decision support for regionalization: a spatial decision support system for regionalizing service...

Cornput., Environ. and Urban Systems, Vol. 15, pp. 37-53, 1991 Printed in the USA. All rights resewed.

0198-9715/91 $3.00 + .OO Copyright 0 1991 Pergamon Press pk

DECISION SUPPORT FOR REGIONALIZATION: A SPATIAL DECISION SUPPORT SYSTEM FOR

REGIONALIZING SERVICE DELIVERY SYSTEMS

Marc t? Armstrong, Gerard Rushton, Rex Honey, Brian T: Dalziel, and Panos Lolonis

Department of Geography, The University of Iowa

Suranjan De

Department of Management Sciences, The University of Iowa

Paul J. Densham

National Center for Geographic Information and Analysis and Department of Geography State University of New York at Buffalo

ABSTRACT. The problem of finding an optimal number of regions, and service locations within each region, to serve a dispersed geographical pattern of demand is treated as an interactive location- allocation modeling problem. Distinctive elements of the problem involve controlling the location of region boundaries, solving for multiple objectives that involve minimizing average and maximum distances to clients from central facilities, ensuring that a minimum number of clients are served in each region, and, under user-defined circumstances, using existing facilities in selected locations. A prototype microcomputer-based spatial decision-support system is described. We also discuss its use by members of an Iowa state government Workgroup charged with developing recommendations for the geographical reorganization of educational services provided to Iowa school districts from central facilities.

We acknowledge support provided by the Midwest Transportation Center at The University of Iowa, and an Interdisciplinary Research Grant from University House, the center for advanced study at The University of Iowa. Several individuals also provided valuable assistance: David Forkenbrock, Director of the Public Policy Center at The University of Iowa, Guy Ghan of the Iowa Department of Education, members of the AEA Workgroup, and George Fotis of the National Technical University in Athens, Greece.

Address for correspondence and reprints: Department of Geography, The University of Iowa, 316 Jessup Hall, Iowa City, IA 52242.

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38 M. I? Armstrong et al.

INTRODUCTION

Determining the number and locations of central facilities to provide services to a geographi- cally dispersed population is a problem with a rich theoretical and applied literature, In conventional approaches to this problem (Brandeau & Chiu, 1989; Love, Morris, & Wesolowsky, 1988) decision-makers describe their objectives and any constraints on realizing these objectives to analysts. The analysts then retire to a computer laboratory where the problem is for- mally specified in such a way that an optimal solution can be determined using available location-allocation models.

Such conventional approaches often fail to find acceptable solutions to locational problems for several reasons: First, they remove decision-makers from the solution stage of the decision- making process even though decision-makers often find in solving regionalization and facility location problems, that they must explore their problem in its real context before they can determine the objectives that should be met by the best solution. In addition, all relevant data describing the geographical environment may not be available to support decision-making; spatial data are often expensive, and constantly change. Finally, in many cases important geographical details are known only by decision-makers and cannot be captured in a computer system. Because of these characteristics, many locational problems are semi-structured (Alter, 1977; Hopkins, 1984).

An alternative to the conventional analytical approach must be adopted in which an interactive system supports iterative decision-making, and provides feedback to decision-makers about the performance of different patterns of locations. In this paper we describe an example of a semi-structured locational problem and a prototype spatial decision support system (SDSS) which we developed to solve such problems. Though spatial decision support systems can be applied to the solution of structured locational problems, they also can be used when decision-makers have difficulty in specifying one or more of the following: (a) a comprehen- sive set of relevant criteria at the outset - decision-makers discover relevant criteria as they discuss the merits and problems of proposed alternative solutions; (b) the weights to be assigned to criteria - decision-makers need to know how the characteristics of the system change as the weights assigned to criteria change; and (c) site-specific constraints before decision-makers know the consequence of imposing these constraints.

