College and Research Libraries J. V. BAUMLER and J. L. BAUMLER A Si~nulation of Reserve Book Activities in a College Library Using GPSSJ360 The reserve book activities of a typical college library were analyzed by means of a computer simulation. Service levels were determined for various combinations of reserve book stocks and class sizes. Of particular importance was the relationship between reserve book utilization and service levels provided. The computer model contained behavioral assumptions as to the student population served. The model also allowed library policy decisions to be examined. MODERN MANAGEMENT TECHNIQUES are being applied in almost every .adminis- trative setting. Libraries are no excep- tion, and the results of research in the areas of mathematical model building, operations analysis, and computer appli- cations are increasingly being applied to library activities. This paper describes the use of such techniques to analyze reserve book activity in a simulated col- lege library. Through the use of GPSS I 360 (an advanced simulation language), a computer model of reserve book op- erations in .a college library was devel- oped. This appears to be a worthwhile area to investigate by means of com- puter simulation, because library admin- istrators obviously wish to limit their in- ]. V. Baumler is associate professor, Col- lege of Administrative Science, The Ohio State University, Columbus. ]. L. Baumler is former staff librarian, Belmont Memorial Library, Belmont, Massachusetts. The au- thors acknowledge their thanks to the In- structional and Research Computer Center at the Ohio State University for providing computer time in support of the research reported here. 2221 vestment in multiple copies of reserve books while at the same time providing adequate service to their patrons. Re- sults of the simulation provide .an un- derstanding of the factors affecting ser- vice levels in reserve book operations. THE MODEL The computer model represented a portion of a college library. This li- brary was open from 8:00 a.m. until midnight, a total of sixteen hours daily. The policy of the reserve desk activities simulated was that books were provided to students on a first-come, first-served basis. If the book was not available, the student could have his or her name put on a waiting list. Further, no reserve books were checked out within thirty minutes of closing time. There were three key features of the computer simulation model. First, it al- lowed a wide range of parameter values to be used. For instance, the number of students expected per day was set at 30, then 75, and finally 300 to represent three different patron groups. For each of these three patron groups, three dif- ferent reading assignments were simu- lated, one at a time. A very short assign- ment required only ten minutes for the average student; a longer assignment averaged thirty minutes; and a third as- signment averaged one hour. Finally, for each of these nine combinations of patron group size and length of reading assignment, six different quantities of books on reserve were represented. Thus a total of fifty-four different combina- tions of parameter values allowed the representation of wide variations in group sizes, reading assignment lengths, and the number of books on reserve. The second basic feature relates to the behavioral assumptions about stu- dents embodied in the model. The model represents students as ( 1) having different reading speeds, ( 2) being heavier users of the library at certain · times of the day (afternoon arid eve- ning) than .at others (morning); and ( 3) having personal time constraints, hence being reluctant to join long queues to obtain a book and growing in- creasingly impatient while waiting for a book. The third key feature of the model is that it incorporates library policies. The major policy tested was the impact of .a one-hour limit on reserve books. The longest reading assignment, which required more than one hour for many of the students, was simulated two ways, with and without a one-hour policy lim- it. RESULTS Two measures of service were used. The most obvious such measure is the portion of the patron group which was able to obtain the reserve book sought. To illustrate: with a daily demand of seventy-five students, a reading assign- ment requiring thirty minutes for the average student (some taking more time, some less), and five copi~s of the book on reserve, a service level of 98.2 Reserve Book Activities/ 223 TABLE 1 RESULTS OF SIMULATION: READING AssiGNMENT OF TEN MINUTES Number of Size of Reserve Percent Percent Served Patron Group Books Served without Delay 30 1 99.2 70.6 30 2 100.0 94.4 30 3 100.0 98.4 30 4 100.0 100.0 75 1 85.1 20.3 75 3 100.0 92.6 75 5 100.0 100.0 75 8 100.0 100.0 300 1 33.3 .4 300 5 95.8 68.1 300 10 100.0 99.0 300 20 100.0 100.0 percent was obtained. That is, almost all of the seventy-five students would be able to obtain the book, and the library could be reasonably satisfied with the level of service provided. However, a second measure of the level of service was .also used. That was the percent of each patron group who obtained the reserve book without delay. The model contained a queue for stu- dents to join if the supply of reserve books was exhausted. It should be re- called that student behavior in the mod- el depicted impatient students, reluctant to join long queues. For example, no student would wait for a book if he or she would be more than tenth in line, and there was only a fifty-fifty chance that the student would wait if he or she were to be fifth in line. As midnight approached, the closing time of the library, he or she was even less likely to join a long queue. The model represented a reserve desl operation which strictly maintained a first-come, first-served policy. In the il- lustration above, five books were almost sufficient to serve the patron group fully. But in terms of service without delay, only 76.4 percent of the patron group was so fortunate. It would require eight books to provide virtually complete ser- vice without delay for seventy-five stu- 224/ College & Research Libraries • May 1975 TABLE 2 RESULTS OF SIMULATION: READING ASSIGNMENT OF THIRTY MINUTES Number of Size of Reserve Percent Percent Served Patron Group Books Served without Delay 30 1 77.7 29.3 30 2 99.2 69.8 30 3 100.0 89.7 30 4 100.0 96.2 75 1 39.0 3.2 75 3 86.2 35.0 75 5 98.2 76.4 75 8 100.0 99.3 300 1 11.0 0.3 300 5 52.7 5.6 300 10 85.5 41.7 300 20 99.7 