LIBRARY OF THE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAICN 510.84 1463 c *o.5l-GO ENGINEERIN G AUG 51976 The person charging this material is re- sponsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft, mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN ENBlittm . i >•(!>' ,?■>. y no CONI u oct ism OCT 1 MAY 3 1990 HAY 7 FEB 21 M MA « 5 ieci L161 — O-1096 ENGINEERING LIBRARY UNIVERSITY OF ILLINOIS URBANA, ILLINOIS UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN URBANA. ILLINOIS 61801 CAC Document No. 51 A GENERALIZED ILLIAC IV URBAN LAND USE PLANNING MODEL By Robert M. Ray- October 1972 Digitized by the Internet Archive in 2012 with funding from University of Illinois Urbana-Champaign http://archive.org/details/generalizedillia51rayr CAC Document No. 51 A GENERALIZED ILLIAC IV URBAN LAND USE PLANNING MODEL By Robert M. Ray Center for Advanced Computation University of Illinois at Urbana-Champaign Urbana, Illinois 6l801 October 1972 This work was supported in part by the Advanced Research Projects Agency of the Department of Defense and was monitored by the U.S. Army Research Office - Durham under Contract No. DAHCOU 72-C-OOOl. W6INEEMN6 LIBRAS r\0,5\-bO Abstract This paper outlines the rationale and the nature of an urban land use planning model that should prove applicable to the metropolitan transportation-land use planning process. To make clear the scope and functional objectives of the modeling effort proposed, we describe first a basic system of models necessary for effective computer assis- tance in rational metropolitan planning. The position of the urban land development model within this system is indicated, and alternative modeling strategies are discussed. After making our case for a more generalized predictive-prescriptive model of the urban land development process, we define the metropolitan land use planning problem more specifically, and explore a number of mathematical programming imple- mentation techniques. From this analysis, a dynamic optimization model emerges that is potentially capable of simulating over time the out- comes of incremental free-market land development decisions, and also capable of determining courses of metropolitan land development that are optimally efficient. Having strongly argued the potential advan- tages of such a land development model, we discuss the possible imple- mentation of such a model on a fast processing parallel computer such as the Illiac IV. TABLE OF CONTENTS Page 1. INTRODUCTION 1 2. A SYSTEM OF MODELS FOR METROPOLITAN PLANNING 2 3. THE LAND USE PLANNING PROBLEM 9 k. AN OPTIMAL GROWTH MODEL 11 5. A PLAN DESIGN MODEL IT 6. A DYNAMIC LAND USE PLANNING MODEL 19 7. THE APPLICATION OF ILLIAC IV 21 REFERENCES 22 1. INTRODUCTION The rationality of the metropolitan transportation-land use plan- ning process presently suffers from a general lack of any quantitative procedure for identifying and evaluating socially efficient courses of land development. While sophisticated computer methods exist for assessing the costs and benefits of future transportation system alternatives, such plans are typically evaluated with respect to projected, not planned, development patterns. Although plan optimiza- tion techniques have been proposed frequently elsewhere, few modeling efforts have survived the most preliminary feasibility studies. The success of all computer-oriented plan optimization techniques to date has been severely constrained by the basic limitations of available serial processing software and hardware. The vastly expanded compu- tational power of parallel processing computers such as the Illiac IV warrant a re-examination of the feasibility of plan optimizing models. We propose to investigate the application of Illiac IV to the problem of dynamic land development optimization to provide a more rational basis for generating and evaluating metropolitan transportation-land use plans. 2. A SYSTEM OF MODELS FOR METROPOLITAN PLANNING A general system of models for metropolitan planning is shown in Figure 1. In many respects the system depicted resembles the tradi- tional mix of operations that characterizes the existing transporta- tion-land use planning process. Our system here, however, differs from traditional operations in that the components shown would be integrated into a general system of computer models, all interacting with one another in real time and responding quickly to frequent manual interventions by the planner himself. The complete system is composed of three major subsystems of models that (l) simulate metropolitan travel patterns, (2) optimize transportation networks, and (3) gener- ate the associated metropolitan land use arrangements. While our immediate research focuses primarily on the land use component of the system, it should be helpful to examine more closely the operations of the overall system. Activity Simulation . The function of the activity simulation component within the larger system of planning models is to provide at any stage of plan development an adequate description of the volumes of travel between land uses and through networks within the metropoli- tan region. Such a simulation of metropolitan travel