmetic. In fact, you will find this true for most other widely used applications of cost and output numbers. 
Your first step in comparing the four different levels of output recorded above would be to convert the total cost for each month into average cost per unit for that month's output: 
Table 2 
Output  4,000  5,000  2,000  3,000  
Costs  36,000  46,000  19,000  27,000  
Cost/Unit  9.00  9.20  9.50  9.00  
Comments:  

Since costs per unit were lower in some months than others (and since we are assuming 
that the change in volume of work done was the only significant change from month to month and that no addition was made to the facility's 
physical capacity), it is clear that your facility operated more efficiently at some levels of output than others. But the precise relationship is hard to visualize from the monthly data format. 
If the numbers are plotted instead on a graph showing unit costs on the vertical axis and the amount of monthly output (rather than its 
chronological sequence) along the horizontal axis, it quickly becomes apparent that the lowest unit costs were associated with output in the range of 3000 to 4000 units per month. 
When workloads were either larger or smaller, unit costs rose. A curve joining the points which represent actual observations wottld take a Ushaped form. (See Figure 3.) 
When an average unit cost curve takes this shape, it tells us that the facility in question has a "best" or low-cost rate of operation for its present physical capacity and that operating at 
any other level-either higher or lower-will make each unit more expensive. 
The data might have produced quite a different sort of curve-one which sloped up or down throughout the entire range of observations, for instance, or one that was V-shaped or was level over a wide range of outputs. The "U-shaped curve" is customarily used for purposes of illustration because most facilities do 
22 

operate more efficiently around the workload they were designed to handle. But some activities can adjust their operations (and their costs) to increased or decreased loads far more readily than others. Where this flexibility does not exist (where a facility's given capacity permits only one efficient level of operation), the curve may be V -shaped so that costs at higher or lower levels quickly become prohibitive. Downward or upward sloping curves, on the other hand, would indicate that your data covered a range of outputs all of which fell short of the facility's most efficient level of operations or, conversely, were already overtaxing its capacity. Only by analyzing data for your activity over the relevant range of outputs could you identify the probable impact on your costs of a specific proposed change in output. 
A graph like that in Figure 3 would give you important information about that impact, but another way of using the date could tell you considerably more. Most management decisions involve possible changes from some existing level of operations; put in another way, you always start from where you are (and usually this is not zero.) Whatever your level of decision makingimmediate supervision of a single facility or overall planning responsibility for a major activity-your questions usually concern the impact of change, upward or downward, from the existing level. 
Analysis which focuses on the changes is sometimes called incremental analysis because it is concerned with successive additions to (or subtractions from) outputs and expenditures. Economists call it "marginal analysis" becauseat least in principle-these are decisions made "at the margin:" one unit more or one unit less. In practice, of course, changes in the operation of an on-going activity would rarely, if ever, be considered one unit at a time. You would ordinarily be directing .your attention to a specific increase or decrease of some minimum size. 
Using once again the data presented above, suppose your activity had a current workload of 4000 units per month but that next month you expected it to be 5000-an increase of 1000 units. Figure 3 would tell you that if this change occurred, your average costs would rise from $9.00 to $9.20, and you might infer from this that the 1000 units would cost $9200. But Table 2 tells you clearly to expect your total costs to go from $36,000 to $46,000-a jump of $10,000. Looked at from this perspective, the additional 1000 units achieved as a result of spending an additional $10,000 would, on the average, be costing not $9.20 but $10.00 each. (Note that the point indicating an average cost for the 1000 additional units is plotted on Figure 4 at 4500, half way between the 4000 and 5000 unit levels.) 
Cl 
u $ 8.50 
$ 8.00 
0 ~~~~~~~~~~~ 
o: 
The use you might make of this sobering information would depend on the level of your management responsibility. If your workload were determined entirely by forces outside your 
23 


control, you would use it to demonstrate convincingly that your budget must be increased by $10,000 to handle the 1000 additional units. (Your budget officer, looking at the $9.00 per unit cost figure associated with your current 4000 unit operating level, might want to give you as little as $9000.) 
At higher levels of management, you might consider how urgently the additional 1000 units were needed: Were they worth $10.00 a piece? Could some of this work be postponed until loads were lighter? If the increased workload seemed likely to be permanent, should the facility be expanded to provide new capacity, or could the additional work be assigned to some other facility where additional output might add less to total costs because current operations were below its most efficient level? 
If your options included the possibility of expanding the existing facility (or constructing new capacity elsewhere) your analysis would have to take account of additional factors (the time needed to expand capacity, the investment cost, the more efficient scale for a facility of this type, etc.) and would become more complex. 
Section 5 deals with some of the factors you would need to consider. Further, any decision involving significant capital investment would require application of the analytic procedures outlined in the Economic Analysis Handbook cited earlier. 
The possible advantages of allocating work among existing facilities can be illustrated from the figures in Table 2. Suppose your current operating level were not 4000 but 2000 units per month. Under these conditions, the table reveals that 1000 more units could be obtained for only $8,000 in additional costs (an increase from $19,000 to $27,000). Your facility would be operating more efficiently after the increase than before, and, as Figure 4 shows, the additional 1000 units would be costing, on the average, only $8.00 apiece. The other possibility, an increase in operating level from 3000 to 4000 units per month, would leave efficiency unchanged; total costs would rise by $9,000, the added units would cost $9.00 apiece, and average costs would also be unchanged at $9.00. 
The same considerations which are important in assigning additional work also apply in determining the cost savings which might be expected if output requirements were decreased. Again using the data presented in Table 2, if your facility were currently working at the 5000 unit per month level, a reduction in workload by 1000 units would bring it closer to the "best" level of operations for its existing capacity and, allowing for some time lags and friction in cutting back on costs, would permit a monthly savings of $10,000 rather than the $9,000 to $9,200 suggested by the average cost figures. 
From a current operating level of 3000 per month, on the other hand, a 1000 unit reduction would not save more than $8000. In both cases, the impact of the change would depend not only on the size of the change but on "where you started from." And once again, you as a manager could anticipate what changing output requirements would really mean to you 
much better from analyzing the incremental change in aggregate costs than from average cost figures. 
If your responsibility included decisions on how to allocate work among two or more facilities, you could use this analysis to discover where additional work could be done for the least added cost and where a cutback would result in the largest savings. The answers to these questions would depend not only on each facility's operating level just prior to the proposed change ("where they started from") but also on the shape of the cost curve at each. 
Suppose two facilities are engaged in turning out the same work-engines overhauled, vehicles serviced, meals served, X-rays taken, recruits trained, etc. (Locations A and B in Figure 5). Suppose further that each is currently operating at the "best" level of output for its existing capacity (for purposes of illustration, 100 units), and that each has identical costs of $1.00 per unit when operating at that level. But there the similarity ends. As Figure 5 shows, adjustments in output around this technically "best" operating level appear to be much more difficult (and expensive) at Location A than they are at Location B. The cost curve for Location A approaches the V -shape discussed earlier while that for Location B is nearly flat for a considerable range of outputs on either side of its best level. 
These diverse relationships would be very significant if you needed to increase combined output for the two facilities to 225 units or if overall requirements fell to 175. As the numbers beside the graphs indicate, Location A is already operating at the only level where the facility 
( 

24 

Figure 5 
2.00 
..... 
::J Marginal Cost 
.....
0 0.. 1.50 \ LOCATION A ...... 
0 
..... . . .: ; 1MARGfNAt/COST I
AVERAGE. •· ·· · ·· ·· ·· ·' . I
c: 1.00 cosr ·' totAl': ·.'·A~ERAGE I
::::> /
Average
L... 
Q) 
75 $ 86.75 $1.15
Total
0.. 
$13.25 $0.53 
..... Cost 100 100.00 1.00 
VI 
0 .50 37.50 1.50 
125 137.50 1.10
u 
o~-.....~o---'---...___....__ _..._ __. 
0 50 100 150 200 250 
Output per Unit of Time 
LOCATION B 
!; ..... I
MARG'INAL COST I-TOTAL AV.ERAGE 
I
IOUTPUt\.· 
;...., 
COST COST TOTAL' AVERAGE I
... ;~ I 
2.00 
75 $ 76.50 $1.o2 r>, >· $23.50 $ .94 
..... 100 100.00 
1.00 t~:
::J i'' 27.50 1.10 
0.. 125 127.50 1.02
..... 
1.50 
::J Marginal Cost
0 
...... 
0 
..... 
c: 1.00 r::::> 
""' Total Cos;


~Average
L... 
Q) 
0.. 
..... -
VI .50 
0 
u 
I I I I I
0 
0 50 100 150 200 250 

Output per Unit of Time 
functions efficiently. Short of adjusting capacity would be expensive: adding 25 units would through an investment decision, any change in boost costs by $37.50 (an average of $1.50 for requirements in either direction from that level each additional unit); .a cutback of 25 units 
25 


would save only $13.50. The additional 25 units could be obtained much more cheaply at Location B where the total added cost would be only $27.50 (or $1.10 apiece). On the other hand, Location B would also be able to adjust better to a cutback, that is, the reduced workload would permit a savings of $23.50, $10.00 more than could be saved at Location A. 
Assuming that total requirements rose from 200 to 225 and you were free to make your decision solely on economic grounds, you would assign the entire 25 unit increment to Location 
B. Conversely, if total requirements declined, operations at Location A should remain unchanged while a cutback to 7 5 units occurred at Location B. 
In light of the evidence assembled here, this conclusion is self-evident. But if you did not have quantitative information of the kind described above on the way costs were related to changing output levels at both locations, it would not be evident at all. 
26 
) 

ll-3 

THE COST, , I 
' I 
THE WHOLE COST AND 
NOTHING BUT THE COST 

Are they or aren't they? 
. 
These are the pertinent costs? 

These are the costs we agreed to use 
For this purpose they are 


3. The Cost, The Whole Cost and Nothing But the Cost 
I 
n order to perform the arithmetic of analysis, as described in the preceding section, you need numbers-actual numbers for your own activity. The amount of help that analysis can provide in making management decisions depends largely on the accuracy with which cost and output are measured. Important as record keeping is to this process, more is involved than setting up a reporting format. and assigning someone to collect the numbers. This section and Section 4 which deals with output will explain why. 
When you read, "It costs 9¢ to deliver an 
airmail letter." or "It costs $1.50 per meal to 
feed military personnel," the numbers attract 
your attention. They are specific, and in print. It 
would appear that they are the cost of delivering 
letters or providing meals. But a different 
accounting system might have produced entirely 
different numbers, ones which might have been 
either half or twice as large. And any of the 
three sets might be equally legitimate for the 
purpose for which they were collected. 
If this statement shocks you, it should not. 
Cost figures do not, and cannot, have a single 
generally accepted meaning. In both government 
and business, data are collected for a variety of 
purposes, and the particular elements of cost 
which should be included depend on the use to 
be made of them. When cost data are used for 
the kind of analysis being discussed in these 
pages, they must meet several criteria. First, 
they must match-timewise-the output data to 
which you are relating them. Second, they must 
include all ' the cost elements relevant to the 
particular decision you are making. Third, they 
must include only those cost elements which are 
relevant to that decision. Finally, and often 
most important, they must be interpreted in the 
light of your own experience and judgment. 

How do you decide whether your cost data 
provide the right numbers for a particular 
analytic use? The answer depends both on what 
specific items of expense are included as costs in 
your records and on when each item is entered 
as a cost id those records. The second question 
is, in many ways, the more crucial since it 
applies to all types of cost/output analysis. You 
cannot relate what was accomplish&~ in a 
particular time period to the resources used in 
obtaining that output unless you are able to match the two sets of data. And this will not always be the case with figures drawn from government accounts. 
Government agencies have always kept detailed records of expenditure, but these-as explained earlier-have traditionally been geared toward control over the use of resources: making sure that obligations to spend did not exceed amounts authorized and that disbursements did not exceed amounts obligated. Since resources are not used at the time they are ordered, delivered or paid for, records based on order, delivery or disbursement dates are not useful for measuring the costs associated with 
particular output. 
In 1956 Congress recognized the need for relating specific expenditures to specific output by directing federal departments to prepare budgets based on the expected cost of particular programs rather than dollar obligations or dis
bursements (Public Law 863). But, for many 
years, little was done to provide a statistical 
basis for the budget estimates required by this 
instruction. 
Records providing data on resources used 
during a specific time period (accrual ac
counting) have become more available in recent 
years. In 1966 the Department of Defense was 
the first federal department to begin collecting 
many cost data on this basis. In the numerous 
areas where records are now being kept in this 
fashion, cost data are-for the first time
comparable with measures of accomplishment 
over the same time periods. 
But you still cannot take for granted that all 
costs for all activities with which you may be 
concerned are posted at the time resources are 
used. Remember too, that activities which do 
record costs on this basis also keep other sets of 
records which show the same expenditures on an 
appropriations or a payments basis. Accordingly 
you need to look at the actual numbers you 
propose to use for analysis to make sure they 
do, in fact, show resources · used during the 
period covered by your output data. 
Your second obligation, that of identifying 
relevant costs (those appropriate for use in your 
particular analysis), is not so easy to define. In 
fact, there is no generally applicable rule to use. 
Items of expenditure may be significant cost 
elements for purposes of reaching one decision 

29 


but have no place in analysis directed toward a 
different problem. 
Ideally, you should have a record of all cost 
items from which to select or exclude those 
which are or are not relevant to a particular 
decision. In practice, you may find that your 
records now omit some numbers which are 
needed for much cost/output analysis. This 
happens because we usually think about costs in 
terms of budgets. As a resource manager, you 
take account of those expenditures which have 
an impact on your budget. These are your costs. 
But other resources may also be employed in the 
course of your operations. Are they also your 
costs? Should they be included in your records 
and used in your analysis? 
The manager of a military activity is likely to encounter this sort of problem because, in many cases, the activity's own budget will consist entirely of items included in the O&M appropriations. Military personnel assigned to the operation are paid for out of another appropriation. The labor they supply in meeting your activity's workload is, of course, a cost, but it 
does not seem to be your cost and is likely not to be entered as such in your records. For many purposes this is a straight-forward pragmatic approach to the management function, concentrating attention on those resol.!l"ces over which you have control and leaving to others the management of those over which you do not. 
Such deliberate selectivity will provide the numbers needed for many management decisions. But if cost records are kept only on this restricted basis, analysis of the sort explained in 
the preceding section can yield misleading answers. Consider an example similar to those in Section 2 which related cost to output over a 
range of outputs. Suppose, for instance, that your activity provides food service and is currently supplying 40,000 meals per month. 
Suppose further that your records also include data relating cost to operating levels of 30,000 and 50,000 meals per month. With this information, you can predict the impact on your costs of specific changes up or down in the number of meals your facility serves. You can not only estimate future budget needs but also-and perhaps more importantly for higher level management decisions-identify where, within this range, your facility operates most efficiently. 
30 
Let us assume that your budget, and con
sequently your recorded costs, include all O&M 
items but only those items: food, civilian per
sonnel, labor contracted for, transportation, gas 
and electricity, cleaning supplies, etc.-a total 
which varies from month to month depending 
on the number of meals being provided (see 
Table 1). In this operation you also utilize 
military personnel assigned to you but not paid 
for out of your-budget. Since the number of 
personnel assigned has been constant throughout 
the period covered by these records, military 
payroll associated with this item has amounted 
to $12,000 per month regardless of the number 
of meals your facility has served. 
Parts B & C of Table 1 show two alternative ways of relating the cost of providing food service at your facility to the volume of service provided. Part B considers only your budgeted costs; Part C includes these and military pay as well. For purposes of analysis, which cost basis is relevant? The first and most obvious difference between the two, of course, is that total and average costs for all service levels are lower when only those cost items charged against operation and maintenance accounts are included. Since the excluded military labor was both used and paid for, the cost to the taxpayer of providing (food service is understated by that amount. But this does not necessarily mean that the numbers are not suitable for analytic use. 
Suppose the intended use of this information is limited to preparing your budget estimates for expected future workloads and for monitoring expenditures out of the current budget. In this 
case, you would be concerned only with O&M costs which could be varied according tci the service level required. In both Parts B and C, the columns headed "Marginal Cost" indicate that an increase of 10,000 meals per month (from 40,000 to 50,000) would require an addition of $17,000 to the budget while a decrease to 30,000 would permit a reduction of only $12,000. This "marginal" cost calculation could be computed from cost figures recorded on either the O&M or the "full cost" basis, but the constant "military pay" item, in itself, is neither necessary nor relevant in determining your budget needs. 
Suppose, however, that this information will be used to decide the best way of allocating an increased workload among several food service centers. For that analysis, cost data must permit 
c~ 