In our example of a real location selection problem, described below, decision-makers encountered difficulties in meeting each of these conditions. After conferring with them, it was

agreed that our prototype SDSS should allow them to combine their knowledge of the opera- tion of the service activity with general knowledge from location theory and related methods of locational analysis incorporated in the SDSS. The specific criteria that are applied to location selection problems are, of course, domain-specific, but the methods of implementing the criteria in any real application involve the use of generic knowledge about the theories and methods of locational analysis. The prototype SDSS reflects our belief that it is possible to develop a system of analysis that will enable decision-makers to use these general concepts and to apply them, along with their rich domain-specific knowledge, to the solution of spatial problems.

A SPATIAL DECISION SUPPORT SYSTEM FOR REGIONALIZATION

Spatial decision support systems are designed to encourage problem-exploration, and to provide interactive assistance in the solution of semi-structured spatial problems (Densham & Rushton, 1988). Although semi-structured problems cannot be solved using structured approaches alone, important elements within such problems can be solved as structured problems using conventional modeling techniques. When the structured elements of their problem

Decision Support for Regionalization 39

have been solved, however, decision-makers must be able to evaluate the results obtained from the models, and then make decisions about elements of the problem that cannot be structured. This capability is needed because experience has shown that a straightforward application of mathematical modeling often fails to capture important dimensions of spatial problems because such problems often contain aspects which cannot be represented in a form that is suitable for optimization algorithms.

A typical SDSS normally consists of a database, a suite of spatial data processing models, and a set of procedures for generating displays and reports which summarize results of alternative solutions (Armstrong, Densham, & Rushton, 1986). Whereas the database is often a simple repository of locational data and descriptions of entities, the spatial processing models can be drawn from several different analytical traditions, although in most instances optimization models are employed. These components can be combined to provide an iterative and partici- pative decision-making environment. The basic set of modules comprising the SDSS are:

1. Database; 2. Spatial analysis models;

(a) Data transformation utilities; (b) Software to find shortest paths through a transportation network, and to pre-

pare the distance data for input to optimal location algorithms; (c) A heuristic location-allocation program which can solve all the objective

functions in Hillsman’s (1984) unified linear model; (d) Software to reallocate demand to meet user-defined constraints;

3. Visualization software; (a) A report generator which provides the user with statistical information about

characteristics of solutions; (b) Mapping software.

Each component is shown in Figure 1 and is described below in greater detail.

) Declslon-Maker b-

1 Generator 1

FIGURE 1. Architecture of the SDSS.

40 M. P Armstrong et al.

Database

The database serves as the foundation for the SDSS because the analytical elements of the system require information about the amount and location of demand, candidate sites for supply of services, and linkages among places in the form of a transportation network or a surro- gate. Decision-makers are required to identify candidate sites for the supply of services, and in some cases they may insist that certain supply locations be constrained to be centers in the solution. Demand may be represented by a population variable, although analysts often wish to identify and specifically measure that segment of the population that is likely to require services. The complexity of the geography of real environments is abstracted by assuming that interaction among nodes occurs on a set of links which approximates a transportation network (e.g., Densham, 1990; Goodchild & Noronha, 1983; Hillsman, 1980). While this method of

representation is often applied to data sets in which area1 units of demand are aggregated to nodes on the network, disaggregated data also can be modeled using this technique. The pro- duction of graphical displays also requires access to a database.

Data Transformation Utilities

Data manipulation procedures to reformat data and to ensure that output from each module is compatible with others in the system are written in Pascal. Procedures have been written, for example, to reformat output from the location-allocation models so that it can be displayed by cartographic software. Other utility procedures have been prepared to compute polygon centroids, and to prepare files for analyses.

Shortest Path Software and Distance Editing Procedures

A shortest path procedure generates a data set containing minimum weighted distances

between each demand node and all candidate locations that might serve it. These distances are then used by the location-allocation software to optimize objective functions. The procedure uses a version of an algorithm developed by Dijkstra (1959) to find shortest distances between demand and candidate locations.