97.8 dents a day if the reading assignment averaged thirty minutes. Tables 1 through 3 present the two performance measures-percent served and percent served without delay-for the various combinations of parameters simulated (patron group size, length of reading as- signment, and number of books on re- serve). One of the striking results evident in these tables is the added expense in- volved in providing a high level of service in terms of service without delay rather than just in terms of complete service with delay for some students. In the il- lustration discussed above, five books were adequate to allow virtually all stu- dents to fulfill their reserve book read- ing assignment, but eight books, or a 60 percent increase, were required to pro- vide virtually total service without de- lay. As a broad generalization, the full data in Tables 1 through 3 also suggest that to move from virtually complete service with some waiting to virtually complete service without delay would, in general, require about a 60 percent increase in reserve books. This repre- sents a rather sizable investment, a fact which administrators setting service lev- el objectives should keep in mind. While the results in Tables 1 through TABLE 3 RESULTS OF SIMULATION: READING AssiGNMENT OF SIXTY MINUTES Number of Size of Reserve Percent Percent Served Patron Group Books Served without Delay 30 1 52.3 19.8 30 2 81.0 39.6 30 3 94.5 63.4 30 4 98.3 85.0 30 5 99.2 96.0 30 6 100.0 95.2 75 1 21.6 2.0 75 3 55.0 14.1 75 5 80.2 32.3 75 8 97.5 69.0 75 10 99.3 90.6 75 15 100.0 100.0 300 1 5.6 .0 300 5 27.7 1.7 300 10 53.5 7.6 300 20 85.7 45.1 300 30 9'8.6 92.5 300 40 100.0 99.7 3 are of some interest in their own right, the primary task of analysis was to derive generalizations from the data which could possibly apply to reserve book activities elsewhere. One such gen- eralization was discussed above-the 60 percent increase in books required to eliminate delays in service. Another area in which generalizations were sought was the relationship between service lev- els and reserve book utilization. For- tunately, a regression equation was found which related utilization with service level. The interesting thing about this equation is that it closely fits the data obtained from all the simu- lations · conducted. Thus, there were no significant economies of scale observed in reserve book activities. The relation- ship between level of service and utili- zation is largely independent of the size of patron groups, the length of reading assignments, and the number of books on reserve. This being the case, a simple graph (Figure 1) can be constructed to relate reserve book utilization with ser- vice level. Since the relationship be- Percent of Day Reserve Books Are Utilized 100 90 80 70 60 50 40 30 20 10 Reserve Book Activities j 225 Percent of Patron Croup Served Fig. 1 Utilization of Reserve Books Versus Service Level 226 / College & Research Libraries • May 1975 Gain in additional patrons Loss in incomplete assignments Top of shaded area is the portion of the patron group obtaining the book with the one-hour limit Bottom of shaded area is results without one-hour limit Bottom line is proportion of patron group completing assignment with one-hour limit Number of Books on Reserve Fig. 2 Effect of One-Hour Limitation on Use of Reserve Books: Patron Group of Seventy-five, Reading Assignment Averaging One Hour tween percent utilization and service level does not depend upon the number of books on reserve, the size of the pa- tron group, or the length of the read- ing assignment, Figure 1 is thought to apply to all reserve book operations, at least approximately. One way in which this chart could be used is to investigate a complaint that for a particular title the reserve book supply is inadequate. The librarian may not know the exact size of the patron group using this book or the amount of time each student re- quires to complete his assigned reading; but the librarian could determine the utilization of this title. If it is found that this book (or set of books) is used 75 percent of the day, use of Figure 1 would indicate that only 87 percent of the patron group is being served. Figure 1 also indicates the large slack required to provide full service. To serve 95 percent of a patron group, enough books must be on hand that they are no more than 57 percent uti- lized. · An important part of the simulation was testing the effect of library policies limiting the time for which a reserve book may be held. Consider the follow- ing illustration from the data in Table 3. A patron group of seventy-five stu- dents will come to the library in a par- ticular day seeking a reserve book of which the library has five copies. The average student will require sixty min- utes to complete his assignment, but it may take up to ninety minutes for some students. The library's stock of this book is somewhat inadequate. If each student fortunate enough to obtain a copy of the reserve book keeps it until Reserve Book Activities / 227 he or she has finished his reading, only 80.2 percent of the patron group will be served. In such a situation the library could limit use of this book to one hour. Such a step would increase the number of students who obtain access to the book but reduce the number of students completing their reading as- signment. In the above illustration, the percent of the patron group obtaining the book increases from 80.2 to 82.9 by imposing the one hour limit, a very modest increase. But such a limit reduces from 80.2 percent to 55.8 percent the portion of the patron group that com- pletes the reading assignment. Figure 2 depicts the gain in those obtaining the book and the loss in fulfillment of reading assignments for a patron group of seventy-five with a reading assign- ment averaging one hour when a one hour policy limit is imposed. Figure 2 indicates the high price, in terms of in- complete reading, that is paid for the slight increase in exposure to the book. As a broad generalization, data from all three patron groups suggest that a time limit on reserve books results in approx- imately four students having to turn in the book before completion of their as- signment for every additional student this policy allows to obtain access to the book. Hence such policy time limits could be counterproductive. CoNCLUSION Modern management techniques are finding ever-increasing applications in today's library. 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