Table 1 
Part A • TOTAL COST 

Operation and Military Pay 
Output TOTAL
Maintenance and Allowances
(units) $
$ $ 
30,000 48,000 12,000 60,000 40,000 60,000 12,000 72,000 50,000 77,000 12,000 89,000 
Part B ·OPERATION AND MAINTENANCE COST ·ONLY 
Total Cost Marginal Cost Output average average(units) 
$ $
per unit p~r unit 
30,000 48,000 $1.60 12,000 $1.20 40,000 60,000 1.50 17,000 1.70 50,000 77,000 1.54 
Part C • OPERA liON AND MAINTENANCE COSTS • PLUS MILITARY PAY AND ALLOWANCES 
Total Cost Marginal Cos~ O~.o~ ut 
average average
(~ni~) $ $ .., .
per unit per !Jmt 
i 
30,000 60,000 $2.00 
40,000 72,000 1.80 
50,000 89,000 1.78 

you to identify the volume of meal service at operating level was in the vicinity of 40,000 which your facility operates most efficiently. meals per month where average costs would 
If cost data are drawn only from your O&M amount to $1.50 per meal. If 10,000 additional budget and exclude military pay (Table 1, Part meals were served, the cost of the added meals B), you would conclude that your "best" would average $1.70 per meal-or 20¢ per meal 
31 

more than the apparent low cost rate. As a result, the average cost of serving 50,000 meals would rise to $1.54, an indication that the facility was operating beyond its most efficient rate. This analysis would suggest holding operations at or near the 40,000 meal level if practical, and feeding additional personnel elsewhere. If this were not practical, consideration might be given to enlarging your facility's capacity to avoid higher unit costs. 
But when all costs, including the services of military personnel, are taken into account (Table 1, Part C), this picture changes. On the more inclusive basis, 40,000 meals are being served for $1.80 per meal. The added cost of serving 10,000 additional meals would still be $1.70 per meal, but this is now 10¢ per meal less than the current average cost (including military pay) and indicates that your facility's capacity is actually underutilized at the existing service level. Far from raising average costs, the proposed increase in workload would cause the unit cost of providing service to decline slightly. 
For purposes of identifying a facility's most efficient operating level, the labor supplied by military personnel is a relevant cost. Clearly, a manager responsible for allocating meal service among several centers would be handicapped in reaching his decision if available cost records do not permit him to include this item along with other relevant costs for each facility to which an additional workload might be assigned. 
Failure to include relevant costs may also affect the validity of comparisons among two or more operating facilities. In the example above, for instance, a comparison between your facility and one operated entirely by civilian labor (whose wages would, of course, be included in its budget) would not be valid unless your recorded costs included military pay for comparable work performed. But, as has already been noted, the military pay item should be shown separately since you may wish to exclude it in considering many questions of internal management. 
Indeed, when using cost and output information for analysis, deciding what cost items to exclude from a particular analysis may be at least as important as making sure that the records include all relevant costs. Management decisions are oriented toward the future, not the past, and are concerned with choices. Once a cost has been incurred, management has no 
32 

choice regarding its outlay for that particular item. In analysis focusing on the composition or level of future output, relevant costs are those about which management-at some level-still has the option of spending more or less or not at all. 
Short-run operating decisions usually involve increases or decreases in output around a current workload and within a facil1ty's existing capacity. But longer range decisions often involve a wider range of options-changes in capacity, the replacement of obsolescent equipment, the inauguration of major projects or the outright abandonment of existing ones. Some analytic techniques helpful in reaching decisions of this sort will be discussed in Section 5, but it is important to recognize here that, wherever such options exist, the relevant cost items will be those future expenditures-and only those future expenditures-which could be avoided or greatly reduced by deciding not to begin or expand or continue the output in question. 
Once a specialized facility has been built and equipment installed, a decision not to utilize that capacity will not bring a refund of the original outlay; but for projects not yet begun, all costs, including research and development as well as construction and other capital investment, may still be optional and therefore relevant. In a military environment, the expected output of the new investment over time (and therefore the amount which would be chargeable against each unit of that future output) would depend largely on judgment. 
Record systems can and should display clearly and separately all the elements of cost associated with any given activity, but record systems cannot identify which components are appropriate for a particular analysis. You as the user must be prepared to exercise your own informed judgment. 
Judgment may also be required in deciding what items of expense are associated with particular output. Consider, for example, cost items which are shared by two or more activities. How should these be divided? One way to split an electric bill among various activities using electricity would be to install separate meters for each, but would the expense required to make such an accurate allocation be warranted? Perhaps minor expense items should be allocated according to a formula or not at all. Only someone familiar with an activity's oper
ation and also with the use to which data will be put can answer such questions. 
If an added responsibility is assigned to an office where the work force is already fully occupied, the manager may be compelled to hire another worker. Suppose the new responsibility requires only half of this employee's time. Should his salary be charged entirely to the new activity, or should the added expense be shared by other activities which may benefit from the expanded work force? In cases of capital acquisitions, how should the cost of a new machine be allocated if its full capacity is not being used'? 
These have been examples of specific questions which require an exercise of judgment in measuring certain specific cost items. Far more pervasive in its impact on the analysis of cost and output data is the existence of quality differentials among the resources which managers can choose to combine. These differentials will figure in your management decisions whether you are engaged primarily in operations, research and development, procurement or any other area of activity. In all of these environments, output (accomplishment) results from combining people and things, and most of the necessary skills, materials, services and equipment are available in several quality grades. The differences are reflected in their relative prices. 
If you elect to use a lower quality of any one item, your recorded cost for that item-when compared with the more expensive alternatives-will reflect the exact number of dollars you will apparently have saved. But your decision to use this less expensive alternative may also have some adverse impact on your other costs or on the quality of your activity's output, or both. Such changes may alter, in some cases dramatically, the story told by the initial price comparison, and if they do, you will need to modify your calculations to take account of those changes. 
Suppose, for instance-as was the case recently in a department at a military school-that your activity has been renting a copier (Brand A) that provides first class copies for about 41h cents each. Funds are not available to consider buying this or any other copier, but price comparisons show that a different brand of copier (Brand X) would tum out copies at 2% cents apiece. Both prices include rental, paper, ink, service contract, etc. with the only dif
• 

33 

ferential between the two lying in the quality of the reproduction itself. 
The department at the school concluded that its direct outlays for copying could be cut by about $1000 per year by accepting the poorer copies. The reduction in direct costs you could achieve through a similar substitution would, of course, depend on the use made of the copier in your activity. 
But what repercussions might the acceptance of lower grade copies be expected to have on your activity's other costs-or on its output? Quite possibly, none-so long as Brand X copies are, in fact, good enough to be used successfully in the same ways and for the same purposes as the higher grade Brand A copies. (This assumes, of course, that purely aesthetic considerations may be ignored.) 
In the case of the school department where Brand X was actually substituted for Brand A, however, the change did, in fact, tum out to have unfavorable repercussions both on other costs (it led to increased secretarial workload) and on teaching effectiveness (the inferior copies proved unacceptable for· last minute handouts to students and other teaching aids previously available). Such repercussions obviously offset part (possibly all) of Brand X's cost advantage, but they are diffuse, hard to anticipate and even harder to quantify. The dollar figure recorded as a direct outlay on Brand X copies understates their real cost, but no statistical record can measure the extent of understatement; this requires ultimately an exercise of judgment. 
In summary, good recordkeeping procedures are vital to good management, but cost records do not and cannot provide a single unequivocal figure for the cost of an activity, project or program. Good records are like a good cafeteria; they supply separately the specific items of cost which were used in your ~.ctivity over a specified period of time. You will have to match these items with specific output; you will have to decide which items are relevant to the analysis of a specific problem or bear on a particular decision. You will even, in certain cases, have to modify data on direct cost outlays to take account of indirect costs or other factors which may be impossible to quantify in the records themselves. As in the case of a good cafeteria, a variety of dishes will be provided, but only the user of the food can decide what makes up a balanced and satisfying meal. 
ll-4 

• I
ACCOMPLISHMENT: , I WHAT ARE WE GETTING FOR OUR MONEY 
What are we measuring? \ 
I 
I need more than 11 level of effort11 
Some call it output; some call it effectiveness Don •t forget about quality 

4. Accomplishment: What Are We Getting For Our Money? 
S
uppose you asked five lunch table companions "What did you accomplish in the yard last weekend?" and got five replies. One might say, "I laid out fifteen dollars for bedding plants and fertilizer." Another, "I mowed the lawn." The third, "I put in four hours working in the garden," while the fourth reported, "We finally finished the foundation for our new retaining wall." There might even be someone who said, "I had a couple of interesting ideas while I was sitting in the sun." 
Any of these answers would be acceptable in conversation, but none of them actually measure the speaker's accomplishment, and only two are descriptive of what got done. Two replies are not even responsive to the question: neither the first speaker's $15 outlay (cost not output) nor the third speaker's four hours of work (an input not an output) tells us what. improvements, if any, were made in either garden. And the other answers do not quantify the jobs that were done; that is, they do not express output in countable Wlits such as square yards of grass mowed or cubic feet of foundation placed per hour. None of your companions would be able to relate costs meaningfully to accomplishment. 
Yet all of these situations can be thought of as representing types of government activity whose managers are expected to explain what use they have made of funds already received and to justify the. amounts they are requesting for the future. And each of your lunch companions exemplifies a type of response some managers have made-and are still making-to these questions. 
Traditionally, managers of government activities have, like the first speaker, relied heavily on records of expenditure to show what they did with funds received. But the funds were allocated to accomplish some specific objective, not to hire people, buy equipment and pay for·supplies. You, as the manager of a government activity, cannot demonstrate that you have achieved your assigned objective by showing that you have in fact spent the funds you received for that purpose. 
Suppose you try moving to a physical unit of measurement by substituting "man-hours" (a socalled "intermediate indicator" of output) for total dollars spent. You will simply find yourself in the position of the weekend gardener who labeled four hours of work as his "accomplishment." For analytical purposes, this is actually a worse measure than dollar costs since everyone knows that the man with the hoe and the man with the rototiller do not produce the same results in an hour's time. 
To show the combined result obtamed from all resources, you must find a direct, quantitative measure of output. Of your five lunch table companions, the one who mowed his lawn could most easily meet this requirement. If he knows the size of his lawn and the time he spent mowing it, he could express his output as\ a specific number of square feet or as square feet mowed per hour. With this measure he could do a number of things-not only identify what he accomplished last weekend but also declde what time to allow for the chore next week or estimate how much mowing-time would be added if he planted more grass in place of the junipers. (He might decide to buy a power mower or to hire his son to do the job.) In short, this output measure would provide him with information which might be useful in reaching a variety of decisions. 
Similarly, if your activity is a repetitive operation which turns out a flow of readily identifiable end products such as X-rays taken, students graduated or engines overhauled, you may find it relatively easy to select a unit of measurement and to collect output numbers. Moreover, these numbers will do more than simply show what you have accomplished for past expenditures. If they are collected for your activity or others like it over a range of outputs, they can also be used to anticipate what effect any specified change-up or down-in your job assignment is likely to have on costs. 
Once you have output records to match with your cost records, you can relate the two sets of numbers graphically as was shown in Section 2 by plotting costs on the vertical axis and corresponding output along the horizontal axis. (Figure 1.) Each cost and output combination within the range covered by_ your records will become a point on the graph (A, B, C and D), and you will be able to read directly from the cost axis the additional dollar outlays that have been associated with changes in output from A ~B, from B ~C, or from C ~D. If you draw aline (curve) joining these actual points, you can 

35 


also forecast (on the basis of past experience) the total dollar costs for any output level within that range. 
Without an appropriate unit for measuring output you could not do either of these things. You could still calibrate the vertical "cost" axis in dollars, but not the horizontal "output" axis (X-rays taken, students graduated, engines overhauled, etc.). Although your cost records would show differing dollar amounts for various time periods, you would not know what the operating level had been in each period, and you could not identify the cost of "marginal" changes. If you were given a future job assignment which represented a change in operating level, all you could do is describe (in words) the new job you would be expected to do. Graphically, this could be shown only as a vertical line placed at some arbitrarily selected point-level of effort-on the horizontal axis. (Figure 2. ~ 
You could then try to find the least costly way of doing that job, but in the search you would not be able to use the very powerful tool of marginal analysis either in the ways that have already been shown in Section 2 or through more precise techniques that will be explained in Section 5. If your activity is one which has an obvious output unit, the benefits of keeping accurate statistical records are obvious. 
But suppose you are engaged-not in turning out a continuing flow of identifiable end-products like X-rays or repaired engines-but in carryin€ 
out a five-year construction project or in pro
curement or in research. Perhaps, like your 
fifth lunch table companion your output yester
day was an idea; can anyone quantify an hour's 
worth of thinking? 
It may seem that there are two distinct 
categories of government activity--repetitive 
operations whose output is readily measurable 
and therefore subject to analysis and another, 
more variegated range of activities whose man
agers are excluded from these advantages because 
their output is not. In other words, it may seem 
that output measurement has its "haves" and its 
"have-nots." 
But both parts of this conclusion are mislead
ing. Even if you are engaged in an activity where 
choice of an output unit seems self-evident, you 
will still encounter pitfalls in measuring output 
and using the numbers for analysis. If, on the 
other hand, your activity does not result in a 
repetitive flow of uniform end products, you will 
still find many important applications for quanti
tative analysis; to find them you must measure 
those aspects of your work-load which are meas
urable, compare them with those which are 
comparable and tailor the uses you make of cost/ 
output information to your own management 
decisions. 
Undertaking a five-year construction project, _for example, is similar to the position of the 
weekend gardener who reported progress on his 
retaining wall. Weekly, monthly and even annual 
36 

output consists of progress not completion-a sequence of dissimilar stages from building plans to site preparation and foundation work to electrical wiring and finishing the interior. Illustrations of ways to use output information which are drawn from repetitive operations could not be applied directly to this situation. Each stage of construction would require a different unit of measurement, and information drawn from records for one stage-say, site preparation-would not provide a basis that could be used in the next stage for laying the 
foundation. In order to be useful, it is obvious that applications of analysis to a construction project must differ from those made in an operating environment such as food service. 
For a large scale construction project, cost/ output analysis is first applicable in the planning stage when the feasibility and scope of the entire project depend on the planner's ability to obtain accurate cost estimates for each phase of construction. Those estimates become more accurate and reliable if they are based explicitly on quantitative analysis. The records from which 
data for each phase can be drawn must relate to earlier construction in a relevant size range, with output units suitable for that particular stageacres cleared, cubic feet of concrete poured, 
linear feet of wiring strung, etc. 
Once construction is underway, records are 
maintained for purposes of management control 
over the project, and the appropriate "unit of 
measurement" would be geared to this need. 
Since a prime objective of management is to 
match actual progress with expectations and 
actual expenditures with cost estimates, each 
successive stage of construction may be con
sidered an output unit in this process. A data 
format like that illustrated in Section 1 will pro
vide usable information rather than mere num
bers on the project's current status. 
This is only one instance of ways in which cost and output data may be adapted to activities other than repetitive operations. The application of numbers to analysis does not start by collecting numbers but by deciding what comparisons would be helpful in making decisions and then selecting units of measurement which can be used for those comparisons. Different measures may be required for different purposes. 
Possibly the reason most frequently given for 
not collecting and using output data in a 
particular activity is the feeling that its output 
• 

cannot be quantified-that the task performed is too diverse or too qualitative to be expressed successfully in numbers. This problem is actually one of degree. Few operations are so routine that quality variations can safely be disregarded; numerical units of output are not, in themselves, an adequate measure of accomplishment. 
In fact, one of the pitfalls of output measurement systems is that managers who find an obvious output unit may ignore qualitative factors in their analysis. The following pages consider ways of bringing quality changes explicitly into the process of decision making. If you have been discouraged from using output data for analysis in your activity by the obvious significance of qualitative factors, these techniques may help you find more precise ways of relating costs to accomplishment. But they are also addressed-perhaps even more directly-to those who have found appropriate output units for their activities without difficulty and are collecting accurate numbers. Those in the latter category need to remember that these numbers measure only the activity's operating level and not necessarily its accomplishment. 
As early as April 1968, the Department of Defense stated in a directive that output statistics "must be relatable to significant organizational missions and functions ... and to resources allocated and consumed." This directive assigned a dual function to output measures. A measure of operating level clearly satisfies the second of these: X-rays taken, engines overhauled, or tonmiles of freight moved are all relatable to resources consumed over the same time period. But an organization does not fulfill its mission by turning out a specified number of units; it fulfills that mission by meeting a specified need, and by maintaining a specified quality standard. 
The mission of a transport organization is not 
to move freight but to see that items are delivered 
where they are needed when they are promised 
and in usable condition. The mission of a recruit 
training base is not simply to graduate trainees 
but to make sure they have specified skills. 
In both of these organizations, the "product" 
has two dimensions: one of volume (ton-miles 
of freight moved, number of recruits graduated) 
and one of specifications (standards set and 
maintained, such as damage-free deliveries made 
on schedule or the competence of trainees to do 
particular jobs). Whatever your activity, its 
performance will be judged on the basis both of 
37 

volume (physical units of output) and of quality this decision made by default, he should be able 
c

(how adequate its specifications are and how to define the existing quality or service level ofwell they are met). 
his activity and to show how much improvement
Moreover, if you are considering possible could be achieved with a specific budget increase,changes for the future, your options may include or alternatively how much deterioration wouldchanges in either volume (operating level) or follow a specific cut in funds.specifications (quality level) without necessarily 
We have defined an operating-level output
changing the other. Either sort of change might 
measure as one capable of recording the numberbe expected to increase (or reduce) your costs ofan activity's end products per time period overand also to increase (or reduce) the extent to 
a range of outputs. For mission oriented analysis,
which your organization is meeting its specified an additional measure is needed-one capable ofneed. Either type of change (or some combinarecording that product's quality level over ation of both) would be a "marginal" change in range of levels. This measure should be indeoutput. But if you are using an output measure pendent of the unit used to measure operatingsuch as number of engines overhauled or tonlevel since decisions to change quality levels aremiles of freight moved the data will show only likely to differ from decisions to change thethose changes which expand or cut back the number of output units. And like the unit usednumber of units turned out. to measure operating level, it should be relatableSuch a measure will be perfectly serviceable to costs. Unless you are able to relate servicefor day-to-day operating and budgetary decisions levels to costs, analysis can be of little help inso long as you are able to make a working asmaking decisions which involve changes insumption that the quality or service level of the quality.units counted remains constant. When you relate Suppose an air transport operation is responsioutput-as measured by this yardstick-to comble for delivering freight to a certain destinationparable costs data for the same period, you can and that accurate records are kept of the volumeput the resultant statistics to all the uses moved (in ton-miles), but the level of service isdemonstrated in the preceding pages. You can undefined; that is, a standard transit time has notestimate budget needs for different levels of been set or maintained. Constant complaintsfuture operation, identify your facility's best 
might convince the director of this operation
operating level, compare your facility with other 
that present service was not satisfactory, butsimilar ones or decide where to allocate an inwhat sort of case could he make for funds tocreased workload among two or more facilities. speed up schedules and make them more reliable?But there are other decisions for which meas
Without being able to define the existing
ures of operating level alone will not be enough. quality of service, he could neither specify the
Such measures tell how many engines were reamount of improvement a given budget increasepaired in a given time period, but not how reliable would make possible nor request the amountthose engines have been after being put back into 
needed to achieve a given improvement. He
service; how many ton-miles of freight were could only testify to his belief that the existingmoved, but not whether delivery schedules were service was inadequate and then submit a budget met; how many recruits were graduated, but not based on the measurable cost of handling nexthow well prepared they were for their subsequent year's expected freight volume at current (unassignments. specified) service levels plus an additional sumWhatever your activity, its costs of operation (whatever he thought reasonable) to be used in(and your future budget needs) depend not only upgrading service (again to an unspecified extent).on the amount of work required but also on This is not good enough. To make a strong casehow well it is expected to be done. While many for appropriations to improve an organization'sday-to-day management decisions can use cost/ mission performance, the manager needs to showoutput statistics which ignore this dual relationhow much improvement could be provided for aship by taking quality level for granted, program specific outlay.evaluations and long-range planning cannot. For this purpose, the ideal measure of anSomeone, at some level, decides-either explicitly activity's service level would be a single numericalor by default-how good is good enough. Ifthe unit like that used to measure operating level.manager of an operating activity does not want With such a measure, you could present a budget 
38 
c 

for your activity and say with confidence that a five percent increase in expenditures, for instance, would permit a ten percent improvement in quality of service. Unfortunately, for most activities such a unit would be hard to define and the appropriate numbers even harder to collect. 
But if there is an explicit standard of performance prescribed for your activity, you can use this standard in conjunction with a numerical measure of end-products to define your current performance level. In measuring quality of output, as in measuring output level, you "start from where you are." If you were to draw a graph for your activity like that in Figure 1, the costs associated with each output plotted on the horizontal axis would be those required to provide this existing service level. You can "measure" proposed or actual changes in quality as deviations from that level. 
, 
How precisely you can predict the effect a specific change in performance standards would have on actual performance and on costs will depend on two factors. One concerns the type of standards applicable to your operations: they may be precisely quantitative (permissible tolerances for retooling engine parts) or broadly descriptive (the curriculum at a training base and 
the proficiency scores required for graduation). Second, your output may or may not be subject to routine testing for purposes of administrative control. The more explicit the specifications and the more rigorously they are adhered to, the more precisely you can identify quality changes and relate these to costs. 
But in any case, the analytic approach can be demonstrated very simply with a graph like that in Figure 3. Suppose you are operating the training base mentioned above and the solid curve X (based on actual cost and actual output records) shows the cost of training varying numbers of recruits to meet currently accepted standards of skill. If you are graduating 1,000 trainees in each class, Point A on this curve indicates your present level of operation and the cost associated with that level. The added cost of increasing class size by a given number of 
1 
students would be indicated by moving up to the right along cuive X; budget savings would be possible by cutting back the number of students (moving down the curve to the left). 
But decisions to tighten or ease training standards are as much marginal decisions as those to change the number of recruits trained. Each modification in existing standards would add to costs or permit their reduction, and Figure 3 shows how you can represent graphically the added expense or saving associated with a proposed change. 
A recruit trained to a higher level of skill represents a different and more costly end product than one meeting the existing standard. The cost of bringing varying numbers up to this higher level would lie along a new (estimated) curve Y somewhat above and to the left of X; every possible number of graduates at level Y would represent a greater aggregate expenditure than the same number trained to level X. The added cost of raising skill levels for a given number of recruits from X to Y would be measured by the vertical distance between the two curves at that point on the graph. 
While curve X is based on records and reflects actual experience in training recruits according to the present curriculum, the distance between X and Y would have to be estimated from the component costs needed to raise training standards (more time, more instructors, more training materials, etc.). Since these additional costs might not be the same when the training base was operating at different levels curve Y would not necessarily parallel X at all points. Like Y, the curve Z is an alternative curve, but one representing the costs that would be associated with a less rigorous and therefore less expensive training program. 
39 