allows at any point an evaluation of the efficiency of a particular transportation- land use arrangement as a summation of all public and private costs of travel and land development. Moreover, by such simulations, the marginal costs and benefits of incremental plan alterations can be evaluated (e.g., the travel costs saved by reducing the distance between two activity locations, or the efficiency to be gained by the addition of another lane along some expressway link). Since real FIGURE 1 time interaction between all component models in the system is assumed, system control would alternate between plan evaluation and plan revi- sion until the simulated pattern of metropolitan travel suggested no further efficiency increments to be gained from marginal improvements. While it is of course impossible to predict in any detail the future levels of all activities within a metropolitan region and the travel flows between them, much information valuable for planning purposes can be obtained through approximate forecasting and simula- tion techniques. Regional economic models should serve well as exo- genous systems for forecasting metropolitan aggregate activity levels by land use categories and discrete time periods. Whatever success transportation planners have experienced to date seems in large measure due to the accuracy by which urban travel volumes can be simulated by simple regression and gravity models. Transportation Planning . For the specification and scheduling of metropolitan transportation facilities we accept the general goal of economic efficiency within the constraints imposed by certain "minimum level of service" requirements established exogenously by planners and decision makers. Thus, for any level of public expenditures on travel facilities, that system of networks would be chosen which satisfies all minimum service levels and offers maximum net benefits. Generally, public funds should be invested in transportation facilities to that point where marginal returns from additional expenditures are just equal to returns in other sectors of public finance. Lacking any comprehen- sive regional capital budgeting process, however, we could assume an infinite bond market and invest in network facilities until the sum of public and private travel costs is a minimum. Alternatively, we could assume some rate of return to prevail in all investment sectors and invest in transportation facilities until that condition is just satisfied. Of course, no methods exist for determining optimal transportation networks where design freedom is great and alternatives are too numer- ous for exhaustive evaluation. However, because landscape features and the nature of existing transportation facilities greatly influence the efficiency of alternative network improvements, we will assume that heuristic procedures (either manual or programmed) can be used for making marginal improvements to a current system of networks in response to an alteration of the regional land use pattern and the con- sequent change in the system of metropolitan travel volumes. Through manual selection and specification of a number of different networks, and evaluation of these alternatives by separate executions of the modeling system, the planner could conduct a computer-assisted search for an optimal network configuration. Land Development Models . The urban land development model may have any one of several purposes within the metropolitan transportation-land use planning process. Depending on the objectives of the analysis at hand, a model here may be used to simulate the free-market land develop- ment process, to evaluate the effectiveness of various regulatory policy packages on this process, to predict the land use consequences resulting from the economic influence of planned transportation facilities, or to determine normative plans for courses of land development that would be desirable in a social efficiency context. Here we will outline the rela- tive advantages and disadvantages of three distinct types of land develop- ment models. A descriptive model of the metropolitan land development process attempts simply to simulate (or describe) development as it is observed to occur. We use the term descriptive in this case to denote a first level of modeling sophistication where the objective is simply to replicate observable phenomena •without any structural analysis of the system generating the phenomena. Such models are convenient for the planner since they involve little theory construc- tion or validation, but on the other hand, they are of only limited value for predicting future system states, since such models are simply fitted statistically to whatever available data observations appear significant. While descriptive land development models have been expedient for metropolitan planning efforts in the past (e.g., the EMPIRIC model initially developed for the Boston Regional Plan- ning Project, see Hill, 1965), we feel that a truly rational planning methodology demands a more theory-based understanding of the land development process. A predictive model of metropolitan land use employs to some degree a structural theory of the urban land development process