Distance data can be stored in the form of a full distance matrix, but such an approach is inefficient for storage and processing particularly when centers serve only part of a study area. In the SDSS, therefore, the performance of the locational analysis system is increased by elimi- nating unnecessary data, and by implementing two kinds of data structures: demand strings, and candidate strings. For each demand site a demand string lists all candidate sites and their costs of serving it. For each candidate site a candidate string lists all demand sites that it might

serve and the costs of serving them. This reciprocal storage structure speeds the execution of location-allocation models by reducing the amount of searching that must take place (Densham, 1990). Both kinds of distance strings are used to create an additional structure - the allocation table - that is used to implement the location-allocation software used by the SDSS (Armstrong et al., 1990; Densham, 1990).

Location-Allocation Software

The location-allocation software, which is a Pascal implementation of a heuristic vertex substitution algorithm (Teitz & Bart, 1968) solves the p-median problem. The p-median problem minimizes total distance of demand from the closest of p centers in the system. It can be formulated in the following way:


Minimize z = cc ~0 * Cij,

where xij = 1 if demand node i is allocated to facility j, 0 otherwise; and Cij is a metric of interaction that can take various forms including distance, transportation cost, or travel time. For the case where distance minimization is the objective,

where Wi is the amount of demand to be served at the ith location and du is the distance from the ith to the jth location, Further constraints are placed on this formulation to ensure that all demand is allocated to a facility, and that a node has a facility before it can provide service (Hillsman, 1984, p. 307).

The cii coefficients are edited so that an appropriately coded algorithm for the p-median problem can be used to solve for any one of a large variety of locational objectives besides minimizing average travel distance (Hillsman, 1984). Among the locational objectives that the prototype system is able to solve are the following: (a) find p locations and the areas they serve to minimize average travel distance subject to a maximum distance constraint - the p-median problem; (b) find p locations so that a maximum amount of demand is within distance s of its closest location - the maximal covering problem; and (c) find the minimum number of locations so that all demand is within distance s of the closest of the selected locations - the set-

covering problem. The software is menu-driven, and the user can select from among these and other commonly

used objective functions. In addition to the commonly used modules described above, we developed two new functions not available, to our knowledge, in any other geographical information and analysis system. These are described in the next two sections.

Adjusting Regions to Meet Demand Requirements

A requirement of many regionalization problems is that all regions achieve a minimum size, as measured by demand. This requirement is often translated into a need to create compact regions in which either an equal or a minimum amount of demand is met (e.g., Weaver & Hess, 1963). Political redistricting, for example, is a special case where approximate equality of population in regions is required. The ADJUST procedure in the SDSS permits political redistricting to be accomplished by a replicative, objective method, rather than by subjective swapping of small areas between contiguous districts, which appears to be the method adopted in current commercial GIS software.

ADJUST uses a two-stage solution process. An initial solution is derived such that each unit of demand is assigned to its closest facility, and the total demand served by each facility is then computed. In the second stage, surplus demand is reassigned to those facilities which do not reach their demand requirement. Reassignment of surplus to regions with deficits is made in the following way:

1. Find the region with the largest deficit. 2. Compute P = a * D, where P = amount of deficit to be covered in current iteration; a =

user specified percentage of deficit to be reassigned in current iteration; D = demand deficit of current region.

3. If the total demand that is reassigned is < P, then (a) identify the demand unit assigned to a region with a surplus for which the increase

in distance, if it were reassigned to the center with the largest deficit, would be least;


(b) assign that unit to the center with the deficit; (c) update assignment of demand for each region; (d) continue until reassignment exceeds P, or no improvement can be made during an iteration.

4. Process the region with the next largest deficit of demand. 5. Iterate until all regions meet the demand requirement, no improvement can be made, or

until the increase in distance through reassignment is larger than the decision-maker is

willing to accept.