With such a family of curves-and there could be many lines representing more or less ambitious program revisions-you would be able to visualize either the extra cost of training alll,OOO recruits to the proposed higher standard of skills (point B) or the cutback in class size (to point C-800 recruits) that would be required if you were to stay within your present budget and still adopt the new training program. 
Of course, not all management decisions would permit such trade-offs between quantity and quality. If you were reviewing the costs of maintaining a building with a given amount of floor space, for instance, your "choices" would ordinarily relate only to the level of maintenance not to the number of square feet to be maintained. For equipment used in space flights, on the other hand, no reduction in maintenance standards would be acceptable, so variations would have to be in the number and type of missions flown. 
But in situations like that represented by a training base where changes can be made in numbers, curriculum or any combination of the two, Figure 3 provides an analytic technique for pulling together the full range of options open to a mission-oriented and cost-conscious policy maker. What it does not do is answer the ultimate question: Which option will enable the training base best to fulfill its mission? That decision must be made on the basis of judgment and experience. 
Note that the vertical distance between lines X and Y does not measure the extent of quality differential between graduates of the existing course and those who would complete the proposed program. It measures, instead, the cost differential for the inputs that would be required to operate the more ambitious training program. The amount of upgrading in skill that would be achieved through this more expensive program is defined as the difference in specifications for the two courses and the relative levels of proficiency demanded in each. This list of differences would provide a detailed and explicit description of the additional training each recruit would receive and the higher proficiencies he would be required to demonstrate. 
How much better equipped for future assignments recruits would be as a result of this training remains-at least to some extent-a matter of judgment. The numbers in Figure 3 would give (_ you the capability of matching a range of class sizes with costs for both present and proposed training standards. They would enable you to relate specific changes in either quantity, or quality (or both) to specific outlays. The numbers would not relieve you of the need to exer-· cise judgment but they would make it possible for you to exercise better judgment. Unless you know what a specific quality change would cost, you can hardly decide whether or not it is worth what it would cost. 
Obviously in any particular case, the relative importance ofjudgment and quantitative analysis will depend on the circumstances. In some situations the numbers themselves may come close to providing a definitive answer. Suppose a statistically demonstrable relationship exists between engine life and precautionary maintenance, and you are called on to decide how extensive (and expensive) a maintenance program to set up. If you can identify the additional expenses that would be associated with specific proposals to increase the frequency and thoroughness of routine maintenance, you may be able to caluclate. precisely which proposals would produce additions to engine life that exceeded their cost and which would not. 
At the other end of the spectrum, suppose you are a research director passing on staff proposals for a series of experiments to test a particular hypothesis. You too would need numbers-cost and output information---to determine what resources would have to be allocated to carry out these experiments. But such information would be of secondary importance unless you had first concluded that the proposed experiments were relevant to a problem worth solving and that the hypothesis was promising enough to be worth the cost of testing. 
The usefulness of output numbers in decision making is most direct for activities which turn out a stream of relatively uniform end products. But output information (numbers combined with explicit specifications or service standards) is important to all managers whether or not they can quantify their activity's ultimate mission. The better your records are for the measurable aspects of your job, the better judgment you will be able to use in those decisions which depend, in the last analysis, upon the exercise ofjudgment. 
40 c~ 

li-5 
III I . 
HOW TO GET THE MOST 
, I 
I; FOR OUR MONEY I : : i 
l 
!
I 

Cost and output must be matched. 
'Now I see how to get (where we want to go 
These charts 
tell how it is Sometimes a picture
is better than a lot
of numbers 

~ TEcHNICIAN ~~~~. 

5. How to Get the Most for Our Money 
anagement decisions, like New Year's resoluMtions, are directed toward the future. By the time cost and output numbers have been collected and recorded, they are history. 
Historical records provide a basis for post mortems; they permit comparisons between what was expected and what was attained. They permit comparisons between your activity and other similar ones. They permit you to formulate future plans on the basis of past experience. They do not tell whether past results were the best that could be achieved with the budget available or, alternatively, whether the same results could have been achieved for less money. Even if conditions have not changed, conclusions drawn from historical records and applied directly to current decisions would simply enable you to repeat history. This is not enough. 
When we use resources (people and things) to accomplish a purpose, we want to be sure we are using them in such a way as to get the most for our money. To achieve this objective we need to know-at least approximately-how costs would be affected by using alternative combinations of resources. We also need to know-at least approximately-how costs would be affected by changes in assigned levels of output, either at a single facility or among a group of facilities with different operating levels. 
Almost any job can be done in more ways than one. An office manager may handle , a higher workload either by hiring more clerks or installing more sophisticated equipment (or some of both). Bulk cargo can move by truck, barge or train (or a combination of these). Hospital services may be provided through separate facilities in a number of locations or centralized regionally. Ideally, each decision maker should be able to identify all eligible alternatives for reaching a specific level of output and meeting specified quality standards and then choose the best. 
The "best" alternative in a particular set of 
circumstances will not necessarily be the least 
costly one in dollar terms. Conserving some 
resource that is likely to become very scarce in a 
few years may be an overriding consideration
water in an arid region, gasoline during an oil 
shortage, possessors of any specialized skill that 
requires years of training; these are all possibilities 
• 
that come to mind. But under most conditions, 
43 

the relative scarcity of particular resources is likely to be reflected in their market prices, and the decision maker needs only to identify which way of carrying out his assignment has the lowest total price tag for all relevant costs. 
Please note that, after identifying this low cost alternative, a different course may still be chosen. Suppose, in the example noted earlier, 
that analysis showed a specified quality of hospital care could be provided most economically at a large centralized facility. It might still be decided that convenience to patients and their families justified greater geographic dispersion. Identifying the least costly way of providing service does not eliminate other options. But by providing a basis for comparison, it puts a price tag on them. It displays the cost of choosing each alternative. 
This section does not provide a formula for identifying the least costly way of reaching specific objectives or of establishing what output levels should be required. What it does provide is an analytic approach for comparing alternatives. The numbers you use in making comparisons among your particular alternatives will be drawn partly from actual cost and output records (past experience) but will also include estimates 
(past experience modified to incorporate proposed changes in specifications, in output levels, in time·· schedules, in the prices of relevant cost items). 
If data can be assembled for the alternative ways of carrying out a specified assignment, the techniques described below will help in identifying the least expensive way of combining cost items. Such a "least cost" combination is called an "economy solution." If, on the other hand, you start with a fixed budget allocation, these same techniques could be used to identify the maximum results which could be achieved with that budget (an "efficiency solution"). And if your options include choosing among several output levels-either for a single facility or for several-the level which results in the lowest cost per unit would identify the most efficient scale (size) of operations in your activity. For a number of technical or policy reasons, you may not achieve these solutions immediately or precisely, but analysis of alternatives can help you make better management decisions. 
We often think of choices among alternatives as "either-or" propositions: Shall I drive the car to work this morning, or ride the bus? But the choices managers face in finding the best way to carry out a given assignment are more likely to require decisions on "how much of each." You, as a manager, are responsible for combining resources (people, buildings, equipment, supplies, materials, etc.) to accomplish a purpose. You may "mix" these resources in widely varying proportions, but neither an empty-handed workforce nor undirected machinery (automation notwithstanding) will get a job done. When considering broad resource categories, all managerial assignments demand "some of each." 
Such physical requirements of "production" may seem applicable primarily to factories or repair shops, but they also apply if you are managing an office or a hospital, directing research, controlling inventories, or providing transportation. In each case, the process of identifying the best "mix" of human and material resources for a particular task is still "analysis." 
Suppose, for instance, your immediate mission is to move specified ton-miles of cargo by air to several specified destinations within a time frame which does not permit round trips or round robin flights to more than one destination. Suppose further, aircraft of Type A could make all deliveries in 10 flights, but Type B transports would need only 5 flights to complete the assignment. Flights by Type A aircraft cost $400 each as compared with $1000 for a single flight by the large B transport. 
Your first reaction would probably be that this is an "either-or" decision. Ten flights by aircraft A would cost $4000 as against $5000 for 5 by Type B. This would seem to make aircraft A the obvious selection. But your choices are not limited to 10 of A or 5 of B; you might move some cargo by Type A and some by Type B. 
Again your first reaction might be that this physical possibility is irrelevant since transport B seems to have twice the capacity of aircraft A, and therefore substituting a B flight at $1000 for two A flights at $800 would merely add $200 to your costs. But, and this is of crucial importance, you cannot assume that, on this particular mission, one B flight would always replace precisely two A flights. 
If bulky or oddly shaped items make up part of your cargo, the dimensions of one plane or the other may be more suitable for those particular items. The quantity to be delivered at one destination may warrant using a larger transport for that run than would the amounts destined elsewhere. And since the 2 for 1 substitution ratio between aircraft Band A may not apply to all flights, you cannot be sure you have made the best decision for this particular assignment without identifying individually the combinations of A and B flights capable of carrying it out. 
Quite possibly, you might find the actual alternatives to be as shown in Table 1. 
Table I  
I Possible Alternatives  No. of Flights A B  A (@$400)  Total Cost (dollars) B (@$1000)  Combined  I  
u  10  0  4000  0  4000  
v  5  1  2000  1000  3000  
w  3  2  1200  2000  3200  
X  2  3  BOO  3000  3800  
y  1  4  400  4000  4400  
z  0  5  0  5000  5000  

These same data are displayed graphically in Figure 1 with flights by aircraft A measured on the vertical axis, those by aircraft B on the horizontal, and each combination capable of providing the required transportation plotted to show the six possible alternatives. With this profile you can more readily visualize the impact on your total costs of substituting one or more flights by Type B transports for some of the 10 flights which would be needed to complete the assignment with Type A aircraft alone. 
The first and most significant observation is that the larger Transport B would be extremely effective for handling part of the shipment. By scheduling a single flight of aircraft B, you could dispense with 5 flights by aircraft A. This might happen because some items had awkward dimensions for loading aboard the smaller aircraft or because enough cargo to make up a full load was being delivered to one destination or for some other physical cause. Whatever the reason, this "tradeoff" (substituting one unit of Input B for 5 units of A) would permit a net saving of $1000. 
But aircraft B appears less well adapted to handling the rest of the assignment. Adding a second flight (Point W) would permit cancellation of only 2 Type A flights (with a net increase of $200 over the cost of combination V), and in each of the remaining alternatives, high cost Type B flights would substitute for less expen
44 

-~ 
_j 
'J ,_, 
Figure 1 
. 4000 

3600 
\ . -.
..j. 
3200 ·_, __ -. ;_ ..... ·-;. 
· ·. :t ...·~r.· .
. •II) 
-~ 2800.
-
C) 
.... ' 
,, . 
: ,',i 
;:;.~. 
)' 
. g•· 1 '·' ..: 
·, •·r 
;,~ 
·y . 
aoo·:;. 2 400· 1 
--· 
0''. 
·0 -~"'"-i111iiiiiiio~~iiiiiilliii......................~......~---.......-~.........~'!'i"--· 

.......'
j)'>· ·:'·':2 '4
3 5. Number of, Ai-rcraft B 
o 1o'bo 2ooo 3ooo 4ooo 5ooo 6ooo tooo 
:~ ' }~ •• . i 
1bollars Spent on ''8" Flights 
sive ones by aircraft A on a one for one basis. 
The profile of flight combinations indicates that, by selecting the least costly way of carrying out this particular assignment, the required transportation can be provided for $300Q-$1000 less than would have been called for by an "either-or" decision in favor of aircraft A. 
The same diagram can also be used to show that the specified transportation is the largest amount that could be provided on a $3000 budget, and that this budget could provide that amount only if the funds were spent in the fashion shown. This is demonstrated by the straight line running diagonally through Point V. It is 
45 

called an "equal cost (budget) line" and shows all the combinations of flights (or fractions of flights) by A and B type aircraft which could be purchased for $3000. The line is significant not as a possible buying guide but because it shows that, even if you could purchase fractional flights, every theoretical $3000 combination of A and B type flights except the one represented by Point V would fall short of fulfilling the mission. Except for Point V, the entire budget line lies below and to the left of the combinations capable of providing the specified amount of transportation. 
The slope of an "equal cost line" depends on the relative costs of using Type A and Type B flights. In this diagram it slopes steeply because each flight by aircraft B costs two and one-half times as much as one flight by aircraft A. This cost relationship dictates that aircraft B be used only for jobs which would have required more than two and one-half flights by aircraft A. 
Now let us add another circumstance to this comparison of alternatives by examining the cost figures themselves. Let us suppose that those used above-$400 per flight for aircraft A and $1000 per flight for aircraft B-are "full cost" estimates, including both the initial cost of the aircraft (spread over its expected useful life) and current operating expenses-those which will be incurred if, and only if, flights are made. But suppose the status of aircraft B differs from that of A in one important respect. Suppose aircraft of Type B are on hand, available for this operation and will, in fact, stand idle unless you put them to use. Suppose that aircraft A, on the other hand, is not owned but is available for immediate delivery. Any Type A aircraft to be used on this assignment would represent a new purchase. In view of the relative status of the two aircraft types, are the $400 and $1000 figures actually the relevant (pertinent) costs to use for comparison? 
Since you must still decide whether or not to incur the expense of buying aircraft A for this and subsequent missions, the "full cost" estimate of $400 per flight is appropriate. The capital outlay involved in purchasing aircraft A cannot be justified unless the opportunities foreseen for using it now and in the future will be worth at least $400 per flight, including its use in this operation. 
But aircraft of Type B are already on hand. The initial outlay, which is represented by-let us 
46 

suppose-$450 out of the $1000 per flight figure ( used above, has already been made. Operating expenses (flight crews, POL, maintenance, etc.) make up the remaining $550 and are the only costs which would be avoided by deciding against use of aircraft B on this assignment. 
As was explained in Section 3, sums which have been irrevocably spent are not relevant costs for future decisions. They would be pertinent for an inquiry into the historical wisdom of deciding to acquire aircraft B. (On the evidence, such a post mortem would have to render an unfavorable verdict; if uses worth $1000 per flight existed for aircraft B, the planes would not be standing idle and available for this mission.) But in comparing the cost of providing a specified amount of future air transportation through alternative combinations of flights by aircraft A and B, the appropriate cost per flight for aircraft B would be, not $1000 as illustrated in Table 1, but $550. 
How would this change in the cost figures affect your decision? Using the appropriate relevant cost figure of $550 for aircraft B would not change the appearance of Figure 1 in which the location of points U through Z are determined by the physical capabilities of the two aircraft to provide a specified transportation service. But when the total cost of each combination was recomputed to reflect the "relevant cost" for flights by aircraft B, a new "least cost combination" would be identified at point Wtwo flights by aircraft B and three by aircraft A. (See Table 2.) 
Table 2 
I 
No. of Flights Total Cost (dollars) 
Possible 
Alternatives A B 
A B (@$400) (@$550) 

Combined 
u 10 0 4000 0 4000 
v 5 1 2000 550 2550 
w 3 2 1200 1100 2300 
X 2 3 800 1650 2450 
y 1 4 400 2200 2600 
z 0 5 0 2750 2750 