in predicting future development patterns consistent with aggregate growth forecasts. The "black box" simulation of the descriptive model is replaced by a causative theory of the development process that imparts to the model- ing effort a provisional knowledge of the forces at play and the chain effects of these forces between circumstances and process outcomes. Such a structural basis for modeling land development patterns can be borrowed directly from microeconomic theory. Here it is assumed that land developers maximize profits in servicing the real estate market and that households, firms, and other land-using activities trade off optimally the costs and benefits of all real estate alternatives. Thus, knowing something of the relative costs of developments in difference tracts and the values of these developments on a forecasted market, we should he able to predict with some accuracy the pattern of development resulting from these market conditions. Furthermore, with such a theory-based predictive model we should be able to study the consequences of deliberate modifications of the actual land development process (e.g. changes in property taxation policies or housing construction subsidies). The residential activity distribu- tion model of Herbert and Stevens (i960), formulated as a linear programming problem, is representative of this class of predictive models. A prescriptive model of urban land use attempts to determine those patterns of development that are maximally efficient for the community as a whole. While the predictive model attempts to report the proba- ble course of land development, the prescriptive or normative model strives to reveal a socially desirable land development outcome. Such a model requires much the same theoretical inputs as the predictive model, but here the microeconomic understanding of the land development process must be extended to include a causative knowledge of all social costs and benefits associated with alternative development decisions. Furthermore, since there exists a general interdependence between all land use decisions stemming from the travel flows between separated land uses and the psychological interaction of contiguous land uses, a prescriptive model of land development must treat certain spatial effi- ciency considerations that market mechanisms necessarily fail to optimize, Schlager's work (1965, 19^7), bold if premature, represents an initial attack in this area of land use modeling. Within the general system of models depicted in Figure 1, we pro- pose to develop a model of metropolitan land development that can he used in both prescriptive and predictive models. Such a general purpose model 'would serve the dual function within the metropolitan planning process of generating socially efficient land use plan alter- natives, and evaluating the feasibility of these development plans. Before developing any further the nature of this predictive-prescriptive model, however, we should describe more specifically the structure of the metropolitan land use planning problem we hope to probe. 3. THE LAND USE PLANNING PROBLEM Given an aggregate description of all projected development "by- land use categories, the type and scale of all activities entering the metropolitan region and the travel flows generated by them, and an exogenously determined transportation network, the land use plan- ning problem requires the determination of an optimal distribution of activities to locations within the landscape. We define an optimal configuration of activities as one that maximizes community efficiency through optimal land use. Land use efficiency is deter- mined simultaneously by three sets of relationships. First, there are the efficiency relationships between the various types of activities to be distributed and the alternative locations available to them. For purposes of analysis we may divide the com- plete landscape available for development into a system of develop- ment zones, choosing these zones in such a manner that each defines adequately a specific location within the region, and such that land- scape features within' zones are approximately homogeneous. Then, with an adequate knowledge of the private and social costs and benefits associated with the development and use of land in each zone for each activity type, we may compare the relative efficiencies of all zones for any activity type. We may choose to represent these relative efficiencies between zones for each activity as a vector of cost coefficients (one coefficient for each zone) representing the effi- ciencies derived and the opportunities foregone by development in any one zone. 10 Second, there are relationships between activities that serve to determine the total efficiency of any regional distribution of land uses. Travel flows between any pair of activities create real transportation costs proportional to the network distance separating the two activities. In the case of projected travel flows between locating and located activities, the transportation costs across existing and planned networks can be included in the calculation of relative zonal efficiencies for the locating activities. In the case of projected