The principle behind this heuristic algorithm is that demand should be reassigned from regions with a surplus to regions with deficits such that the increase in distances in the system is least. The iterations provide information that allows the decision-maker to monitor the increase in distance that any unit area incurs as it is reassigned to a deficit region to meet the minimum demand requirement; these distances increase monotonically as the algorithm pro- ceeds to meet this requirement.

Controlling Boundaries of Regions

A procedure was developed which can be used to perform location-allocation analyses when the study area is divided into two or more districts. The problem is to identify the number, locations and service areas of facilities in each district such that the total number of facilities in the study area equals a given number and the costs of service provision are minimized (ReVelle & Elzinga, 1989). The necessary data to solve this problem are the total number of facilities which must be located, the cost of serving each demand location from each candidate location, an arbitrary initial solution and the demand and candidate locations that are enclosed by each regional boundary. The last piece of information specifies the set of candidates that can serve each demand location. The problem is solved using existing optimization procedures by modi-

fying the costs (c$ of serving the ith demand site from the jth center when they are in different districts. Specifically, if a candidate is on the opposite side of a boundary from a demand loca-

tion then the candidate cannot serve it, and a large penalty value is added to the cg coefficient. Accordingly, when the objective is to minimize costs in service provision, the allocation of demand in one district to a facility in another district causes the value of the objective function to increase substantially, and this forces the algorithm to search for less costly alternatives within the district. This technique is conceptually simple, enables analyses to be performed quickly, works with both exact and heuristic algorithms and thus is more efficient than altema-

tive techniques described in the literature (ReVelle & Elzinga, 1989).

Display Generation

The mapping component of the SDSS relies on the use of commercial software to generate displays used by decision-makers. In the prototype system the software (Atlas) is used to generate several kinds of thematic maps including choropleth and dot distribution maps. Although these maps are useful for displaying spatial data in many different contexts, they fail to show the relationship between service demand and supply. We, therefore, have created a procedure for generating “spider” maps (Allard & Hodgson, 1987; Charest-Berglove & McKeagney, 1983) which indicate the allocation of demand to facility sites. For each solution, such displays convey to the decision-maker the locations of the facilities, and the allocation of demand to those facilities. The results of the location-allocation models also can be used to create displays depicting region boundaries that would result from the solutions. In this case, chorochromatic maps are used in which each region is assigned a color solely to differentiate it from its neigh-


bors. The system works especially well when two computers are lied because one machine can be used to perform analyses while the other is used concurrently to display maps and prepare reports. The two machines also can be used to display two solutions for decision-makers to compare and evaluate.

Hardware Environment

The system is implemented in an IBM PC (and compatible) environment using DOS. For the problem described in the following section, a Hewlett-Packard RS 25 (Intel 80386, 80387, 25 mhz) and an IBM PS/2-80 (Intel 80386, 80387, 16 mhz) were used. Each system uses a VGA display for generating maps and graphs, and hardcopy output is produced by a HP Laserjet II printer. The computer systems are able to exchange data through a high speed communication link that connects their parallel ports.

USING THE SDSS IN DECISION-MAKING

Public and private sector facility location problems can be addressed using the prototype SDSS, including political redistricting, school facility location and attendance area definition, and regional public administration problems. The SDSS environment allows decision-makers to explore the nature of their problem, and to apply their expertise during the process of searching for a solution in two ways. First, it allows them to specify criteria and constraints and to find the corresponding optimal administrative centers and the regions that they serve. Second, it allows them to examine results and to discuss among themselves the implications of adopting either a plan generated by the system, or one which is suggested by the results of analyses (Figure 2). Such discussions, in which domain-specific knowledge of decision-makers is applied to problems, frequently lead to the formulation of new criteria, or to respecification of the same criteria with different constraints. In addition, solutions can be rejected on the basis of information provided by the system about the performance of a solution on a selected set of

criteria, or for other reasons that may not be part of the system, but which may be important to the decision-maker.