Note that this least costly combination would still justify capital outlays for some new aircraft of Type A despite the opportunity for putting into service Type B transports which would otherwise stand idle. Because of transport B's high operating cost per flight, its use still would be economical only for runs where a single flight could replace more than one flight by aircraft A. 
c: 
Only the shift from combination V toW would provide a two for one trade-off; further substitutions would be on a one for one basis. 
In this example, the specific outcome is unique to a particular mission with special cargo characteristics, amounts of freight being shipped to given destinations and time schedules to be met. In many management situations-particularly if you are not conducting a repetitive operationthe choice among alternative ways of accomplishing a specific objective may depend on just such a detailed knowledge of special circumstances. You must be familiar with these conditions, identify the specific alternatives capable of fulfilling your mission (in this instance, the half-dozen flight combinations) and price them out to find the one with the lowest cost. 
• 
A more general form of "production analysis" is applicable to repetitive operations which are engaged in turning out readily identifiable end products. This analysis addresses itself first to finding the "least cost" combination of resources for carrying out a specified assignment or spending a specified budget, and second to finding the most efficient levels of output for particular activities and-so far as possible-distributing workloads to take advantage of these. Its answers to both questions take account not only of the physical conditions under which people 
and things can be combined in a specific activity 
but also their relative prices.1 
When two or more categories of input (say the 
people you hire to handle a given workload and 
the equipment they work with) can be combined 
in a variety of ways, it would be cumbersome or 
impossible to price out every possible combina
tion. Fortunately, this is not necessary. When 
you are seeking the least costly manpower/ 
equipment combination, the eligible alternatives 
will follow a predictable pattern reflecting the 
physical requirements of the work being done. 
These requirements can be illustrated in terms 
of any operating facility-say, one making auto
motive repairs. If you found yourself in charge 
of a superlatively equipped workshop with a 
• 
1 If complete information were available for all alternatives and met certain simplifying assumptions, analytic techniques would yield precise and determinate answers to these questions. For a clearer conceptual understanding of "production analysis," see the appendix to this section where these techniques are developed more explicitly• 
heavy workload but only one mechanic, it would be obvious that a second mechanic could contribute more to meeting the schedule than some of the less essential equipment. You would make such a trade-off immediately. But if you embarked on a process of disposing of more and more equipment in order to hire additional mechanics, each new-comer would contribute less than his predecessor. The more important job assignments would have been given out first; moreover, after each successive substitution, your mechanics would be getting along with less adequate equipment. The net effect on the shop's operation of each substitution would depend on the balance which existed between manpower and equipment before that substitution was made. 
Where, in this process of substituting men for machinery, should you call a halt? If you are seeking to complete your assignment at the lowest dollar cost, your real concern would not be with the physical contribution to output made by the last man hired or the piece of equipment he replaced. It would be with the contribution made by the last expenditure on manpower as compared with the value represented by the least essential equipment remaining on the premises. 
By focusing on these "last"-or marginalexpenditures for each category of input and comparing them, you could identify the least costly way of combining people and things to accomplish your particular mission. So long as an additional outlay on manpower yielded more per dollar of expenditure than the marginal outlay on equipment, you would have an incentive to try substituting at least a little more manpower for equipment. The incentive would disappear and the "best" combination be reached when each dollar of your "marginal expenditure" on manpower made the same contribution to output as each dollar of your "marginal expenditure" on equipment and other materials. 
Here we have a very exact definition of the least costly way of accomplishing a particular m1ss10n. But in the real world, how can this help find the "best" combination? Certainly a definition does not provide slots for numbers which can be copied directly from your records and converted into an answer. But it does suggest a method for reaching-or at least approaching-the least costly solution by asking and answering a series of questions. 
47 

If you ask yourself directly, "What is the best whether you should turn out the assigned work
c 
way of carrying out my assignment?" the quesload at the lowest cost and make any surplus
tion may seem almost as unanswerable as "How funds available for other uses, or whether you can we eliminate poverty?" But if you start should strive to achieve the largest output possifrom where you are and ask, "Would a specific ble with all funds available. Within the limited 
c 

small change in the way I am now combining resources bring me closer to the best combination?" you can usually have a good deal of confidence in your answer. If your activity is already combining resources in some identifiable proportions, the costs associated with this combination are a matter of record. You would 
start by considering a single marginal change, say, adding more manpower. 
If you concluded that this shift between manpower and equipment would lower your costs for handling the same workload (or alternatively would allow you to handle a higher workload at the same cost), you would have reason to estimate the probable effect of further trade-offs. If, on the other hand, you concluded the first shift was likely to lead to higher costs, you might want to consider the probable effects of substituting additional equipment for some of your present manpower. Such questions cannot be answered without using numbers, actual or estimated, but by focusing on a sequence of specific marginal changes, you will be able to mobilize the quantitative evidence needed to "test" potentially eligible alternatives. 
In the preceding pages, the term "least cost" combination has been used to describe either that combination of people and things which requires the smallest number of dollars to get a particular job done (an economy solution) or as one which enables you to get the largest possible output from a particular budget (an efficiency solution). If your information in arriving at this "best" combination were accurate and complete, it would not make much difference which formulation you used. The smallest budget with which you could do the assigned job would permit you to complete it if-and only if-you allocated that budget among people and things in the most efficient manner. 
But in the real world data are less than complete, estimates less than accurate, and performance subject to improvement or deterioration. 
Accordingly, you might find that your budget was able to cover more (or less) output than anticipated. And if this happens, it becomes important for you to know whether an economy solution or an efficiency solution is desired: 
48 
framework of decision making described above, 
you would then be operating so as to get the 
most for the taxpayers' money. 
But suppose your authority extends further, and your options include changes from the current operating level or in the total expenditures which should be allocated for your activity. Some changes might, of course, be carried out within the physieal capacity of your existing facility, but a major expansion of budget or operating level would usually entail capital investments. Before making decisions of this sort, the Department of Defense--as has already been noted-requires that uniform analytic procedures 
be followed to take account of specified factors (including the present cost of committing capital for long periods and the probable impact of inflation.) These procedures are explained in 
detail in the Economic Analysis Handbook (cited earlier) which also outlines various techniques for estimating the costs and benefits of proposed investment options. Neither will be reviewed here. 
What will be emphasized, however, is the importance that cost estimates used in making investment decisions-like those used in making operating decisions-should seek to identify, at least approximately, the least costly combination of resources (particularly of capital equipment on the one hand and manpower, supplies, etc. on the other) for each output level being considered. Also emphasized is the importance of identifying the level at which unit costs would be lowest, i.e. the activity's most efficient scale of output. 
This information can seldom be drawn directly from cost/output records though historical records for your own facility and others with higher or lower capacities and higher or lower rates of operation furnish a starting point. Data based on experience can be modified to take account of identifiable differences. (Procedures for this are also outlined in the Handbook.) In seeking the least costly combination of resources for several possible operating levels, you would use such estimates and then consider the same "marginal" questions you would ask for a single output level: A little more equipment or a little 
( 

less? A little more manpower or a little less? 
If your budget estimates cover a wide range, you would not expect to find that successive increases in the total amount of money made available for your activity were always matched by proportional changes in output. For any given activity, some scales of operation will permit more efficient use of resources than others, even though you have been able to specify the most advantageous combination of manpower, equipment and other inputs for each alternative level. 
To visualize more clearly such differences in efficiency at various output levels-and to recognize their implications for decision making
a table may be set up like that in Table 3. Suppose your estimates in that Table showed the various workloads which might be handled at 
your facility with five alternative budgets ranging from $3000 to $7000. 
Table 3 
MARGINAL COST 
I 
UNITBUDGET UNITS OF 
($) OUTPUT COST($) NUMBER DF COST PER 
ADDED UNITS ADDED UNIT ($) 
• 
3000 100 30 20 50 4000 120 33 ' I 
50 20 5000 170 29 I 
20 50 6000 190 32 I 
10 100 
7000 200 35 
I 

In the table, each successive budget shows 
expenditures rising by $1000, but the associated 
increases in output range from a high of 50 
units to a low of 10. The greatest operating 
efficiency could be achieved with a budget of 
around $5000: the 170 unit level where average 
costs are lowest. 
If the facility were already operating at the 
120 unit level, a budget increase of 25 percent 
would enable it to handle better than 40 percent 
more workload. The 120 units already scheduled 
would be costing $33 each; Table 3 says another 
50 could be added at a cost of $20 for each of 
the extra units. This does not mean your facility 
should always operate at the 170 unit level. (The 
world is full of bankrupts who could not resist a 
good buy.) But it does mean that a 170 unit 
operating level is high enough to permit various 
economies associated with larger scale production 
(more specialization, use of larger or n\ore 
sophisticated equipment, etc.). These could not be utilized so effectively by a facility with a 120 unit workload. If this is one of several similar facilities, there might be advantages in consolidation. 
On the other hand, the data assembled in Table 3 would not encourage expanding output at a single facility greatly beyond the 170 unit level except in emergencies. Pushing output from 190 to 200 units for instance, would add $1000 to costs in order to achieve 10 additional units. (Larger scale production may also bring diseconomies: bottlenecks may develop; supply shortages may force use of lower quality inputs; in a complex process, breakdowns at any stage are likely to cause far reaching delays.) 
Whatever your activity, operations over a wide range of outputs or workloads may be expected to show variations in costs per unit, though these might be less extreme than the numbers selected for the illustration. Such variations would occur even though output at each operating level reflected the best possible combination of equipment, manpower and other inputs for that level, 
i.e. was utilizing exactly the capacity for which the facility was designed. From these variations in cost per unit, you could identify the most economical scale of operations for your activity. 
In practice, of course, if your assignment or workload is changing from one level to another, you will often find that the "best" combination of inputs cannot be achieved for the new level without making capacity adjustments. If these would require extensive capital outlays, a decision for or against further investment would have to be made and in any event, time would elapse. Until adjustments were made, the structures already housing your activity and the equipment currently available for carrying it out would be fixed. Output could be increased only by using more manpower and supplies within the limits of your facility's present operating capacity-a more expensive combination of people and things, but the best you could do in the short-run. 
The long-run decision would depend on several factors. A temporary bulge in workload might not warrant any adjustment at all. A permanent shift to the new level might lead, over time, to expansion and installation of equipment permitting efficient operation at that level. But suppose it was already clear that the expanded facility would eventually be called on to carry an even higher workload. If you expected to 
49 

find the new capacity overutilized in the near sion making extends beyond proposed changes
future, you might recommend immediate exin method or levels of operation at an existing
pansion to a level capable of handling the profacility. It is, if anything, more important in the
jected future workloads in the most economical planning stages of a new project or a proposed
fashion even though this meant underutilizing major expansion or contraction of your present
some facilities in the interim. If such a long-run assignment. Here too, you can start--if not
expansion would push the facility beyond its 

from where you are-then from the specifics of
most efficient scale (size) of operations, however, the proposal and consider marginal changes inyou might resist the prospect. either the way resources are to be combined orIn short, information like that assembled in the contemplated level of operations. Ifthe firstTable 3 would not tell decision makers how, or hypothetical "change" seems likely to make ain what quantities, to combine manpower, equipnotable improvement, planners would considerment and other inputs, but it would put them 
moving even further in the same direction; ifin a better position to weigh the relative advanthe probable impact seemed likely to be untages and costs of each alternative. For any favorable, a shift in the opposite direction mightgiven facility, the best available alternative might be indicated. In short, before you are committed
entail combining people and things "uneconomito either a particular combination of resources or
cally" for varying periods of time. 
a level or quality of output, you can consider aWhen cost and output records from several sequence of marginal changes and "try them onfacilities over a range of operating levels are used for size."to help identify what scale of output is technically How close this process of successive approximost efficient for your activity, you should be mations will bring you to the best possiblealert to the possibility that some of these decisions in view of your objective depends infacilities may, for one reason or another, either large measure on the use you make of quantitative
be overutilizing their present equipment or data. Many of these numbers will be estimates,operating with significant amounts of excess but estimates also start from where you are (orcapacity. have been) in the form of historical recordsLikewise in attempting-as managers-to "get which can then be modified to take account of (the most for our money," we must remember changes: changes in the proposed amount of thethat our specific decisions will depend on the end product or service; changes in its technicaltime frame to which they apply. When you specifications, quality or completion dates;initiate a series of "marginal" questions-"How changes in the proposed combination ofmuch additional output would a specified budget resources, in the prices of inputs, in any factorincrease make possible?" "Would a further likely to affect the cost of relevant alternatives.increase beyond that level become more or less If the data drawn from your historical records
costly?"-the answers may be quite different were perfect, good estimates would depend
for the immediate future or for a long-run in entirely on your skill in identifying and makingwhich capacity adjustments can be made. But these adjustments. In the real world, however,whichever time period the decision covers, the good estimates depend also on your skill in using
analytic approach would be the same. imperfect numbers--a topic for the section whichMoreover, this "marginal" approach to deci-follows. 
50 ( 
5. APPENDIX: The Theory of Production Analysis 
WThenever two physical inputs-say, machine
W hours of equipment (Input A) and manhours of manpower (Input B) can be combined in many different proportions to achieve the same output, these combinations can be shown graphically with amounts of Input A measured along the vertical axis and the corresponding amounts of Input B measured on the horizontal axis. Each point would represent a combination of manpower and equipment with which the facility's work schedule could be met, and the points plotted as successive "equal-output combinations" would form a curve shaped somewhat like that shown in Figure A-1. All of the points on this curve are defined as representing the same quality of work and meeting the same time schedule; in short, each point represents the same output. 
Of course, other inputs in addition to manpower and equipment would actually be needed to achieve that output (in this instance, some specified workload of repairs made per week). These cannot be shown on a two-dimensional graph, but by assuming that about the same supplies, replacement parts, materials, etc. per 
output unit would be needed, whatever combination of manpower and equipment was employed, Figure A-1 can focus attention on the various amounts required for these two key inputs. 
The graph records the effect of marginal substitutions of manpower (Input B) for equipment (Input A). If you made such a substitution at a point on the equal output curve where you were using a lot of A and not much B, a small addition of B (shown as the quantity B1 ) would permit a much greater reduction (A1 ) in the amount of A required to maintain the same total output. In other words, at that point on the equal output curve, an added unit of B (manpower) would have a higher marginal product. 
But as the ratio of equipment to manpower (Inputs A and B) declined, use of more B would permit smaller reductions in A, and each successive trade-off would become less advantageous and finally become disadvantageous. (Quantities B2 and A2 .) Bear in mind that this curve reflects a physical relationship and cannot tell you directly when substitutions would cease to be worthwhile in dollar terms. That point would be reached when the dollar cost of your last addition of Input B just cancelled out the dollar savings on Input A. The location of the point depends both on the relative prices of Inputs A and B and on their physical ratio of substitution. 
You can draw an equal cost line for any amount you have budgeted to spend on the combined total of Inputs A and B. If the amount of A you could obtain for the entire budget (say, $4000 per week) is measured on the vertical axis and the amount of Input B available for the same sum is measured on the horizontal axis, a straight line between these points will cover all the ways you could split a $4000 budget between the two, provided the unit price of each input remains constant. If Input~ A and B were completely divisible, you could purchase any of these combinations. (Of course, if the unit prices of the inputs changed depending on the quantity you used, the cost line would become a curve.) 
A higher budget would let you purchase more of both inputs, but (provided the prices of A and B remained the same) the new budget line would have the same slope-be parallel to the first-since the slope is determined by the price ratio between Inputs A and B. The smallest 
A-plus-B budget with which you can achieve a 
51 

Figure A-2 
-c 
Gl 
E 
a. 
::::1 

w C" Output 
-::::1 
a. 
c 
-·-----------i 
particular output will touch that output curve at its least-cost point. 
If your assigned workload were represented in Figure A-2 by Output Levell, this would be the $4000 budget line which includes an input combination capable of yielding Output Level 1. With any lower budget for equipment and manpower you would fall short no matter how the inputs were combined. If, on the other hand, you had been given a $4200 budget, any combination of manpower and equipment at or between points Y and Z on the budget line would enable you to complete your mission. Input combinations Y and Z would each yield output at Level 1, but choosing either would represent a waste of resources since the same output could be achieved by combination X for $200 less. 
If your assignment is to provide end products or services at exactly Output Level 1, only combination X represents the economy solution to your problem. But a $4200 budget would also give you the option of buying larger amounts of manpower and equipment so as to achieve a higher level of output. In this instance, assuming other materials could be made available, the maximum workload attainable in Figure A-2 would be represented by Output Level 2. If you chose to purchase $4200 worth of manpower and equipment, combination W-where the equal cost line is tangent to Output Level 2-would be the efficiency solution, giving you the most for your money. 
Figure A·3 
50 
45 
40 
35
<: 
Gl 
E 30 
-~ 
:> 
a
w 25 
< 20 
-; 
a. 15 
-= 
10 
5 
0 0 2 3 4 5 6 7 8 9 10 
Input B -Manpower 
Figure A-3 extends the situation portrayed in Figure A-2 to encompass a range of equal output curves, each of which represents the highest level obtainable from a succession of five budgets, provided each is used to acquire the best combination of equipment and manpower (Inputs A and B). The hypothetical amounts budgeted for combined expenditure on both inputs rise from $3000 to $7000 in equal jumps of $1000 each. 
The highest output obtainable from any equal cost line will also represent the least costly combination of A and B anywhere along the highest equal output curve it touches. Consequently, a line drawn through each of these tangency points shows, simultaneously, the most efficient way of spending a particular budget for equipment and manpower and the most economical way of using these inputs to achieve a particular output. 
Each thousand dollar increase in combined expenditures on A and B provides additional output, but not necessarily the same amount of additional output for each increase. In fact, the numbers assigned to the equal output curves in Figure A-3 show increases ranging from a high of 50 units to a low of 10 units (associated with a budget increase from $6000 to $7000). 
In the short-run you might not be able to move immediately from one tangency point to the next, since amounts of Input A (embodied in structures, heavy equipment, etc.) would be fixed. Figure A-4, Panel 1 displays such a 

52 


l• 
--~-----~ -~-l 
<(
-:I 
Q. 
c: 
short-run situation when output is increased from the 120 to the 170 unit level. The graph shows capacity adjusted to a 120 unit operating level where you are operating with the least costly combination of Inputs A and B (point X). If you are called upon to supply output at the 170 unit level and cannot immediately increase plant capacity, your only option is to find the point on the 170 unit output curve which can be attained with an unchanged amount of Input A (point Z) and employ whatever amount of manpower is required to make good that output. 
...,_. 
~--·--
~----------------
---~
~-
Input B 
A capacity adjustment to the 170 unit level is shown in Panel 2 where the new fixed amount 
of Input A (plant and equipment) is that associated with point Y. But suppose longerrange plans already called for an eventual increase in output to the 190 unit level. An expansion now which adjusted capacity to the 170 unit level might soon result in operations being carried out at point V in order to satisfy future requirements. This would be an "uneconomical" combination of equipment and manpower for a facility operating at a 190 unit level 
53 

and, as the budget line passing through point V shows, would add $300 to the minimum cost of handling work at that level. 
Given this long-run prospect, you might choose to raise operating capacity immediately to a level which would enable you to handle the 190 unit workload in the most economical fashion (point U on Panel 3). For the immediate future, however, this decision would mean that 170 unit operations entailed an unnecessarily high $5200 outlay on manpower and equipment 
(point W). 
Aside from the time involved in making capacity adjustments, possible combinations of Inputs A and B which do not lie along the 
diagonal line joining the tangency points in Figure A-3 become irrelevant for long-range planning. Whatever level of output is under consideration, the best way of combining manpower and equipment to reach it will lie somewhere along the upward sloping diagonal joining the points which have now been identified as "least-cost combinations." Each of these points represents a specific output or service level and also minimizes the budget for Inputs A and B needed to reach that level. 
We can now set up a new graph, Figure A-5, with the various output levels represented in Figure A-3 measured on the vertical axis and the 
54 