travel volumes between only locating activities, the problem is not so easily solved. Other important relationships among activities, both locating and located, stem from possible nuisance effects between activities. We must constrain the land use planning problem to deny contiguity of incompatible activities. Third, spatial relationships existing and planned between develop- ment zones enter into the determination of land use efficiency. Here the obvious case in point is the effect of network distance between any two development zones. Travel time as well as distance might also be considered. Equally important are the existing and planned network links to locations already developed to and from which increased travel volumes have been projected. Given this general outline of the efficiency determinants of alter- native land use plans, we now turn to an examination of three specific prescriptive models of the metropolitan land development process, and formulate the mathematical programming solution for each case. 11 k. AN OPTIMAL GROWTH MODEL An optimal growth increment model of the metropolitan land develop- ment process can be formulated quite readily as a mathematical program- ming model in a variety of ways . Essentially, we wish to allocate the land available in development zones to projected incoming activities in such a way that all land development and land use costs are minimized. Formulating this problem as a linear program, we may write: n m min I I a. ,_ x j,k j,k n s.t. I x > A k = 1, ... , m j=l J ' k k m 2 S i k X i k " B i J = ls J - 1, ... , m x > k = 1, ..., n where: n = number of development zones m = number of activity types A = number of activity units of type k B. = number of land units in zone j J s. = units of land in tract j required for J ' each unit of activity type k a. = costs of developing and using land in tract j per unit of activity type k x. = number of units of activity type k J ' located in tract j. 12 The objective function of the linear programming problem simply expresses the summation of all social and private costs of development. The two constraints require that all forecasted activity be located within development zones, and that the land allocated in any one zone not exceed the area available for development there. Of course, all elements of the solution vector are restricted to non-negative values since relocations are not considered. While the general linear programming formulation has a certain theoretical elegance, and in fact allows a different rate of transfor- mation of land into activity for every development zone and for every activity type, serious problems result from the use of such allocation techniques. Specifically, the necessary assumption that all activities are finely divisible does not conform adequately to the nature of the planning problem at hand, and activity distributions derived through linear programming methods usually contain fractional allocations of essentially discrete activities, such as hospitals, schools, shopping centers, etc. Due to the assumed linear objective function, there is also the additional problem that all activities of a single type tend to cluster together in a single zone (e.g., all high schools are allo- cated to contiguous parcels.) While it is true that we could further restrict the problem solution with certain zero-one constraints, the resulting mixed-integer programming problem expands rapidly, and no practical solution techniques exist for problems of the size encountered here. Given the fundamentally discrete nature of urban land use activities, and given the general failure of continuous mathematical programming methods to manipulate these activity units as discrete elements, we turn 13 to an alternative modeling strategy. Without too much distortion of reality we may assume that all development zones are subdivided by a common regular grid of the city block scale. We will call these equi- area subunits of development zones land blocks . In a similar fashion, we will assume that all land development within the metropolitan area occurs in block-by-block fashion, with each block development charac- terized by a single land-using activity. These discrete and equi-scale elements of land development (such as a block of single-family dwellings, an apartment complex, an elementary school, or a downtown office tower) will be called land use modules . Furthermore, it is assumed that all forecasts of growth increments are expressible in quantities of modules of each type and that all travel within the metropolitan region is simulated as volumes between modules. Our regional land use distribution problem is much simplified by such assumptions, and discrete optimizing techniques are readily available. By simply adding a number of dummy agricultural or open space modules to the forecasted number of new land use modules in order to have as many modules to locate as blocks of land to allocate, the linear programming problem reduces to the much more easily solved transportation programming problem for which solutions necessarily have the property of integral allocations. In programming notation we may write: n m min 2, Z a - v x * J=l k=l J ' X