Flexibility and improvement in supporting locational decision-making is gained by placing

FIGURE 2. The Decision-Making Environment.

44 M. t? Armstrong et al.

the location-allocation software in an interactive system with other software modules. Because the prototype analysis system is undergoing continual development, no effort has yet been made to design it for direct use by people who are unfamiliar with the methods of locational analysis used in the system. Most decision-makers are untrained in the methods of multi-objective optimization and, therefore, require an analyst to work with them to establish a logical framework for generating and evaluating alternatives. If, for example, a decision-maker intro- duces many place-specific constraints when defining eligible service locations, the analyst might suggest an analysis in which there are no place-specific constraints and might advise the decision-maker that the reason for doing this is to estimate the cost, in terms of decreased system performance, of the constraints. In the example problem described in the following section, we worked closely with the decision-makers at each step of the problem-solving process to ensure that system performance was as transparent as possible. This enabled us to monitor the status of the decision-making process as alternatives were developed and evaluated. By closely observing the decision-making process we gained knowledge that helped us improve the organization of the system for future use.

APPLICATION OF THE SDSS TO THE GEOGRAPHICAL REORGANIZATION OF IOWA’S AREA EDUCATION AGENCIES

Area education agencies (AEA) in Iowa “are primarily service agencies for local school districts” (Iowa Department of Education, 1987, p. 11). Each of the 15 current AEAs is charged with serving the public school districts within its boundaries by providing special education support, media and other services to public and nonpublic students. For example, twice each week books, films, and other educational materials that are ordered by teachers are delivered from each AEA regional office to schools in its service area. Other specialized personnel such as speech clinicians, psychologists and social workers, travel a regular itinerary to serve stu-

dents at several schools. The 1986 session of the Iowa General Assembly passed a law stating that the State Board of

Education should restructure school districts, area education agencies, and merged area schools, with a specific emphasis on combining the area education agencies (Iowa Department of Education, 1987). The 1987 session of the General Assembly amended the 1986 legislation (Iowa Department of Education, 1987) by specifying that:

. . . the state board shall develop plans for redrawing the boundary lines of area education agencies so that the total number of area education agencies is no fewer than four and no greater than twelve. . . The plans relating to the area education agencies and merged area schools shall be submitted to the general assembly not later than January 8, 1990. (p. 1)

TABLE 1. The Seven Workgroups Established by the State Department of Education to Oversee Reorganization of the Area

Education Agency Regions

Distance Learning Instructional/Educational Services Library/Media Setvices Management Services Operational Relationships Special Education Delivery System Structure


FIGURE 3. The 433 Iowa School Districts Which Serve as the Unit of Analysis.

The intent of the plan is to “assure more productive and efficient use of limited resources, equity of geographical access to facilities, equity of educational opportunity within the state,

and improved student achievement” (Iowa General Assembly, 1986, p. 1086). In response to

FIGURE 4. The Current Area Education Agency Regions.

46 M. t? Armstrong et al.

this mandate, the State Board of Education appointed seven work groups (Table 1) to review services provided by the area education agencies. One of the work groups (the Delivery System Structure Workgroup) was charged with coordinating the results of the other six and to make recommendations to the State Board of Education for restructuring the regions.

There are 433 school districts in Iowa (Figure 3), which are merged into 15 AEA regions (Figure 4). Large differences in the number of students exist among these regions. For example, in 1988 the number of school children in one region was 12,344, whereas the number was substantially higher (108,963) in another. Since resources for providing AEA services are based on the number of students served, it is clearly more difficult to offer comparable levels of specialized services for regions with small enrollments than for those with large enrollments. Average and maximum distances from service recipients represented by school districts to the AEA regional offices also vary greatly. Such differences in accessibility can be found for many service delivery systems in Iowa. Though commonly perceived as a rural state, its urban population is now large, and the urban areas have superior accessibility to services. The feeling still runs deep in Iowa, however, that people should not be disadvantaged by their rural location. Most decision-makers would agree that a service delivery system is needed that provides equity and efficiency. The need for geographical restructuring is evident.