(_ 

minimum budgets for equipment and manpower needed to obtain them measured on the horizontal axis. When the least-cost points from Figure A-3 are plotted on this new graph, they will form an upward sloping S-shaped curve from which you can read directly the minimum combined expenditures on equipment and manpower (Inputs A and B) which would be needed to achieve various possible levels of output or service. 
With this S-shaped curve, the technique for making marginal comparisons can be extended to identify the cost of changing the quality or service specifications of your output. Output which is designed to meet higher quality standards or more exacting specifications would be a different and more costly end product from 
the units you are now turning out. Estimated costs for the modified units could be plotted alongside minimum costs for the standard units 
at each output level on a graph like Figure A-5. From this new graph (Figure A-6) you would be able to visualize either the impact on costs of a change in quality specifications at the same operating level (a shift from point A to B) or the output which would be lost if an existing budget were stretched to turn out the premium units (a shift from point A to C). 

ll-6 

GETTING INFORMATION 
FROM OUR NUMBERS 

~e'l 
~0 
v<. 
0 
~o' ~"' 
The~0 
~, 
Imperfect data; there are no other kind. 
Better data would be very expensive to get 
ACCOUN~Ni~· 
The data we used are good enough for this purpose 
: i 
' I 
I 
\ 
} ' 
This information 
will change my 
decision 
c 

I 

6. Getting Information From Our Numbers 
C
ost and output data are useful to resource managers primarily because they make possible meaningful comparisons. The basic unit of comparison is the individual cost/output observation. Each observation relates a specific accomplishment to the specific resources used in achieving it. 
With such observations a manager can com
pare (or anticipate) costs at different levels of 
output or for different qualities of output; he 
can compare (or anticipate) the results of 
combining resources in alternative ways or of 
assigning workload among several facilities in 
alternative ways; he can compare actual per
formance with expected performance; he can 
anticipate the impact of proposed changes: the 
added cost of additional units or of setting 
higher quality specifications; the savings that 
might be realized through a cutback. In short, he 
can use these comparisons either to bring his 
budget realistically into line with his objectives 
or to tailor his ·objectives until they fit his 
budget, or to do some of both. 
These uses have been illustrated in the 
preceding sections by hypothetical examples. 
The examples yielded precise information 
because, by definition, the cost/output observa
tions on which they were based by definition, 
differed from each other in the respect being 
compared and only in that respect. For instance, 
in plotting a curve which showed the relationship 
of cost to output over a range of outputs, each 
point represented output units which were 
identical except for the number of units turned 
out. In short, the numbers were perfect for the 
purpose to which they were applied. 
"Of course," you may be thinking, "I could 
do a better job of managing resources if I had 
that sort of accurate cost/output information. 
But the numbers available for my activity do not 
meet those specifications. Collecting data that 
good would cost more than we could afford, and 
furthermore, it just could not be done." 
Such a reaction might be partly right. Analy
sis of actual cost and actual output numbers can 
never result in information as precise as that 
derived from hypothetical examples. "Real" 
numbers will be imperfect; there are no other 
kind. But this does not mean that useful 
comparisons cannot be made with "real" 
numbers drawn from the records of your own activity. It does mean that some rules for living with imperfect numbers must be observed. Data must be scrutinzed carefully, since invalid comparisons are easy to make and may result in misleading conclusions. Moreover, imprecise data has to be interpreted, and this often requires statistical techniques somewhat different from those described earlier. 
You are also right to be concerned over the cost of setting up and maintaining records. Collecting better and more precise data than are needed is, itself, a wasteful use of resources. Numbers that were easier to obtain might be 
precise enough for many analytic uses. In fact, one of the first questions you must face in living with "real" numbers is precisely this: how good is good enough? 
The question does not have a single definitive answer. In many cases, the use of "imperfect" numbers for analysis will simply make your conclusions less precise than those in the hypothetical examples presented earlier. But this is not always the case. Numbers may also be defective in ways which would render invalid any conclusions based on them. For purposes of cost/output analysis, it is emphatically not true that any numbers are better than no numbers at all. 
As a general rule, data are not good enough for analysis unless the individual observations being compared relate specific accomplishments to the resources actually used in achieving those 
results. Records should be set up in such a way 
as to do this. Costs should be recorded not when 
resources were ordered, delivered or paid for but 
when they were used. The units in which output 
is recorded should measure directly what was 
accomplished and not simply restate in physical 
terms an input, such as man-hours. Both of these 
requirements were explained in detail in Sec
tions 3 and 4, and if the numbers being collected 
for your activity do not meet these criteria, they 
should not be used in the ways described here. 
Unless such numbers are needed for other 
purposes, collecting them may be a waste of 
resources. To build a data base for analysis, 
record systems should, if necessary, be modified 
to meet these two con.ditions. 
Assuming that your records do satisfy these 
basic criteria, the numbers will yield valid
though not necessarily precise-conclusions so 
57 

long as you avoid comparing cost/output obseryour activity. Such changes might precludevations which are not comparable. Applying this entirely certain types of "before" and "after"rule is not so simple as it sounds. In the comparisons. For an aircraft engine reworktheoretical examples presented earlier, comfacility, for instance, the transition from overparable observations were defined as those hauling piston to jet engines might constitutewhich differed only in the respect being comsuch a decisive discontinuity.pared. But if observations had to be identical In other cases, comparability may best beexcept for selected characteristics, numbers served by excluding individual observations. Ifwould have to be collected under the conditions you identify an "abnormal" cost/output obserof a laboratory experiment (all other variables vation as being associated with some temporaryheld constant). "Real" observations-those factor ( a flood, say, or a transportation stopdrawn from operating records-must differ from page), you might exclude it from comparisons.each other. Each is unique. 
You might also exclude individual observationsReal observations represent work done at 
where the accuracy of reporting seemed seridifferent times or different places or both. ously suspect.
Entries may have been made in different More general adjustments may also berecords-with varying degrees of accuracy-by 
required. Cost/output observations made over_adifferent clerks. Between one observation and considerable period of time should not bethe next, input prices may have changedcompared without taking the impact of susselectively or across-the-board. Seasonal or geo
tained inflation into account. Appropriate
graphic variations may have occurred. The comadjustment factors might be applied to cost dataposition of a facility's workload may have 
and thus built directly into the statistical
changed-temporarily or permanently. Techanalysis; in other cases, it may be enough fornology may have changed; needs may have you-as the user of the analysis-to be aware of
changed; the activity's assignment may have inflation and allow for it in interpreting the
been redefined. results. Allowing for it is part of your job as aIn a laboratory environment, any of these 
manager. There are also standard techniques for
changes might be sufficient cause for rejecting comparing monthly data in an activity wherethe observation, but in using real numbers, your operations are subject to measurable seasonaltask is to distinguish between those which-in fluctuations. As noted earlier, comparisonsthe absence of explicit adjustments-would inbetween investment projects which differ invalidate comparisons and those which merely extent of capital investment and useful lifemake them less precise. The distinction is a require application of a discounting technique tomatter of judgment and, if you are familiar with measure tpe present value of both.the circumstances, can usually be settled by But comparability among cost/output obsercommon sense. 
vations cannot be assured simply by adhering to
Suppose your organization has been assigned standard statistical procedures, or by applyingan additional function for which resources must 
standard criteria. Consider the apparently obvibe used (perhaps a training base is given a direct ous requirement that "comparable" cost/outputrole in some community activity). If your observations should include the same comrecords simply continue to record output in the ponent elements of cost. This would usually beold unit (number of recruits graduated), true, but as the example of choosing between"before" and "after" cost comparisons would be two aircraft types to transport specified cargomisleading. There are various options for ad
(Section 5) showed, there are times when onejusting cost or output records (the most satis
alternative should allow for acquisition costs andfactory solution might be to allocate costs and 
the other should not.keep separate records for the two functions), Decisions to adjust certain observations or
but the important requirement is that you 
exclude others from analysis always requirerecognize the need for making an adjustment personal familiarity with the data being coland do so. lected, the activity being analyzed and theOften comparability can be restored by purpose for which the analysis is being made.adjustments, but you need also be alert to This process of "cleaning up the data" is itselfidentify permanent changes in the character of an essential part of analysis. 
58 
c 

But "clean" numbers will still be imperfect numbers, because they are subject to a wide 
range of unpredictable and unsystematic variations. These variations do not render comparisons invalid, but they may make such comparisons very hard to interpret. In order to extract useful information from variable data, you will often need the help of statistical techniques designed for that purpose. These too are patt of the process of "living with imperfect 
numbers." 
Unless you are engaged in a very simple, routine operation, the units included in your output records will not be completely uniform. At different times or in different places the same number of units will represent differing accomplishments which embody differing amounts of work. For instance, the output unit most commonly used for freight transportation is the ton/mile. But one hundred ton/miles might equally well represent the movement of one ton of freight for 100 miles or the movement of 100 tons for one mile. Although these two outputs would appear the same in the records, the amounts of travel and handling would be very 
different, and their cost almost certainly would 
not be the same. Similar variations occur for 
II 
measures which might be applied in almost every type of activity: patient days in a hospital, 
personnel actions processed, experiments con
ducted, contracts negotiated, orders filled. 
Let us consider this problem in terms of an 
extreme example. Suppose you were in charge 
of the automotive repair shop discussed in 
Section 5 and were seeking a unit of output 
measurement. Over the course of a typical week, 
the shop's workload might run the gamut from 
replacing sparkplugs to major engine repairs. 
Choosing an output measure for such a facility 
presents serious problems. If each completed job 
were counted as a unit of output, it would seem 
that the disparities among observations must 
make analysis meaningless. But alternative solu
tions would also pose difficulties. 
One alternative might be to segregate various 
categories of repair work and maintain separate 
cost and output records for each. This procedure 
would entail complex cost allocations among 
categories. Record keeping would become 
expensive-perhaps prohibitively so. 
Another approach might entail creating an 
abstract output unit to provide a common 
denominator for diverse repair jobs. These could then be assigned differing values (1-unit, 3-unit, or 10-unit jobs). Even if engineering studies or other objective criteria were used in evaluating specific "jobs," output measurement would risk becoming a disguised restatement of one or more inputs. A sophisticated unit of measurement would be more_ ambiguous to define; it would also be more expensive to collect than a simple tally of completed repair jobs and more subject to reporting error. 
As a practical matter, managers may often find that they will not have cost and output records available for analysis unless they are able to develop meaningful information out of variable data. And even with a measure like "jobs completed" at an automotive repair facility, this might be done. In the first place, lengthening the time period covered by each cost/output observation should greatly reduce the disparity among them. Jobs completed per day, per week or per month would become increasingly likely to 
encompass a typical selection of major and minor repairs. And the longer the time period chosen, the greater the probability that most observations would represent a similar "mix." 
Nevertheless, this "mix" would never be identical; most periods would deviate somewhat from the average and some, almost certainly, would deviate a great deal. So long as these deviations did not reflect a major and enduring 
change in the character of repair procedures (such as a decision to substitute replacement parts and ship the originals off for overhaul instead of doing repairs on the premises), they would not destroy the validity of comparisons among cost/output observations. 
But even if comparisons were valid, would 
they also be useful? Weekly costs might differ 
for a dozen reasons related to the nature of the 
jobs done rather than the weekly number of 
output units. How could you discover what 
differences in costs were attributable specifically 
to disparities in output level? 
Certainly if you plotted individual observa
tions on a graph like those illustrated in Section 
2, (see p. 21) with output measured along one 
axis and associated costs on the other, these 
observations would not form a line or curve as 
did those shown in the examples. Instead you 
would find yourself looking at a "scatter 
diagram" like that in Figure 1. You might have 
to examine the diagram rather closely to recog
nize that higher expenditures and higher output 
59 

Figure 1 
.. 

Gl 
..Q 
E •
:I 
z • 
en
.. • •
• 
0 
a. • • 
Gl • • 
ac: • 
• 
Cost -Dollars 
levels did in fact tend-at least very roughly-to be associated. 
While a positive relationship between cost and output levels could thus be identified by inspection, the information-scarcely surpnsmg
would not be precise enough to help in decision 
making. Is there any way in which you could make it so? You might, if your observations were so positioned that they formed a distinct band, enclose the band with two lines and thus establish the probable range of costs to be expected at each output level (Figure 2). By 
Figure 2 
.. 
Gl 
..Q 
E 
:I 
z 
en
.. 
0 
a. 
Gl 
ac: 
doing this you would also identify any observations notably outside the band and might earmark these for investigation. 
But this very elementary analysis would still fall far short of the use you could make of a line (or curve) from which you could read directly 
the aggregate cost to be expected at any selected level of output. Such a line (or curve) would be even more useful if you also knew how close most weekly observations could be expected to lie to the estimated values and how often the costs for individual weeks might be expected to deviate by more than some specified amount. By applying appropriate statistical techniques, variable cost/output data often can be made to yield just this information. 
Suppose you took a ruler and drew a straight line lengthwise through the scatter of cost/ output points (Figure 3). If the visual "fit" of 
this line were good, i.e. if the observations above and below seemed to be about equal in number and distance from the line, you might use it as an estimating tool in budgeting for expected workloads or in calculating the probable impact on costs of workload changes. Depending on how good the fit appeared to be 
and how you intended using the estimates, this visually drawn "regression line" might meet your analytic needs. 
But greater precision could be obtained by fitting a linear regression line statistically. Such a line is based on an equation derived from the 
Figure 3 
.. 

Gl 
..Q 
E 
:I 
z 
en
.. 

0 
a. 
Gl 
ac: 
c 

60 
I 
Cost -Dollars 
Cost · Dollars 
entire range of cost/output observations and is constructed so as to minimize the extent to which costs actually reported in the individual observations deviate from those shown by the regression line for appropriate output levels. In addition to fitting a regression line, this estimating equation could be used to identify the operating level at which unit costs would prob
ably be lowest and to compute the "marginal" costs involved in moving from one output level to another. 
With such an equation it would also become possible to determine mathematically the relative importance of output level (workload) as compared with other variables in accounting for recorded differences in weekly costs. (The closer the relationship between costs and output level, of course, the greater the predictive value of the regression line.) If a sufficient number of weekly observations were available, it would also be possible to compute measures of deviation and establish a dollar range above or below the estimated cost within which most weekly observations would be expected to fall. 
These computations are not difficult and can be performed by any statistician. If you would like to fit a regression line to data yourself, you can readily find the techniques in elementary statistics texts. 
It may turn out, however, that a straight line 
does not provide the best description of your 
data. In fact, a reexamination of the "scatter 
diagram" suggests that a curve like that fitted 
visually in Figure 4 would give a better repre
sentation of the apparent relationship between 
the weekly number of repair jobs and their 
aggregate cost. In moving from very low oper
ating levels to somewhat higher ones, costs seem 
to rise very modestly compared with the in
crease in work completed. But at heavier work
loads, the cost of turning out additional jobs per 
week climbs more rapidly. 
This type of curve (a parabola-or more 
properly a segment of one) can also be fitted 
mathematically to a scatter diagram of cost/ 
output observations, and statistical tests similar 
to those used for a linear regression equation 
would show whether a line or a curve describes 
better the relationship of cost to output for a 
particular activity (i.e., provides a better "fit" 
for the data). The equation required to fit a 
curve of this sort is somewhat more complex 
than that used for a linear regression. But it too 
Figure 4 
... 
Cll 
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E 
:I 
z 
...
"' 
0 
Q. 
Cll 
IX 
Cost -Dollars 
is a standard statistical procedure, described in elementary texts, and one which any statistician can readily perform unless you choose to make your own computations. 
Which equation would provide a better fit for data drawn from your activity would depend on several factors. As the hypothetical examples suggested, data collected over a wide enough range of outputs would reveal a cost/output relationship in the form of a curve. Starting from very low output levels, a large increase in work completed by a facility of a given physical capacity could be achieved with a modest increase in expenditures. Beyond some point, however, additional increases in jobs completed would become increasingly expensive and eventually prohibitively so. In theory at least, there would eventually be a point beyond which trying to increase the number of jobs would so clog the system as to actually reduce the number completed within the week. 
Observations drawn from actual operating experience, of course, would rarely if ever encompass this entire range. And it is quite possible that the segment of the range covered by your operating data could be described most simply by a straight line. In either case, "real" and imperfect numbers will yield valuable information for analysis if we use elementary statistics to make sense out of scatter diagrams. 
Both the benefits and pitfalls of using "real" numbers for analysis can be illustrated by a case 
61 


history involving data taken from actual oper
ating records and put to actual analytic uses. 
The numbers in the following example were 
collected by 13 food service centers and related 
the number of meals served at each center over 
the course of a fiscal year to the non-food costs 
of serving them. The first objective of analysis 
was to determine what relationship existed 
between facility size (annual volume of meal 
service) and serving costs. Factors which might 
obscure that relationship (i.e., cause individual 
observations to "scatter" around a regression 
line) included the likelihood that the 13 facili
ties differed in many respects other than size 
and that records might be kept differently at 
different locations. 
Analytic uses to be made of the cost/output 
relationship-once established through a regres
sion line-included .performance evaluation 
(comparing the operating efficiency of indi
vidual food centers) and long-range planning (cost considerations in decisions to centralize or decentralize food service) as well as the obvious one of estimating budget needs for various facilities on the basis of their expected service loads. 
Table I 
FOOD SERVICES · FY 1969 
(Excluding Cost of Food) (13 locations) 
(1) Actual Expenses i
-----r'-
(2) (3)Meals Served 
Total Dollars $Per Meal 
i 
23.766 83,600 3.52
212,581 
265,600 
1.25
245,827 244,600 1.00
255,557 
204,200 
.80277,858 164,300 .59302,153 197,200 .65339,597 212,900 .63464,932 
258.400 
.56 
3,824,230 1,249,000 .335,045,711 1,304,700 .266,563,607 2,033,200 .317,432,668 1,610,100 .2220,596,557 4,539,300 .22 
In Table 1, the figures collected from the 13 locations hav:} been arranged in ascending order of magnitude according to the number of meals served annually at each location. Column 2 gives aggregate serving costs at each location, while serving costs per meal have been computed in Column 3. One important analytic conclusion could be read directly from that column: feed
62 
Figure 5 
6 2 4 6 8 10 12 14 16 18 20 
Millions of Meals Served 
ing large numbers of people at a single location 
evidently permitted notable savings in the cost 
of providing service. 
Figure 5 graphically confirmed that conclusion. Only six points were plotted on the graph because the wide spread among annual service loads-ranging up to 20 million mealsnecessitated a grid on which c !Jservations for all eight locations serving fewer than 500,000 meals were represented by a single dot. But the linear regression line describing the relationship of the scattered points was "fitted" by an equation derived from all13 observations. 
This equation appeared to establish two conclusions: first, the slope of the regression line showed that, as meal volume increased, serving costs rose much less than proportionately, and second the line itself provided a very good "fit" for the observations. Statistical tests indicated that 98 percent of all cost variations among the 13 locations could be accounted for by their differences in meal volume. 
This high correlation seemed to clear the way for putting the regression line and the equation on which it was based to all the analytic uses mentioned above: budget estimation for facilities of all sizes throughout the range, long-range planning and performance evaluation. But a substantial number of management decisions involved facilities serving fewer than 500,000 meals annually, and these observations could not be identified separately on the grid used in Figure 5. Consequently that portion of the graph was expanded and the individual observations for these facilities were replotted on a greatly enlarged grid. 
( 