J,Ji n s.t. I x = IL k = 1 m Ik m I x = B j = 1, ... , n k=l J >* J j =1, • •• , n x jjk > , k = 1, ..., m where: n = number of development zones m = number of land use module types A = number of modules of type k B. = number of blocks in zone ,i J a. , = costs of developing and using a block ■J' in zone j for a module of type k x. , = number of blocks in zone ,i allocated i k to modules of type k. The notation of our problem can be simplified further at this point by doing away with the grouping of blocks by zones and the group- ing of modules by types. We may express the resulting model as an ordinary assignment problem for which a solution is necessarily a one- to-one matching of modules to blocks. n n min / ; a. n x. , Ak=i j > k j > k n s.t . J x = 1 k = l,...,n J-l J ' I x = 1 j = 1, ..., n k=l j,k k = 1, .. . , n 15 where: n = number of blocks and number of modules a. = costs of developing and using block j J ' for module k x = the fraction of block j allocated to J ' module k. Since special properties of the assignment problem imply that allocations occur as integral matchings, the solution matrix [x. , ] is always a permutation matrix and hence we may represent any solu- tion to the problem as that permutation p associated with the optimal matching of blocks and modules. This fact leads to the following even more simple notation for the problem: n min V a . p A J > p (j) which implicitly contains all of the constraints of the assignment problem. While assignment programming methods might be used for modeling optimal growth increments of land development (especially where travel volumes are generated for each module separately, not by module types), for most prescriptive growth modeling the transportation programming algorithm would prove most effective. We have developed, however, the assignment problem structure and notation in order to provide a smooth transition between the opt imal growth increment model and the more powerful static design and dynamic planning models. Although the optimal growth models just formulated with linear programming and assignment programming techniques were presented as methods for prescribing efficient incremental development, these same models, with only minor alterations, might be employed for purely predictive purposes. Expression of only the private costs of land 16 development and land use would convert all of the above models into simulations of the real estate market, with the optimal solutions to the mathematical programming problems serving as predictions of the outcomes of decentralized free-market land development decisions occur- ring within the specified time period. Such an optimizing simulation of the land development process has been formulated elsewhere by- Herbert and Stevens (i960), and by Harris (1962). The theoretical validity of such projection techniques suggests a primary hypothesis to be tested within the proposed modeling effort: that predictive and prescriptive development models are interchangeable within a short planning horizon if social costs can be internalized in market deci- sions through policy constraints on development. While optimizing incremental growth models may serve the dual pur- poses of predicting probable growth and prescribing socially efficient growth, they provide no method for optimizing long range development patterns, nor do they serve well in the design of a new community. The restricted optimizing potential of the optimal growth model is due to the complete neglect of whatever locational interdependencies that might exist among all locating activities. If the time period is short, and if most travel flows occur between locating and located activities, then interdependence is minor and can be properly neglected. However, if the planning horizon stretches far into the future, or if for any other reason activities to be located comprise a major proportion of the land use system to be planned, then travel volumes between locating activities will dominate efficiency evaluations and completely negate the optimizing mechanisms of prescriptive growth models. In such situations we must turn to more powerful models for optimizing the efficiency of the land use plan. 17 5. A PLAN DESIGN MODEL An opt imal plan design model internalizes in all efficiency calcu- lations the transportation costs among all locating activities, as veil as the costs of travel between locating and located activities and the costs of land development itself. In mathematical programming notation we may write: n n n n n n in y y y y x. . c, _ x. _ d. . + y y a. . x. . A A k =i 1=1 x > k k > 2 J' 1 x *J A k=i J ' k J '- n s.t. I x = 1 k = 1, ..., n n k=l J ' k x > o J =i> •••> n j,k k = 1 n where: n = number of blocks of land and the number of locating and located modules a. , .= the cost of developing block j for activity module k c = the cost per unit distance of transpor- tation volumes between module k and module 1 d. = the network distance separating block i 1,J and block J x. = the fraction of block j allocated to 3i module k. Or, more conveniently, we may express the optimal plan design problem as n n n min T J c,.v, ,. d. .+ Y a. , . » p ^ jSi Pd) P(j) i,J .