Following discussions with the Iowa Department of Education in May 1989, we were invited to a meeting of the AEA Delivery System Structure Workgroup in Des Moines, Iowa, in July 1989. We were asked by the Workgroup Chairman (Ghan, 1989) to consider the following questions before the meeting:

1. How do geographical and transportation elements relate to the number of AEAs to be determined?

2. How does population density, and the location of metropolitan areas and dominant com- munities relate to the determination of the number of AEAs and the regions they serve?

3. Should existing AEA facilities and boundaries be respected as much as possible, or should boundary planning start from the beginning?

4. How do current and potential central offices and satellite offices relate to the determination? 5. How can logical boundary lines, encompassing compact territory, be established, in order

to provide equitable services statewide, and in order to develop governmental units that will last well into the next century?

While the general problem of determining the number of regions, their centers, and their boundaries seemed straightforward, in fact it was not. Legislation determined the minimum (4) and maximum (12) numbers of regions, but little else. Furthermore, the questions posed by the

Chairman contain several aspects which are not clearly defined. The relationships among the questions, and the specification of formal criteria that can be used for modeling and for con-

straining solutions are also unknown. The problem as posed by the Chairman, therefore, is semi-structured.

We worked with the Chairman to specify several specific criteria of interest to the decision- makers. This allowed us to use the prototype SDSS to assist the Workgroup in finding a solution to the problem of reducing the number of AEA regions and altering their associated boundaries. The prototyping phase is one in which important features of the analysis system are progressively changed as reactions from users are received and evaluated. Thus, our activi- ties led us to add the new capabilities described in section 2 as we gained experience with working in this locational decision-making context with the AEA Workgroup.

Prior to the meeting with the Workgroup - consisting of 22 individuals - we prepared a set of alternative solutions to demonstrate the capabilities of our prototype system, and to provide the Workgroup members with information about selected criteria that might ulti-


mately play a role in an adopted plan. Several important decisions were made about the specification of the problem, and its representation in the SDSS. These decisions grew out of discussions about the geographical representation of the problem, the kinds of analyses that would be required, and the way in which the analyses would be implemented.

Geographical Representation

Different approaches for arriving at a solution to the AEA problem were originally considered by members of the Workgroup. A key difference between these approaches was the selection of an appropriate unit of analysis. One plan proposed the use of existing AEA regions as a set of building blocks from which the final solution would be constructed by merging existing regions. It was clear, however, that merging existing regions would lead to large distances between the new centers and the places which they serve, and this would translate into long travel times for providing student services. Because of this problem, and because school districts serve as a more meaningful level of aggregation in providing AEA services, we suggested that each school district be used as the basic tile of the analyses (Figure 3).

A base map was obtained from the State Board of Education which delineated the borders for each of the 433 school districts in the state as of 1989. This map was digitized so that maps showing the assignment of districts to regions could be produced for decision-makers. From this outline map, the centroid of each district was calculated to serve as a demand node. An area1 centroid, rather than one weighted by the internal distribution of pupils within each district was used because the coordinates of the locations of schools and their associated enroll-

ments were not available to us. These centroid coordinates were also used to compute distances among the districts. Although many methods for estimating distances have been developed, we adopted a Manhattan metric (Love et al., 1988, p. 5) because of the generally rectilinear config- uration of Iowa’s road network.

Demand Weights

Total public and private enrollment for each school district in 1988 was obtained from the State Board of Education and was used as the measure of demand. Enrollment is an appropriate measure because AEAs provide services not only to children, but also to teachers (and schools) whose numbers also are proportional to student enrollment. For the analyses, the enrollment weights were assigned to the school district centroids.