When this was done, it immediately became apparent that deviations from the regression line among these smaller facilities were very significant relative to their own level of operations. The absolute dollar amounts of deviation were too small to affect correlation tests because the aggregates were dominated by facilities serving millions of meals annually. Routine application of standard statistical procedures had obscured the fact that facilities operating at such widely disparate levels might not be really comparable. A separate regression line, fitted to facilities in the 100,000 to 500,000 meal range, seemed likely to provide better information for those concerned with their management. 
Furthermore, in fitting the original regression line, data from all 13 locations had been accepted uncritically. Now the accuracy of those observations which were furthest "out-of-line" was called into question. Review of the suspect numbers revealed that data reported for the smallest food service location were unusable, and that observations for several others were not comparable as reported. 
After adjusting for these discrepancies, revised cost/output observations representing seven facilities in the 100,000 to 500,000 meal range 
were plotted in Figure 6. The revised regression line fitted to these points is shown as a heavy line. Drawn more lightly is the old regression line based on uncorrected data supplied by 13 facilities of all sizes. The two lines differ as a result both of reexamining the raw data (cleaning up the numbers) and of limiting coverage to the "under 500,000" size range. 
How significant to decision makers would these revisions be? Note first that none of the changes in any way challenged the main conclusion to be drawn from Table 1 and Figure 5-that notable economies in serving costs could be achieved by concentrating all food service at facilities providing five million meals or more per year. But considerations of geography and transportation would almost certainly rule out this solution. Realistically therefore, facilities in the smaller size ranges would remain, and managers seeking to make the best possible decisions would be better served by using the revised regression line in Figure 6 and its underlying equation. 
The value of using "clean" and comparable data for budget estimates can be demonstrated quantitatively from Table 2. The original regression equation would have yielded the cost estimates for five selected service levels shown in Column 2. The revised equation provided the lower estimates in Column 3. Reliance on the original equation would have resulted in unnecessarily high budget requests at all five levels, and especially at the smaller facilities. 
Table 2 
ESTIMATED FOOD SE-RVICE COSTS· FY 1969 
(Excluding Cost of Food) 
100,000  214,000  120,000  94,000  
200,000  236,000  160,000  76,000  
300,000  266,000  198,000  60,000  
400,000  280,000  238,000  44,000  
600,000  300,000  276,000  26,000  

Next, suppose both sets of estimates were being used to help develop long-range plans for the size and location of food service centers. Analysis of either set would indicate that operating savings could be achieved by serving larger numbers of meals at fewer locations. But the revised figures would show a smaller saving than the original analysis. Suppose a total of 500,000 meals were to be provided annually. If two locations were set up-one providing 200,000 meals and the other 300,000-the estimated annual serving costs at the combined locations would, according to the old equation, amount to $494,000 ($236,000 at the first and $258,000 at the second). If instead, the entire 500,000 meals were served at a single location, total non-food expenses would be only $300,000-an 
63 

indicated saving through consolidation of judging relative performance. The comparisons c 
c 

$194,000. Revised estimates would indicate a potential saving of $83,000-less than half as great. 
Since either analysis would have predicted savings through consolidation, the differences in amount might seem unimportant. But direct operating expenses are not the only criterion in deciding the size and location of facilities. Factors such as capital expenditures, quality of service, convenience to diners, time and transportation to and from meals, etc. might favor smaller, more conveniently located facilities. In weighing proposals to consolidate, the undisputed fact of some cost differential in favor of larger service units might be less important than its probable size. 
Either regression line could be used by managers to identify those facilities which were "out-of-line"-where the cost of serving meals was notably above or below what might have been expected solely on the basis of size. By screening out the effect of size difference on costs, the line would make possible direct comparisons among individual facilities. For these comparisons to be significant, the line must be based on observations which were accurate and suitable for comparison. In our example, the revised regression line would clearly be more reliable on both counts as a basis for themselves would not constitute performance evaluation, but only its first stage. The real challenge to management would lie in identifying (and if possible correcting) the specific problems which accounted for unexpectedly high expenses at some locations and-perhaps even more importantly-in identifying (and if possible adopting elsewhere) the conditions or methods that produced superior performances. 
Like an X-ray camera, the statistical technique of regression analysis has the ability to "see through" a scatter of individual observations to an underlying bone structure-their measurable cost/output relationship. And this relationship is the basis for most of the analysis discussed in the preceding sections. In order to obtain valuable information for decision making from "real" numbers, you need only make sure that two prior conditions are met: your records must be kept on a basis permitting valid cost/output observations, and the data must be "clean"individual observations must be accurate and comparable for the purpose at hand. These conditions apply whether the management function involves research projects, inventory control, capital goods acquisition or the operation of facilities such as food service centers discussed here. 
64 


c~ 
II-7 
USE A CHECKLIST: : I 
DO IT RIGH.-.
I; 
I 
I I 
' 
I carry my check I ist 
all the time Maybe I shouldn 1t depend on my memory 
I call mine a reminder Iist 
• litHNICIAN : 

7. Use a Checklist; Do It Right 
Analysis cannot help you in your job as a .tl.decision maker unless you have the right numbers available in the right places at the right time. You cannot wait until you are confronted with a deadline to decide what numbers you need for analysis and then collect them. Analysis depends on an adequate data base-one which can be built only by setting up appropriate cost and output records and maintaining them over 
time. 
Moreover, since "real" numbers will never be perfect, it is highly important for you and other users of these data to know how the records are collected and precisely what they contain. 
If you have read this far, you have encountered a number of criteria for maintaining records which will provide the right numbers at the right time. You probably have most of them in mind. But in the same way that airline pilots use a checklist to make sure that all essential tasks have been completed every time they take off or land, you may find the following list a useful reminder. There is no single "right" answer to any of the questions on this list, but each raises a point you need to consider in the light of your own circumstances. 
I. 	CHECKLIST FOR ESTABLISHING A DATA BASE 
A. What Uses for Cost and Output Data: 
1. 
Who will use these data? You? Your superiors? Someone working for you? All of these? 

2. 
What will these data be used for: Improving control of day-to-day operations? Preparing budgets? Evaluating performance? Justifying future budget proposals? Long-range 


planning? 
3. 
At what level will decisions based on these numbers be made? What sort of choices will be open to the decision maker: To make the best use of his present budget? To achieve his mission at the lowest cost? To acquire new facilities or dispose of old ones? To change quality specifications? To seek new solutions for broad problems? 

4. 
If these data are limited or imprecise, for what levels of analysis and decision making can they appropriately be used? 



5. 
How promptly will users of these data need current numbers? Will someone still be revising and analyzing numbers after the deadline for decision is past? 

6. 
What format for presenting these data will be most helpful to major users? 

7. 
Will numbers collected for this activity be compared with those for other facilities? Are they comparable? Is the same format used for each? 

8. 
Do those actually engaged in collecting and tabulating the data have clear instructions as to what numbers to collect and how these should be combined or displayed? Do they have guidelines for identifying numbers which fall outside some expected size range? Are they expected to double-check such numbers for reporting accuracy? 


B. 	What Costs to Count: 

1. 
Can costs be matched to output for the same time periods? Do cost figures cover the resources, and only the resources, actually used in that time period? 

2. 
Can users identify and use separately those cost items which are relevant to their decision or level of analysis? If costs over which you do not have direct control are excluded from your data, are these items available separately for decisions to which they are relevant? Are operating costs and capital costs separately identified? 

3. 
Can costs associated with partially completed output units be excluded from analysis? 

4. 
If your activity has several functions, how are cost items allocated among them? 



C. 	What Output to Measure: 
1. 
Does your activity have a clear and explicit statement of objectives? Is it written in quantifiable terms? 

2. 
Does your activity have a clearly identifiable end product or service? 

3. 
Is this end product or .service defined by a set of standards or specifications which can be used as a measure of quality level? Are routine tests or quality control procedures used to determine how consistently output meets these standards? 



67 


4. 
Does your unit of measurement really represent output or does it simply restate an input in physical terms? 

5. 
Do your output units measure all the output and only the output covered by your cost data? Do the numbers include only completed units? What adjustments do you make for partially completed units? 

6. 
Ifyour activity has more than one end product or service, should these be consolidated in a single measure? Or should costs be allocated 


among several types of output? How? 
II. 	CHECKLIST FOR MAINTAINING A DATA BASE 
A. 	What Changes to Adjust for: 
1. 
Has your activity's mission changed or have its objectives been redefined? Is the existing output measure still appropriate? 

2. 
Have new functions been added? Are they covered by your present output unit? Are they part of your costs? Should an additional measure of output be set up and costs allocated among several functions? 

3. 
Are quality standards for your activity subject to review and change? If they have been changed, do output units reflect these changes? 

4. 
Should comparisons of cost data over time include an adjustment for price level changes? 



5. Have there been significant techc nological changes in your activity? Do these affect the comparability of cost data over time? Are there adjustments which can restore comparability? 
B. 	What Numbers to Collect: 
1. Are existing cost and output data for your activity reviewed periodically to determine what uses are being made of them? If they are not being used, why? If they are no longer useful, can you stop collecting them? 
2. 	If numbers are being collected for 

others, are they still being used? If not, are they worth collecting for your own use? If not, can you stop collecting them? 
3. Could you make more use of cost and output data if they were modified? How much would the modifications cost? Would they be worth making? 
If these are your data-collected for an activity you understand and under circumstances with which you are familiar, you may be like the airline pilot: you would almost certainly take account of all the points raised by these questions without the checklist. Taking account of them is part of your job. But ( competent and experienced pilots still use checklists. Faithfully using the checklist is insurance against some day making a crash landing. 
68 


c_r 

m-1 
----------------· 
-·---
--------------· . ! --:::=:-:.:::..:.--_,:,
~=~==--;;;;:;;;;------------t-1! 
I I . 
: I : 
II 
! I I MONITORING 
! I II : I 
i -~ i , :_ PHARMACY STORE
I I : 
! 1j i i
I II OPERATIONS
I I i I ,I' I j i 
\ i; . Service and efficiency: both 
I II ' 
are necessary. 
j
\ . I ; 
I see the problem, andI I think I know what ( caused it. \
Let1s move fast or we•11 exceed our year•s 
Output is normal but 
budget. 

costs are running too high. 
~ TEcHNICIAN : 

c 

CASE HISTORY 1: MONITORING PHARMACY STORE OPERATIONS 

T 
he situation. In August 1966 when the Department of Defense issued Directive 7000.1 providing for the design and installation of Resource Management Systems, it requiredamong other things-that such systems be established for operating activities and specified that these systems should provide a means of matching cost and output data which would: "1) Focus on outputs and on resources used, i.e. expenses, 2) Focus on managers who are responsible for effective and efficient utilization of resources and 3) Focus on actual performance in relation to planned performance ....." 
A fifteen base training complex for one Service undertook to comply with this directive by choosing output measures for various operating activities and testing these measures over a period oftime. When this had been accomplished for several activities, the Resource Management Center for the complex moved on to the next phase of its program by adopting a uniform reporting format and requiring monthly cost 
Table 1 PHARMACY SERVICE:  BASE W  
100 4866  9386  13437  18217  23137  27452  33843  38683  43458  48248  53258  57908  
4866  
100  
95 5.8  11.6  17.5  23.9  30.3  36.7  44.0  51.2  58.4  64.5  70.5  76.5  
5.5  
-.3  
16  95  
i ·~ ·~  PLAN (09+ 01) ACTUAL (10 + 02) VARIANCE (18-17) %OF PLAN (18 + 17) PLAN (13+ 05) ACTUAL (14 + 06) VARIANCE (22-21) %OF PLAN (22 + 21)  17 18 19 20 21 22 23 24  119 113 -6 95 119 113 -6 95  128 124  146 130  134 131  130 131  148 134  114 130  149 132  151 134  127 134  120 132  129 132  

71 

and output reports for these activities from each 
of the fifteen bases. 
At the time this requirement went into effect, Colonel Albert was commander at Base W-one of those in the training complex. Regular reporting began in July with the start of a new fiscal year. The following month, copies of the initial reports for activities with established output measures appeared on his desk. 
Colonel Albert was not aware of any immediate operating problems which required his attention in any of the areas involved. In the preceding fiscal year, however, costs for operating pharmacy services, which was the subject of one Of these reports, had exceeded the amount budgeted making it necessary to obtain additional funds. Remembering this, he picked out the report for the base pharmacy for a closer look. 
The Numbers. The summary which Colonel Albert examined (Table 1) provided separate panels for, 1) output-prescriptions filled by the pharmacy service at Base W; 2) expenses-including the cost of drugs, in thousands of dollars; and 3) cost per prescription in cents. He saw that the reporting format had been designed to permit a variety of comparisons-from one month to another or between planned and actual performance-and also to relate cost and output through the unit cost panel. Planned levels for output, costs and unit costs over the entire fiscal year had already been entered in the table on both a monthly and a cumulative basis. There were also slots for computing the amount and per cent by which actual numbers deviated each month-and cumulatively-from these expected magnitudes. 
In view of the earlier problem caused when pharmacy expenditures had exceeded the budget, Colonel Albert noted with satisfaction that actual July expenses were now somewhat below the amount currently projected. He had been hearing considerable grumbling about output measurement and the added work these reports would cause, but now he found himself thinking how useful this type of information on pharmacy operations would have been the previous year. Regular reporting might not have prevented the need for additional funds, but at least the developing problem would have become apparent much sooner. 
Indeed, it occurred to Colonel Albert that the filling of prescriptions was an activity where timely reports which compared actual with expected developments would have been especially valuable. The pharmacy manager had probably been aware over the course of the year how high his expenditures were running. But he had no responsibility for the issuance of prescriptions to be filled and thus had little influence on the cost of drugs-the most important element in his costs. If the Surgeon General who did have that responsibility had been receiving a report like this on the new form, he too would have been alerted to the developing excess of actual over expected expenditures. He could have determined whether the trend was due to unavoidable circumstances, such as increased population on base or an epidemic, or to mismanagement which could be corrected. Either way, reports on the new format would have served as an early indicator·of developing needs. 
Obtaining Information from the Numbers. 
Two months passed before the monthly table on pharmacy costs and output again came to Colonel Albert's attention, and on this occasion the numbers were not to his liking. (Table 2.) The first figure which caught his eye was the steep increase to $2.03 in the cost of each prescription filled. Looking up at the cost panel, he saw that monthly costs of $9.9 thousand for September had been 68 per cent above the expected level-a discrepancy far greater than the moderate variance in number of prescriptions filled. In fact, the September cost figure seemed so far out of line that he wondered if a reporting error had not occurred. Accordingly, he called Mr. Zenger, the analyst who coordinated Base W's reporting program. 
Mr. Zenger, it turned out, had also been surprised at the September cost entry and had checked it out with the pharmacy manager. The figure, he reported, was correct. "But," Zenger added, "the extra money apparently went into building up the pharmacy's inventory of drugs." 
"Hold on a minute," said Albert, "do you mean these monthly cost figures aren't associated with prescriptions filled the same month?" 
"Not necessarily. Supplies are entered as costs when they are delivered from the stock fund not when they are used to fill prescriptions." 
"Why?" 
"Because, as a practical matter, that's the only point at which cost records can be maintained easily and accurately for this activity." Zenger 
( 

( 

72 

Table 2 
Prescriptions
PHARMACY SERVICE: BASE W 
Filled 
VARIANCE (06-05) 
%OF PLAN (06 + 05) 
%OF PLAN
) (10 + 09) , PLAN (CUM 09) . , ACTUAL 
, (CUM 10) 
VARIANCE (14-13) 
%OF PLAN (14 + 13) 
VARIANCE (18-17) 
%OF PLAN (18 + 17) 
VARIANCE (22-21) 
%OF PLAN (22 + 21) 
03  -148  822  
04  100  97  120  
05  4866  9386  13437  18217  23137  27452  
06  4866  9386  14111  
07  -148  674  
08  100  98  105  
11  -0.3  1.3  4.0  
12  95  122  168  
13  5.8  11.6  17.5  23.9  30.3  36.7  
14  5.5  12.6  22.5  
15  -.3  1.0  5.0  
16  95  109  129  
17  119  128  146  134  130  148  
18  113  162  203  
19  -6  34  57  
20  95  127  139  
21  119  124  130  131  131  134  
22  113  136  159  
23  -6  12  29  
24  95  110  122  