^ J,p(j) where all constraints are implicitly represented and the solution is represented as the unknown permutation p. 18 This mathematical programming problem was first formulated by Kbopmans and Beckmann (1957) in an effort to determine plant-location optimal assignments where transportation flows between plants repre- sent major costs to be minimized. They call the model a quadratic as s i gnment problem, since the unknown permutation matrix [ x. , ] occurs twice in a single term of the objective function. While no optimal solution techniques are presently known for solving quadratic assignment problems of the scale proposed here, several good approximate methods exist (Gilmore, 1962; Graves and Whinston, 1970). In addition to the techniques described within applied mathematics literature, several other approximate methods are presently being developed at the University of Illinois Center for Advanced Computation that will be particularly well suited for implementation on parallel processing computers. 19 6. A DYNAMIC LAND USE PLANNING MODEL Actually, the problem that we propose to study is more complicated than the quadratic model described above. What needs to be determined by the prescriptive land use model is not a static plan for some single year in the distant future, but a continuous course of metropolitan land development which is dynamically optimal. Here we would reduce to present value the costs and benefits implied by land use patterns in a sequence of future time periods, allowing a dynamic evaluation of a specified course of land development. By making proper trade-offs between the efficiency of activity locations in consecutive time periods, and by charging appropriate penalties to activities relocating between time periods, heuristic approximations of a dynamically optimal course of metropolitan land development may be possible. In its most simple notation, the dynamic land use planning model is written: min I t=l (l+r) ty n n t t n t y y c » d. . + y a. p i£i A p(i) p(j) i.J j£i j. ( j) where: n = number of blocks of land and number of land use modules forecasted by time period T T = number of time periods considered y = number of years in each time period a. = costs in time period t associated with the j.k development of block j for module k c = costs per unit distance of transportation flows k,l between module k and module 1 in time period t t d. = network distance between block i and block j ,d planned for time period t r = annual rate of social discount. 20 With the dynamic land use optimization problem stated in this, its simplest form, it is now possible to view the total complexity of the modeling effort at hand. Our argument is not, however, that we expect to optimize over time all costs and benefits of metropolitan land use by minimizing globally a dynamic quadratic assignment problem. We would hope rather that by defining for the land use problem a rigorous theo- retical structure, and by manipulating this problem structure in a heuristic, hill-climbing manner, that a more practical understanding of dynamic land use efficiency would emerge. Metropolitan land development patterns resulting from the approxi- mate solutions to the dynamic land use optimizing problem formulated above should be to some extent sensitive to the rate of discount r assumed within the analysis. We hypothesize that dynamic optimization with re- spect to a discount rate approximately equal to market rates of interest (e.g., 6-8%) will result in land development patterns closely resembling unplanned free-market outcomes. On the other hand, dynamic optimization with respect to socially appropriate discount rates (e.g., 3-h%) should yield more orderly development, since short term locational benefits would be weighted less with respect to total time benefits. If these hypotheses prove correct, then the dynamic optimizing model could be used both for generating socially efficient courses of metropolitan land development and for evaluating the feasibility of implementing these plans. Since both uses of the model would in some sense represent simu- lations of market forces, simultaneous examination of both development processes would allow the planner to devise a system of taxations and subsidies that would bring about a general redirection of the predic- tive simulation toward the normative one. 21 7. THE APPLICATION OF ILLIAC IV Illiac IV represents an appropriate scale of computational facility for manipulating the system of urban planning models outlined in this paper. Throughout all three components of the complete system of models — urban activity simulation, transportation network optimiza- tion, and land use planning — large matrices must be manipulated and complex system interactions must be analyzed. The dynamic land use optimization problem, of primary focus in this paper, could only be manipulated on a fast, processing, parallel computer such as Illiac IV. Presently on conventional serial proces- sing computers the effectiveness of existing algorithms seems to suggest a maximum size for the dynamic quadratic assignment problem approaching 6k land blocks and 6k land use modules. This represents the scale of a planning problem for a town of about 8 blocks by 8 blocks. We estimate running times of about 2 minutes on existing large scale serial processing computers such as an IBM 360/75. On Illiac IV the probable capabilities would be expanded about 6k times. This would mean that one approximation to the land use planning problem could be generated in about 2 minutes for a city about 6k blocks by 6k blocks in size. This represents adequate resolution for the land use planning process in many intermediate size metropolitan areas. 