System Capabilities

The system is designed to allow decision-makers to explore their problem by examining the

results of analyses using different parameters of their decision criteria. Comparisons between solutions can be made either by visual inspection of two or more maps, or by depicting differences on a single map. In the latter case, for example, differences between the current assignment of school districts to AEA centers, and those which would result from a district being assigned to its closest (proximal) AEA can be shown (Figure 5). The software also allows decision-makers to make comparisons among different objectives. In a p-median solution (Figure 6) the 15 AEA centers are located such that the average distance between school districts and their nearest service center is minimized. In Figure 5 the service centers remain in their present location, whereas in Figure 6, in some cases the centers are shown in different locations.

As constraints are added to a solution, patterns of location also change. For example, the difference in the service areas of a p-median solution and the solution of the same centers with a

48 M. P Armstrong eta/.

FIGURE 5. Differences Between the Current AEA Plan and a Proximal Assignment of Districts to Their Nearest AEA Service Center.

minimum of 25,000 students in each area, show the school districts that would be served by a center other than their closest (Figure 7). The shaded areas represent districts transferred by the

FIGURE 6. A P-median Solution (p = 15) in Which Average Distance Between School Districts and Service Centers Is Minimized.


FIGURE 7. Difference Between the P-median Solution Shown in Figure 6 and One Which Has a Minimum Enrollment of 25,000 Students.

ADJUST algorithm from regions with more than 25,000 students (surplus regions) to deficit

regions with fewer than 25,000 students. Varying the criteria and constraints applied to the solution of a semi-structured problem can

be used to elucidate aspects of the problem which become important to the decision-maker only as the decision process progresses. The set of criteria form a solution space with the results of different analyses occurring at discrete points in this space. By examining the degree to which performance on one criterion is improved when another is allowed to become worse, decision-makers can make trade-offs between the two during the process of investigating the results of alternative solutions.

Sys tern Application

In July 1989, we met with the Iowa Department of Education’s Delivery System Structure Workgroup in Des Moines, where we described our approach and provided several real-time illustrations of the kinds of analyses that could be provided by the SDSS. The meeting began with a description of the capabilities of the SDSS, followed by a discussion about how the system could be applied by decision-makers to generate alternative solutions to the AEA problem. We explained that decision-makers could: (a) vary the number of candidate sites; (b) specify a maximum travel distance between AEA centers and the school districts they serve; (c) specify a minimum enrollment for the AEA service area; (d) define a set of places to be candidates for AEA service centers; (e) require some locations to be sites; and (f) allocate any or all specific

school districts to particular service centers. The dual computer setup (described earlier) was used during the demonstration to enable decision-makers to compare maps showing different


conjurations of regions and school districts assigned to each of the central office facilities. In some cases we used one computer to do the analyses while the other computer showed the results of an earlier analysis. in other cases we printed maps of the solutions.

After they had evaluated several analyses of the problem which they had requested prior to the meeting, and after studying and discussing these results, Workgroup members were able to see the kinds of solutions that were possible. During the meeting, members of the Workgroup asked for additional analyses in which different criteria and constraints were specified. Although they continued to wrestle with competing objectives and constraints, some of which proved to be mutually exclusive given the geographical dis~bution of children and places in Iowa, they were able to focus on the more highly structured aspects of the problem. At the close of the meeting the Workgroup voted unanimously to use the system to continue their search for a solution to the ABA geographical restructuring problem. We invited a subcommittee of the Workgroup to The Public Policy Center at The University of Iowa in September 1989 to spend a day discussing the problem, and to search for alternatives that might best meet their reorg~ization goals.

Before the September meeting numerous requests were formulated by the Workgroup. These requests were forwarded to us for analysis by the committee chair. As a result of their evaluations of these prelimin~y solutions to the problem, the criteria that the Work~oup were particularly interested in were:

1. Keeping distances travelled to provide services from becoming excessive; after seeing the long distances in many of the computed solutions, especially those for which minimum enrollment thresholds had been met (e.g., Figure 7), and believing that a staff member who traveled more than 100 miles in one work day would not provide sufficient service, many of them concluded that solutions which required travel beyond 50 miles from a center were unacceptable.