73 



paused and added, "Of course it makes the data 
less satisfactory. We can't rely on monthly unit 
cost figures for analysis, for instance, because 
the cost of drugs in a particular month may not 
match prescriptions actually filled in that 
month." 
Albert exploded. "So you fellows put out a 
table that simply does not mean what it says! 
What good are these data? How can they be 
used?" 
"With caution," Zenger answered and then explained. "They can be used the way you just did--to question any number that looks out of line. An inventory build-up may explain this number this month, but somebody needs to notice and check the explanation. Furthermore, the pharmacist can't go on adding to inventories every month-or go on drawing them down every month for that matter. We may not be able to rely on the cost/output relationship for any particular month, but over a longer period that sort of thing has to even out." 
"Then I can use the cumulative comparisons to spot a trend." 
"Certainly-but again with caution." 
Turning back to Table 2, Colonel Albert saw that the August numbers had also been "out of line" with costs running higher and service volume below expectations. For the three months already recorded on a cumulative basis, costs had outrun expectations by 29 per cent whereas output (prescriptions filled) had exceeded the planned level by only 5 per cent. Given the limitations of his data, this was not conclusive proof that an adverse trend was developing, but the situation definitely bore watching. 
October data (see Table 3) showed a continuation of this apparent trend with monthly expenses outrunning the budget projection by 22 per cent and with cumulative costs now 27 per cent above planned outlays for the four month period. Since these new cost overruns could not be explained by increased need for service (cumulative costs per prescription had remained at 122 per cent of expectations for a second month), Colonel Albert got in touch with the Surgeon General. 
Use Made of the Information. The Surgeon General was aware of the trend in pharmacy service costs which Mr. Zenger had already .called to his attention. He agreed that a situation similar to that encountered last year seemed to 
be developing again but was reluctant to take 
any action other than an upward revision in the 
budget. 
Colonel Albert probed further. He found that 
the existing estimates had incorporated what 
appeared to be an adequate allowance for in
creased supply prices. The number of prescrip
tions filled had outrun expectations somewhat
but not significantly, as they knew from the 
cost/output report. Nor did general health re
quirements on the base appear to have changed 
much since the estimates were made because 
other hospital-related expenditures were running 
close to their projected levels. 
To Colonel Albert, all this suggested that specific problems existed in pharmacy services which might still be identified and corrected so as to keep annual outlays within or close to the 
budget. While the Surgeon General was pointing out that necessary services, after all, had to be paid for regardless of cost, Colonel Albert was remembering how a new training project had recently been turned down for lack of funds. "Every time we let necessary services cost more than necessary," he snapped, "some worthwhile project gets nickeled and dimed to death." 
The two men eventually agreed that cost rec ductions might be possible in this instance and that the possibility should be explored. They decided that upward budget revisions would be considered only if this effort fell short-or if the total number of prescriptions required rose sharply. 
In order to continue monitoring cost/output trends for pharmacy services without being distracted by dubious numbers, Colonel Albert arranged for Mr. Zenger to furnish him a sum
mary table showing only cumulative data by quarters. (Table 4.) Throughout the remainder of the fiscal year, this quarterly summary provided increasingly favorable reading. 
Despite flu epidemics in December and March which raised the total number of prescriptions for both the second and the third quarters sharply above the level anticipated earlier, the percentage by which cumulative costs exceeded the planned level steadily declined. By the end of the fiscal year, total expenses for filling 64,000 prescriptions· were only 3 per cent above the outlays which had been anticipated for filling less than 58,000. As a result, unit costs for the full year averaged $1.23-7 per cent below the 
74 

Table 3 
Prescriptions
PHARMACY SERVICE: BASE W 
Filled 
%OF PLAN (02 + 01)  03 04  100  -148 97  822 120  81 102  
05  4866  9386  13437  18217  23137  27452  
VARIANCE (06-05)  06 07  4866  9238 -148  14111 674  18972 755  
08  100  98  105  104  
%OF PLAN (10 + 09)  11 12  -0.3 95  1.3 122  4.0 168  1.4 122  
13  5.8  11.6  17.5  23.9  30.3  36.7  
VARIANCE (14-13) %OF PLAN (14+ 13)  14 15 16  5.5 -.3 95  12.6 1.0 109  22.5 5.0 129  30.3 6.4 127  
17  119  128  146  134  130  148  
VARIANCE (18-17) %OF PLAN (18 + 17)  18 19 20  113 -6 95  162 34 127  203 57 139  160 26 119  
21  119  124  130  131  131  134  
VARIANCE (22-21) %OF PLAN (22 + 21)  22 23 24  113 -6 95  136 12 110  159 29 122  160 29 122  

75 

Table 4 
PHARMACY SERVICE: BASE W 

PLAN 	13437 
ACTUAL 	14111 
%ACTUAL pF PLAN 105 
PLAN 	17.5 
ACTUAL 	22.5 
%ACTUAL OF PLAN 129 
PLAN 	130 
ACTUAL 	159 
% ACTUAL OF PLAN 122 
budgeted target of $1.32. This was in contrast to an end-of-September figure 22 per cent above the estimate. 
The first time he encountered the Surgeon General after receiving this end-of-year report, Colonel Albert warmly congratulated him on these developments and asked what operating problems he had uncovered. 
"It's an odd thing," the Surgeon General responded, "there really were none. The chief pharmacist was able to tighten up on some 
27452 43458 57908 29735 48447 64057 108 111 111 
36.7 58.4 76.5 
40.8 	61.2 78.8 111 105 103 
134 134 132 137 126 123 102 94 93 
management procedures; inventories were higher than they needed be. But most of the changes were made in my shop-like saving on the cost of unused medicine by filling each prescription with smaller quantities of drugs and then allowing refills. And we issued a formulary to help doctors prescribe less expensive medications when these would be just as effective. But there really was nothing we would have spotted as a 
problem if that damned cost trend hadn't been so highly visible in these new reports." 
( 

76 


I ill-2 
I
i I I i'I I i\ ; ! •BUDGETING II .FOR PILOT TRAINING 
I \, \ : 
\I \ iI 
I 
I 
Looking for a better way. 
\ 
My job is to train 
better pi lots; not 
to count money 
c-
Miracles don 1t 
happen in this 
business 	They want better pi lots 
and smaller budgets 

CASE HISTORY 2: BUDGETING FOR PILOT TRAINING 

T 
he Situation. Admiral Baker is the Operations Officer for a group of nine separate flight training bases. Recently he was informed that the number of student pilots to be trained throughout his command during the next fiscal year would be reduced by 10 percent from the present level and that he should expect a comparable 10 percent cut in his operating budget. He was also informed that the proposed budget reduction was intended to reflect reduced costs associated with the smaller number of trainees rather than any change in the quality of training offered. 
Admiral Baker's initial reaction was that a cut of the proposed magnitude would greatly impair the quality of a training program which, in his opinion, was already barely adequate. In fact, he was in the process of preparing a recommendation that the training period be lengthened somewhat to improve pilot familiarity with the increasingly complex equipment they would be operating. Consequently he had requested an interview with the commanding officer and, as a result, found himself preparing for a meeting less than a week away. 
He ·knew he could not make a case for 
retaining more than 90 percent of his current 
budget unless he was able to show-convincingly 
and quantitatively-that costs would not decline 
as much as the student load. He strongly 
believed they would not do so, but he also 
realized that neither he nor any of his nine base 
commanders really knew how costs of flight 
training throughout the command were related 
to the number of pilots trained. 
The Numbers. Ideally, Admiral Baker would 
have liked detailed cost records for each of the 
nine bases which related costs to output over a 
range of outputs and over a considerable period 
of time. But the only numbers he was able to 
obtain immediately from his Financial Records 
Section were those summarized in Table 1. 
These were annual figures for the preceding 
fiscal year and showed the number of student 
weeks of training provided at each of the nine 
bases along with a dollar figure for operating 
costs at each base. 
The number of student weeks of training 
provided at the nine bases ranged from slightly 
more than 8000 at Base A to nearly 13,000 at 
Table 1 
A  8,306  $1.,199,500  
B  10,185  1,387,400  
c  10,191  1,377,000  
D  10,540  1,362,200  
E  10,828  1,246,600  
F  11,094  1,392,500  
G  11,716  1,383,400  
H  12,782  1,534,400  
I  12,918  1,646,900  

Base I, with total training carried out at the nine base command averaging out at 10,953 student weeks per base. From the variations in costs reported by these bases, Admiral Baker hoped to identify a general relationship between workload and operating costs-at least over the range of operating levels relevant to the proposed changes in trainee enrollment. 
The Analysis. His first step was to construct a chart with dollar costs on the vertical axis and number of student weeks on the horizontal axis and to plot his cost and output numbers for each base on this grid to form a "scatter diagram" like that described in Part II, Section 6, Page 60. He could see from the diagram that bases with larger training loads had generally (though not always) reported higher aggregate operating costs than smaller ones, but whether the differences in costs were more or less than proportional to those in student load was not apparent. (See Figure 1.) 
If Admiral Baker had been sure that the cost/output data for each of the bases were complete, accurate and comparable, his next step might have been to fit a "regression line" to these nine points as was explained in Section 6. But Admiral Baker decided he was not ready for this because when he looked carefully at the points he had plotted, he saw that some large cost variations clearly could not be explained by differences in student load. Base E, for instance, had reported operating costs which were much lower than those at three bases providing about the same number of weeks of training; Base I had reported costs much higher than those at 
Base H where the training load was substantially 

79 


Figure k 
Costs vs. Stud.ent Weeks 

1700 
I• 
1600 
.!! Ill H•
... 
~ 1500 
0 
-
"a c Ill 1400 
a 
Ill 
:;) 
0 
.c 
.... 
1300 
Ill 
-
0 
u 
1200 
0 \ 
I 
0 9 13 14 
I 
~-.___ j 
the same. Admiral Baker was not personally familiar with the way records were compiled at each base, and some of the numbers on his desk 
struck him as odd in view of his intimate knowledge of operations at all bases. 
It occurred to him that some bases might be including (or excluding) different cost items; there might be reporting errors; one or more of the bases might be reporting abnormally high costs because its physical plant was notably under-or over-utilized, or bases might be improperly staffed for their workload. Until such possibilities had been "checked out" and any necessary adjustments made, he would not be ready to compute an equation from which costs could be estimated for varying training loads. 
80 

But such a complete reexamination of the underlying numbers would take more time than was available before his crucial budget interview. Moreover, a rough approximation of the trend line relating cost differences to size differences would help identify which base statistics were suspect and needed to be reexamined. Accordingly, Admiral Baker used the numbers in 
Table 1 to make some additional calculations which are set out in Table 2. 
First he computed the average cost of providing a week of flight training at each of the nine bases as well as the overall average cost per week for the nine base training command as a whole. He noted that the four bases with the lowest training volume all had reported costs per 
c~ 

Table 2 
Number of 	Average Cost Deviation -from Average Student Week Cost of Student/Week
Student Weeks Total Cost 
(4)(1) (2) (3) 
TOTAL 98,580 $12,529,900 $127_20 
AVERAGE 10,953 1,392,211 127.20 
TRAINING BASES WITH COSTS/STUDENT WEEK ABOVE AVERAGE 
A 8,306 1,199,500 144.40 +17.20 
B 10,185 1,387,400 136.20 + 9.00 
c 10,191 1,377,000 135.10 + 7.90 
D 10,540 1,362,200 129.20 + 2.00 
SUBTOTAL 39,222 5,326,100 
AVERAGE 9,805 1,331,525 135.76 + 8.56 
TRAINING BASES WITH COSTS/STUDENT WEEK BELOW AVERAGE 
E 10,828 1,246,600 115.10 -12.10 
F 11,094 1,392,500 125.50 -1.70 
G 11,716 1,383,400 118.00 -9.20 
H 12,782 1,534,400 120.00 -7.20 
I 12,918 1,646,900 127.00 -0.20 
SUBTOTAL 59,338 7,203,800 
II 
AVERAGE 11 868 1,440,760 121.40 -5.80 
student week higher than the nine base average 	him a rough approximation of the dollar costs which might be expected for varying operating
while the remaining five had all reported costs at levels solely on the basis of size (number ofleast somewhat lower than average. This seemed student weeks). ~
to show that the deviations from average (Col
umn 4) bore a significant relationship to the Then, since his immediate purpose in draw
number of weeks of training provided by the ing the trend line was to discover whether 

reporting bases, but no uniform trend was 	operating costs for training student pilots would 

apparent since other variations among individual 	rise or fall more or less than changes in the 

bases obscured the relationship. number of pilots trained, he gave himself a visual To get a "quick and dirty" approximation of reference by also constructing on Figure 2 a a trend line relating cost to output over the dotted "proportional change" line. If changes in operating costs were exactly proportional to
relevant range of student weeks, Admiral Baker changes in student load, a 20 percent increase in
computed separate sub-totals for aggregate costs and weeks of training offered at the four bases training weeks (from 10,953 to 13,140) should which reported above-average costs (A, B, C, and of course be accompanied by a 20 percent D) and at the five bases reporting below-average increase in costs (from $1,392,211 to costs (E, F, G, H and I). He then calculated the $1,670,653). Conversely, a 20 percent decline average number of student weeks and operating (to 8762) should entail costs of $1,113,769. costs for each of the two groups. In Figure 2, he Any observation on the "proportional change plotted these "above-average" and "belowline" passing through these points would repreaverage" cost/output observations and consent the same average cost of $127.20 per nected them with a solid line which also passed student week as that computed for the previous through the grand average cost/output point for year's operating level. the nine-base complex. This straight line gave An actual cost/output trend line steeper than 
81 
c 

1700 
/ 
a.. 1600 
Ill 
Q 1500 
0
-
0 Ill"'0
~ 1400 Average_for
.Ill 
0:::J Bases E,F,G,H&I 
.t::. A,B,C&D
...... 
1300
Ill 
u0 
1200 
0 0 9 10 12 13 14 
Student W~'eks · Thousands 
this "proportional change line" would indicate If, for instance, the proposed 10 percentan activity in which small operating units were reduction in number of student pilots cut themore efficient than large ones. But a flatter nine-base average training load from 10,953trend line-like the solid line in Figure 2
student weeks to 9858, the aggregate costsindicated a cost advantage for larger bases with associated with that level on the solid trend linehigher operating levels-indicated, in short, that 
would decline from the actual nine-base averagepilot training (at least over the relevant operof $1,392,000 to about $1,330,000-an indicaating range) was an activity in which costs ted saving of only 4.5 percent.increased less than proportionally as output Rough as this approximation of cost/outputrose. And conversely, of course, as output (in relationships at the nine-base training complexthis instance, number of student weeks anwas, Admiral Baker felt he could say withnually) declined, costs would decrease, but less confidence that any decline in number ofthan proportionally. Unit costs (costs per stutraiQ.ees which significantly lowered operatingdent week) would rise because at the lower levels at each of the nine bases would result inoperating level, resources would be used less higher training costs per student week becauseefficiently. bases with smaller numbers of students would be 
82 ( 
operating less efficiently. It seemed probable a base's training load expanded, or could he that a 10 percent cutback, absorbed proporidentify a "best size" of flight training facility within the range covered by the data in Table
tionally among the nine bases, would reduce 
2? Might some bases already be beyond that
operating costs less than 5 percent. On the other hand, if operating levels at point, and could savings be effected by reassignindividual bases could be maintained, there need ing some students to those with under-utilized 
be no decline in efficiency. (This assumes no capacity? In short, could the cost/output inforchange in costs due to price and wage inflation.) mation now on Admiral Baker's desk show him If one base were to be closed entirely, it would how to cut the cost of providing a week's seem that the remaining eight should be able to training by reallocating the workload within his handle the reduced total number of students at command?Figure 3 suggested some interesting pos
no increase in cost per student week because each would continue to operate at its current sibilities in answer to these questions. On this level. This was a highly significant finding, but chart, Admiral Baker plotted cost/output obserAdmiral Baker realized that any decision to vations to show-not aggregate operating costs as close one of the nine bases would have to be in Figures 1 and 2-but costs per student week taken at a higher level and he could not propose at bases with differing annual training loads. While the larger bases in the command were, in
this solution without demonstrating clearly the cost advantage of such a course. The relationgeneral, less costly to operate on this basis than 
the small ones, it was reasonably clear to
ships presented in Figure 2 would supply only 
Admiral Baker that if cost data were accurate as
part of this documentation. 
reported for all the bases in his command,
Turning again to Table 2, he noted that the increasing the number of student weeks at an
smallest base (Base A) had-as might be 
individual base would not continue indefinitely
expected-provided the most costly training: 
to reduce cost per student week. Indeed, these
$144.40 per student week, $17.20 more than average. This was not a reason for criticizing the data, as plotted in a scatter diagram on Figure 3, base commander since total costs for Base A-as suggested that the two bases with training loads 
plotted on Figure 2-were actually somewhat in excess of 12,500 weeks annually might below those which the solid trend line might already be at least slightly beyond the most 
have predicted solely on the basis of the low efficient operating level. Using observations for the eight bases at
student load.
On the basis of last year's cost figures, a 	which he proposed to concentrate next year's reduced student load, Admiral Baker visually
quick calculation showed Admiral Baker that closing Base A would eliminate 9.6 percent of fitted an average cost curve showing a low-cost total operating costs--substantially the amount operating level in the range of 12,000 student of the proposed budget cut-while reducing the weeks per year. As in Figure 2, costs reported at number of training weeks available by only 8.4 Bases E 'and I appeared to be notably "out of line" with those at the other bases: the cost
percent.This calculation was especially interesting to differentials could not be accounted for primarAdmiral Baker since it suggested that he might, ily in terms of size variations. Costs reported for 
by concentrating his reduced enrollment at the Base E were exceptionally low while those at bases which were able to provide training most Base I were far higher than at Base H which efficiently, be able not only to absorb a 10 operated at almost the same level. 
percent budget cut but also to give the smaller Before making dollar and cent estimates for number of students a slightly longer training next year's budget, Admiral Baker would need program. to find out what accounted for these differHe began to ask himself other questions. ences. If they were simply reporting errors, the Could average costs per week be reduced further cost figures themselves would need to be revised. special cost advantages
by distributing the entire workload among only If Base E enjoyed seven bases rather than eight? (This would mean (climate? local labor costs? or whatever) it might annual training lpads in excess of 12,500 student be desirable to concentrate a larger share of the weeks per base.) Would operat!Jlg costs per training program there. Individual instances of student week continue to decline indefinitely as management problems or superior ma~agement 
83 
figure 3 
Average Costper Student Week 
.A. 
Y'
160 
Ill
... 
a 150 
c 0 A• ~ 
~ 
Gl .AIL \ 
Gl y
140 Bl\
3:
.. 
c 
Gl 
-a _AIL 
:::) V'
130
.. 
Cl) •
F 
... 0\ ··; 
~
.. Gl '-...
120
Ill .... ____ 
Gl • G·---4t
0 
u 
g) 
a E 
... 110
Gl 
>
c( ( 
0 ~ ~ ~ ~ 
V' 
0 9 10 11 12 13 14 
Student Weeks ·Thousands 
might also appear in checking "out of line" ted by the solid line) might instead flatten out observations. or even continue downward. (He added a broken The figure for Base I particularly surprised line to indicate this possibility.) 
Admiral Baker since he was familiar with its This was a question of fact to be investioperation which seemed highly efficient. It gated, but for his present calculation, Admiral occurred to him that the numbers for this base Baker accepted the data before him which might not really be comparable with the others, suggested that the most efficient operating level 
that costs assigned to pilot training at Base I for these bases with their existing facilities was might actually include as well outlays for in the range of 12,000 student weeks per year.another function also carried out there. If this When any necessary adjustments for Bases E, I,
had, in fact, occurred, average weekly costs and possibly F had been made, Admiral Baker attributable solely to pilot training at Base I might 
could have a precise curve fitted mathematicallybe considerable lower-perhaps even lower than to the eight observations, but if revisions simplythose at Base G_In that event, the average cost tended to bring data for these bases "into line" 
curve he had drawn, instead of turning up with the pattern already established by the other around the 12,000 student week level (as indica-observations, his visually fitted curve might be 
84 