22 REFERENCES Chapin, F. Stuart, Jr. Urban Land Use Planning , 2nd ed. Urbana, Illinois: University of Illinois Press, 1965. Harris, Britton, "Plan or Projection: An Examination of the Use of Models in Planning", Journal of the American Institute of Planners , Volume XXVI, No. k (November i960), pp. 265-272. Harris, Britton, Linear Programming and the Projection of Land Uses , Paper No. 20, Philadelphia: Penn Jersey Transportation Study, September 1962. Harris, Britton, Basic Assumptions for a Simulation of the Urban Residential Housing and Land Market , Philadelphia: Institute for Environmental Studies, University of Pennsylvania, July 1966. Herbert, John D. and Stevens, Benjamin H. , "A Model for the Distribution of Residential Activity in Urban Areas", Journal of Regional Science , Vol. 2, No. 2 (Fall i960), pp. 21-36. Hill, Donald M. "A Growth Allocation Model for the Boston Region", Journal of the American Institute of Planners , Volume XXXI, No. 2, (May, 1965), PP. 111-120. Gilmore, P. C, "Optimal and Suboptimal Algorithms for the Quadratic Assignment Problem", Journal of the Society for Industrial and Applied Mathematics , Vol. 10, No. 2 (June 1962), pp. 305-313. Graves, G. W. and Whinston, A. B., "An Algorithm for the Quadratic Assignment Problem", Management Science , Vol. 17, No. 7 (March 1970), pp. k53-kn. Koopmans, Tjalling C. and Beckmann, Martin, "Assignment Problems and the Location of Economic Activities", Econometric a , Vol. 25, (1957), pp. 53-76. Lowry, Ira S., "A Short Course in Model Design", Journal of the American Institute of Planners , Vol. XXXI, No. 2 (May 1965), pp. 158-166. Lowry , Ira S . , Seven Models of Urban Development: A Structural Comparison , The RAND Corporation, September 1967. Schlager, Kenneth J., "A Land Use Plan Design Model", Journal of the American Institute of Planners, Vol. XXXI, No. 2, (May 1965), pp. 102-110. Schlager, Kenneth J., "Land-Use Planning Models", Journal of the Highway Division , Proceedings of the American Society of Civil Engineers , Volune 93, No. HW2, (November 1967), pp. 135-1^2. UNCLASSIFIED Security Classification DOCUMENT CONTROL DATA -R&D (Security ctaaalllemtlon ol till: body Of a»«H»cl and Intoning annotation muat bo antarod whan tha ovorall report la claaalllad) I. ORIGINATING ACTIVITY (Corporal* OUthof) Center for Advanced Computation University of Illinois at Urbana-Champaign Urbana, Illinois 61801 i». REDOUT ICCURI TY CLASSIFICATION UNCLASSIFIED 2b. CROUP 3 REPORT TITLf A GENERALIZED ILLIAC IV URBAN LAND USE PLANNING MODEL 4. DIICRIPTIVE MOTH (Typo ol ttpart and rnelualva datoa) Research Report s AUTHOR(S) (Flrot mm, mlddlm Initial, lamt nam*) Robert M. Ray • . REPORT DATE October 197 7a. TOTAL NO. OF PACKS 2SL 7b. NO. OF «EFI .13- •a. CONTRACT OR CRANT NO. DAHCOif 72-C-0001 b. PROJECT NO. ARPA Order No. 1899 •a. ORIGINATOR'S REPORT NUMBER(S) CAC Document No. 51 OTHER REPORT NOISI (Any othor ntmnborm that may ba aaalgnad thla roport) 10. DISTRIBUTION STATEMENT Copies may be requested from the address given in (l) above, II. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY U. S. Army Research Office - Durham Duke Station Durham, NC 13. ABSTRACT This paper outlines the rationale and the nature of an urban land use planning model that should prove applicable to the metropolitan transportation- land use planning process. To make clear the scope and functional objectives of the modeling effort proposed, we describe first a basic system of models necessary for effective computer assis- tance in rational metropolitan planning. The position of the urban land development model within this system is indicated, and alternative modeling strategies are discussed. After making our case for a more generalized predictive-prescriptive model of the urban land development process, we define the metropolitan land use planning problem more specifically, and explore a number of mathematical programming imple- mentation techniques. From this analysis, a dynamic optimization model emerges that is potentially capable of simulating over time the out- comes of incremental free-market land development decisions, and also capable of determining courses of metropolitan land development that are optimally efficient. Having strongly argued the potential advan- tages of such a land development model, we discuss the possible imple- mentation of such a model on a fast processing parallel computer such as the ILLIAC IV. DD ,rr..1473 UNCLASSIFIED Security Classification JJ22 LASSJFIED Security Classification KEV WOROI »OLI WT Economics Transportation Operations Research Linear Programming Miscellaneous (quadratic assignment problem) Land use models UNCLASSIFIED Security Classification