2. Having high enough enrollment, and therefore budget, to employ specialized staff to provide appropriate services; after seeing small numbers of students in some regions, especially in the western two-thirds of the state, many of them concluded that solutions in which there were fewer than 35,000 students in any region were unacceptable.

3. Minimizing change to the current system; after seeing that many of the solutions identified new places as regional centers and did not include some of the current regional centers in which large investments for facility expansion and improvement had been made, many of them concluded that it was important to find solutions in which some of the current regional centers would remain.

At the September meeting, a subcommittee of three persons used the SDSS during the course of a session that had a duration of approximately six hours. Again, a two-computer con- figuration was adopted so that solutions and displays could be generated concurrently. The hardcopy display and report generation capabilities of the system were used to facilitate discussion of the comparative merits of alternative solutions. Each iteration of the process took approximately 10 minutes, and therefore, the solution space could be iteratively examined in near-real-time. Committee members were encouraged to formulate requests or revise criteria using a standard form (Figure 8).

We began the session by providing one set of analyses in which the number of centers was varied while other factors were held constant, and another set, in which other factors were varied while the number of centers was held constant. As members of the work group began to formulate additional requests to explore the decision space, the number of regions became a key point of inquiry, and they discussed the relative merits of varying the number of regions between 9 and 12. Note, however, that even though the legislative mandate provided

Decision Support for Regionalization

Request for Analysis

Number of Centers

Fixed Centers

Distance Constraint

Minimum Enrollment

51

Fixed Assignments of School Districts to Centers

FIGURE 8. The Form Used to Request Analyses for the AEA Problem.

the option to reduce the number of regions to as low as four, this extreme reduction was not explored by the decision-makers at this meeting because they saw that travel costs and travel times would have become excessive. After evaluating several alternatives, the members of the Workgroup quickly reafftrmed that the minimum enrollment in a region, the maximum distance to services in a region, and the proportion of children farther than a given distance were important, and the remaining part of the session focused on these criteria and their interactions. For example, enrollment thresholds were applied to ensure that each region would have a large enough population to sustain a specialized, highly qualified staff.

Following the September meeting the Workgroup made two recommendations to the Department of Education. The first recommended 12 centers and regions with a minimum enrollment of 30,000 students; the second - the one later adopted by the Department and submitted to the Iowa Legislature for approval - recommended nine centers and regions with a minimum enrollment of 40,156 students (Figure 9). In this nine center regionalization, the five regions of eastern Iowa have smaller areas than the four regions in west and central Iowa. This reflects the higher population densities of the eastern part of the State. School districts in south- central Iowa, although farther from a service center than in the current system, would be served by centers with much larger enrollments than in the current system.

CONCLUSION

Better locational decisions by both public and private enterprises will lead to better service systems in the public sector and stronger enterprises in the private sector. These decisions can be supported by computer systems that are designed to provide information to decision-makers

M. I? Armstrong et al.

0 Proposed center - 30 miles

A straight line indicates the assgnment of o district to o center

FIGURE 9. The Solution Chosen by the AEA Workgroup.

about alternative solutions to locational problems. A spatial decision support system can be used to generate interesting alternatives that decision-makers can discuss as part of the process they use to define the problem to be solved. When evaluating alternatives, decision-makers dis-

cover new issues that must be considered during the decision-making process (Hopkins, 1984). The application of our system to the geographical reorganization of AEA regions in Iowa supports our contention that decision-makers are more likely to reach a consensus on a solution to their problem when they use an analysis system to generate a set of possible solutions and then evaluate the relative merits of each.

This SDSS approach represents an evolution of locational problem solving methods from one in which semi-structured problems are forced, prematurely, to be structured, to an interactive, iterative approach to problem definition, formulation and solution. The approach has

potential for application to a wide range of regionalization and location selection problems.

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