quite adequate for allocating students throughout the training complex. 
According to the solid line in Figure 3, there would be an advantage in concentrating training at bases in the 12,000 student week size range, but how significant, he wondered, would the cost differentials be? Some very simple marginal analysis quickly demonstrated the value of making all feasible shifts. In the previous year, for instance, BaseD had provided 10,540 student weeks of training for $1,362,200. Base F had handled 11,094 weeks for $1,392,500. The average cost of $129.20 at Base D seemed only moderately higher than the $125.50 outlay at Base F for a similar accomplishment. But focussing attention on "marginal" rather than "average" costs showed 
that Base F was able to provide the additional 554 weeks associated with its heavier teaching load for only $30,300 additional outlay; the marginal cost of those additional student weeks was only $55 per week. 
Conversely, the apparent "penalty" for providing 12,782 student weeks of training at Base Has compared with 11,716 weeks at Base G was a mere $2.00 differential in average costs-$120 per student week versus $118. But the added cost of providing the 1066 additional student weeks at Base H was $151,000 ($1,534,400 versus $1,383,400) or $141.00 for each of the added student weeks. If, after reexamining data for Base I, it still appeared that the average cost curve did in fact tum up around the 12,000 student week level, this marginal comparison indicated there might be significant diseconomies from assigning individual bases training loads beyond their most efficient operating 
levels. 
His limited data suggested to Admiral Baker 
that bases operating at about the 12,000 student 
week level, should be able to conduct pilot 
training for an average operating cost of $118 
per student week. Admiral Baker did a quick 
calculation: at that rate, even the reduced 
budget would let him provide 95,567 student 
weeks of training as compared with 98,580 last 
year-a reduction in student weeks of only 3.1 
percent. Distributed among only eight bases, 
95,567 student weeks would give each base a 
training load at or near the apparent low-cost 
point as suggested by Figure 3, and nex't year's 
smaller number of student pilots would each be 
receiving nearly 8 percent more training time. 
All this might be permitted by the "savings" generated through a more efficient allocation of training loads. 
Admiral Baker had no illusions that the favorable result promised by his "quick and dirty" computation could be fully realized in practice, but the analysis did convince him of two things. First, to operate the nine existing training bases with a smaller number of students assigned to each meant less efficient operations at most of these bases and would significantly increase the average cost per student week for the command as a whole. Second, if he were authorized to close the least efficient of the nine bases and given a free hand to achieve the most efficient operating levels at the remaining eight through student assignment, he might be able not only to live with a 10 percent budget cut but also to lengthen the training period for the reduced number of student pilots. Neither of these possibilities had been apparent from his 
initial inspection of the cost/output data assembled in Table 1. 
Use Made of the Analysis. Admiral Baker's 
initial budget interview did not result in an 
immediate decision for the coming year. On the 
basis of the evidence he presented, the Budget 
Officer accepted both of Admiral Baker's con
clusions and agreed that the least costly 
solution-at least in terms of operating costs
would be to close Base A and reassign students 
as Admiral Baker proposed among the remaining 
eight. He agreed to recommend this proposal, 
with the additional understanding that any 
savings Admiral Baker might effect over and 
beyond the 10 percent budget cut could be 
applied toward some lengthening in the training 
program as Admiral Baker sought. 
At the same time, he cautioned Admiral 
Baker that closure of Base A might not be 
practical. The closure itself would entail costs 
which, though they would not figure in Admiral 
Baker's operating budget, must be taken into 
account at a higher level-particularly if it 
appeared that the reduction in number of 
student pilots might be temporary. Moreover, 
impact of the closing on the local community 
and other factors would have to be considered. 
Consequently, Admiral Baker should be pre
pared to furnish a detailed estimate of the costs 
which would be incurred for training next year's 
85 

reduced number of student pilots at all nine that the precise estimating equation he and the
bases. 
Budget Officer had discussed would not beAdmiral Baker agreed to prepare this estineeded. Rather he was eager to learn why costsmate as soon as he had "clean data"-i.e. had at some bases appeared to be so greatly "out ofreceived adequate answers to his questions conline" with the performance his preliminarycerning records and operating costs at the bases analysis had indicated on the basis of size.where costs were conspicuously "out of line" Was Base E operated more efficiently than theaccording to his preliminary analysis. He reother bases, and if so, could operations officersemphasized that he expected the final estimates 
at other bases adopt the same procedures? Werefor a training program cut by 10 percent to facilities at Base I being over-utilized, or wereshow costs down by 5 percent or less. If final 
cost data, as recorded, simply overstating costsestimates did confirm this expectation, the attributable to pilot training? Might revised databudget officer agreed to recommend approval of show that some further increase in the numberthe minimum needed to maintain present proof training weeks provided at the larger basesgram quality. 
would in fact lower rather than raise their averagecosts? If so, might he find ways to increase
More Question~More Analysis. Admiral further the length of training given his studentBaker returned to his own desk eager to "get on pilots? 
Admiral Baker had already identified awith his homework." His interest was not so number of useful relationships from the cost/much in establishing a more precise relationship output numbers presented in Table 1, but hebetween costs and operating levels. He was realized what he had been able to do with those
hopeful that top level decision makers would numbers so far was only the beginning of "anal
favor concentrating training at eight bases, so ysis." Much more needed to be done. 
c 

86 

ill-3 
. ! -;==~-;;;;;;;;;-;;;::;;---~:.::;::--.::.._---------tI! 
I 
MEASURING PRODUCTIVITY* !! 
rl, I 
!I I i .
AT ,, I 
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I, I 
I \ ! :
PERSONNEL OFFICES 
1 I
'! 
'I I ;
I i 
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*labor productivity, in this instance 
j 
Remember, I have to think about people and things c-I know how many people we have 
This is a question of how many we need 
~ TEcHNICIAN : 

CASE HISTORY ·3: MEASURING PRODUCTIVITY AT PERSONNEL OFFICES 

T
he Situation. Mr. Dodd was working in the Management Analysis Section of the Comptrollers Office when a problem arose concerning the staffing of civilian personnel offices. The Department of the Army had established an explicit standard for staffing such offices. This standard called for an over-all ratio of one personnel office employee for every 88 civilians employed at the establishment which the office served. A recent survey had shown that personnel offices at manufacturing arsenals, as a group, were "over staffed" according to this stand'ard. 
Fifteen such arsenals had a total civilian payroll of 52,800, while the associated personnel offices reported 622 employees-a ratio of one personnel office employee for only 84.9 civilian employees at the fifteen arsenals. Reaching the established ratio would require a reduction of 22 in the total number of personnel 
office positions authorized. Since Mr. Dodd had had considerable experience with the work done in civilian personnel offices, he was given the assignment of recommending how this reduction should be spread among the 15 offices involved. 
The Numbers. On receiving this assignment, 
Dodd immediately asked what information was 
available for his analysis and was told, "You're 
looking at it." His superior handed him a paper 
listing the number of employees in the personnel 
office at each armory and the total number of 
civilian employees at the same installation. "At 
least you'll be able to find the employee ratio at 
each office and then cut back on the ones that 
are out of line," his boss told him. 
"I hope that's a joke," Dodd protested. 
"Knowing how many employees an arsenal has 
doesn't tell us how much work its personnel 
office is doing." 
"It won't be a joke," answered his superior, 
"unless you find a better way of comparing the 
workloads those fifteen offices handle." 
Dodd's first step in carrying out this assign
ment was to visit the personnel office at Arsenal 
Number 8, the nearest of the fifteen. After 
talking to staff members and examining the way 
the files and other records were kept, he 
prepared a short questionnaire. It covered three 
separate types of personnel department activity 
over the preceding year: the number of personnel actions taken (accessions, changes and 
separations); the number of positions analyzed and evaluated by the department; and the number of hours of off-the-job training sessions conducted. He then gave this data format, together with written instructions for its completion, to a staff member at Arsenal Number 8 who was able to fill out the form for his department in one day. 
Since Dodd was now in a position to show that the numbers he sought from each personnel office could be assembled with only about eight man-hours labor, he was able to secure the Comptroller's authorization for extending the survey to the other arsenals. This he did and soon was in possession of the output data he had requested from each of the fifteen arsenals. 
The 15 questionnaires enabled him to compare directly the number of personnel actions processed in each office during the preceding year; likewise, he could compare all personnel offices in regard to the number of job classifications and evaluations made and in regard to the amount of off-the-job training offered. But these three separate comparisons each represented only part of the personnel activities carried out at all the offices. Moreover, on inspecting the reports, he saw that the relative importance of the three activities clearly differed from office to office as a share of total "output." 
In order to compare the workloads handled at 
various arsenals, he needed a common denomi
nator for the three measures of differing kinds 
of output. A composite measure of "work 
units" which combine dissimilar activities is, by 
definition, abstract. Also by definition, its 
accuracy depends on the judgment of the person 
who decides how to "weight" the diverse units 
of physical measurement: one job classification 
analysis represents more work than processing a 
routine personnel action, but how much more 
work? 
On the basis of his own familiarity with 
civilian personnel work, Dodd established a 
tentative scale for converting his three dissimilar 
sets of output numbers into a common measure 
of "work units." Then he checked his proposed 
scale with several experts in the field and made 
modifications in accordance with their sug
gestions. Finally, he converted the three "out
89 

Table 1 
for the fifteen arsenals on a scatter diagram
I 
Arsenal .... Work Done Number of Employees ; showing the units of work handled at each(Units) (Personnel Department) i personnel office on the horizontal axis and the 
1 35 22 number of employees performing it on the 2 46 21 vertical axis. (See Figure 1.) Higher workloads3 53 21 were clearly associated with larger work forces
4 68 39 
5 84 29 and the relationship appeared, by inspection, to 6 104 44 be linear. Accordingly, Dodd had a straight-line
7 105 36 
regression equation calculated for the fifteen
8 127 39 
9 139 42 manpower/output observations and added the
10 149 47 
regression line shown in Figure 1. (If statistical
11 171 53 
12 181 51 facilities had not been available, Dodd might13 187 58 have based his analysis on an approximation of
14 207 62 
15 this regression line. One way to make such an
210 58 
approximation would have been to calculate the Total 1866 622 average workload (124 work units) and theaverage staff (41 employees) for the 15 offices
Average 124 41 
and plot this average observation on the scatterdiagram (Point X on Figure 1.) He could thenhave selected visually the line passing throughputs" reported for each office into uniformly this point which seemed to give the best fit fordefined "work units" which could be matched the 15 manpower/output observations by rowith the labor force at each arsenal as shown in tating a ruler through Point X. The slopeTable 1. At this point, he was in a position to decided on in this fashion would not have been
compare manpower utilization at the fifteen as precise as the line fitted statistically by thepersonnel offices. regression equation, but it would have permittedmuch the same analysis.)The Analysis. The first step in Dodd's analysis 
For most of the observations, this line pro
c

was to plot his manpower/output observations 
vided a good fit; that is, the actual staffing of 
Figure 1 
80 
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..2a. 60 
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w...

Gl·
a. 40 
Ill
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~ 20
·0
3:. ; 
90 
most personnel offices was rather close to the number of employees which might have been predicted on the basis of workload as reported 
at those offices. But two notable exceptions immediately attracted Dodd's attention. Arsenals #4 and #6 both appeared to need-or at least to employ-significantly more people in their personnel offices than their workloads 
seemed to warrant. This did not, in itself, indicate that these offices were overstaffed since either or both might confront special circumstances requiring more employees. But the differences between actual staff and the number predicted for these output levels by the regression equation warranted investigation. The equation provided a standard for manpower utilization based on experience at all fifteen personnel offices. If these two "out-of-line" offices could improve operating procedures enough to achieve that standard, they could absorb substantially the entire proposed cutback in authorized positions without impairing performance. 
Dodd was greatly encouraged in this regard by his investigation of circumstances at Arsenal #4 where the actual number of employees was 39 compared with an "expected" staff of 29. It developed that the workload at this personnel office had been declining, partly due to a cutback in civilian jobs at the arsenal but more importantly to reduced turnover among the 
remammg work force which consisted predominantly of long-term employees. The personnel director, confronted with his office's relatively unfavorable performance, reviewed procedures and concluded that his current workload probably could be carried out with "average" staffing. If so, about half of the required reduction in total force could be absorbed at this one office without loss of output. 
A visit to Arsenal #6, however, was less encouraging. Arsenal #6 suffered by reason of being at an isolated location, high turnover of civilian employees and a continuing need for active labor recruitment outside the local area. This was a major and time consuming function of the personnel office-and one which had not been included in the composite work units measured by the survey. Dodd concluded that the local personnel director would be confronted with serious problems in doing his work 
if even one position were abolished in this office. 
Since the regression analysis had not suggested serious overstaffing at any other office, Dodd recognized that the further cuts still 
needed to achieve an 88 to 1 employee ratio might well reduce-at least somewhat--the ability of personnel offices to handle their current workload. His problem now was to identify specific offices at which such an outcome might be avoided. With this objective, he turned back to the data in Table 1 and added a column showing work units per employee at each personnel office. (See Table 2.) 
Table 2 
" 
Work Done Number ofo>E~plo~~es-~. Work Units Per 
I 
Arsenal 
(Units) (PersCin~~i·,o,~:~~rtmeiit)' Employee 
1 35 22 1.6 2 46 21 2.2 3 53 21 2.5 4 68 39 1.7 5 84 29 2.9 6 104 44 2.4 7 105 36 2.9 8 127 39 3.2 9 139 42 3.3 10 149 47 3.1 11 171 53 3.2 12 181 51 3.6 13 187 58 3.2 14 207 62 3.3 15 210 58 3.6 
...
622
Total 1866 
Average 124 41 3.0 
This new column showed that large offices 
were, in general, more efficient than smaller 
offices, that is, more work was accomplished per 
employee. This information, in itself, was not 
directly relevant to Dodd's recommendation 
since there was no prospect for consolidating or 
redistributing workload among fifteen personnel 
offices serving different arsenals. Nevertheless, 
he hoped that these figures on average output 
per employee might help him identify some 
offices which should be able to increase worker 
productivity. So he drew another chart plotting 
these numbers for each office against the office's 
total workload (See Figure 2.) And then he drew 
in, by hand, a rough curve to fit the scattered 
points. This visual curve suggested that output 
per employee increased very rapidly with ex
panding office size up to a work load of about 
91 

( 

3.5 
1.5 
0 0 50 
100 composite work units but much more gradually for larger scale operations. 
As in Figure 1, the relatively poor performance of offices #4 and #6 was highlighted. But what struck Dodd particularly about this 
( 
150 200 250 
diagram was the notable differences it revealed among the largest offices. Personnel offices at arsenals #12 and #15 showed strikingly higher 
productivity (3.6 work-units per employee) than those at #'s 11, .13, and 14 with roughly 
92 

comparable work loads. He checked out the possibility that the latter offices faced special problems-such as the ones affecting staff needs at arsenal #6-and found no evidence that work requirements were in any way unusual. 
A brief calculation using the data in Table 2 indicated that an increase in productivity from 
3.2 to 3.5 units per worker at arsenal #11 would enable that office to dispense with four employees without sacrificing output. Similarly, if offices #13 and #14 could raise their productivity to 3.6 units per worker (matching the performance at offices #12 and #15) staff needed to handle the current workload could be reduced by 6 and 4 positions respectively. These cutbacks would be more than enough to achieve the required 88 to 1 overall ratio among personnel office and other civilian employees for the 15 arsenals. 
Use Made of the Analysis. The following week, a meeting was held in the Comptroller's office to formulate a proposal for the Director of Civilian Personnel recommending which personnel offices should be asked to absorb a reduction in staff totalling twenty-two positions. 
It was quickly agreed that only one officethat at arsenal #4-appeared significantly overstaffed on the basis of Mr. Dodd's analysis. The 
recommendation that employment at this office 
be brought "into line" with its current work 
load-a step already anticipated by the office 
director-would provide about half of the re
quired reduction. 
Beyond this, it was not clear from the 
information at hand whether or not the ad
ditional positions could be eliminated without at 
least some adverse impact on the amount or 
quality of work done at the offices affected by 
the cuts. There were wide variations among 
offices in productivity (work units per 
employee), but these appeared to be related 
largely to size differentials rather than in
efficient utilization of manpower at particular 
offices. In fact, the evidence suggested that small 
offices, which generally reported the lowest 
output per employee, would have very limited 
ability to compensate for staff reductions by 
increases in productivity. 
If, on the other hand, the cutbacks Dodd 
suggested were ordered at arsenals # 1 L, # 13 and 
#14, and they protested, it could be pointed out 
to them that the personnel offices at arsenals #12 and #15 were already handling comparable workloads with the level of staffing now being proposed. If arsenals #11, #13 and #14 matched 
that performance standard, the desired employee ratio could be reached without any reduction in activities carried out by the entire group of personnel offices. 
Accordingly, the response forwarded to the 
Director of Civilian Personnel recommended reducing authorized positions at the following offices: 
"I
,.
' :·~J,.};J u: ;~' . I 
·: . <i" 'li·kj !i''l i
Arsenal R-~~·r·<'. > uthonzat•on 
-~~: ~c~t~r .· ~~·.· ·~ :~r> . I
r 
4 -10 29 11 -3 50 13 -5 53 14 -4 58 
More Questions, More Analysis. As the meet
ing concluded, the Comptroller expressed satis
faction that Mr. Dodd's study had produced 
such a direct and workable answer to the 
question raised by the personnel director. 
"This answers the question we were asked," 
Dodd commented, "but I wonder whether we 
were asked the right question." 
"You identified a way of getting the same 
work done with fewer people, didn't you?" was 
the response. 
Dodd shook his head. "We ought to be 
looking for ways to do the work at the lowest 
cost-not just with the fewest bodies. This 
analysis didn't go into salary ranges, and it 
didn't even consider equipment or other costs. 
We don't know whether reducing the number of 
positions at these offices will reduce their total 
costs." The meeting broke up without any 
further discussion. 
Several months later when budget estimates 
were being reviewed, Dodd was called to the 
Comptroller's office and reminded of that con
versation. The Comptroller had in hand budget 
requests for data processing equipment to be 
installed at several civilian personnel offices. 
Dodd recognized the group as including those at 
manufacturing arsenals #11, #13 and #14. 
"The justification statement reads, 'Required 
in order to handle the workload with limited 
staff,' the Comptroller remarked and then 
93 

added, "it is also noted here that data processing "Where?" Dodd asked. Isystems of the type being requested had been The Comptroller paused and smiled. "Thoseinstalled earlier in two personnel offices where offices," he said, "are located at arsenals #12they are functioning very successfully." and #15." 
94 
"(r U.S. GOVERNMENT PRINTING OFFICE: 1973-729·489/6