David A. Schilling

Multiobjective analysis of facility location decisions

Abstract The study of facility siting decisions has a long and extensive history. As this area of research has evolved, there has been increasing recognition that the complexity of these problems is such that they often have more than one objective. For this paper, we reviewed the broad and multidisciplinary literature of location analysis to uncover the scope of research that has examined the multiobjective aspects of this problem domain. In all, 45 papers were found in a total of 20 journals. Four broad categories of objectives were uncovered. The largest category was, not unexpectedly, cost minimization, which included distance minimization. The second most common category was for demand-oriented objectives which included demand coverage and demand assignment. Only about ten percent of the articles included objectives in either of the last two categories. Profit maximization was one of these while objectives addressing environmental concerns comprised the other. Structurally, the models studied typically reflected the general population of single objective location models. That is, quite often they were siting multiple uncapacitated facilities among a set of discrete, finite location alternatives with deterministic parameters over a single planning period.

Equity measurement in facility location analysis: A review and framework

Abstract In selecting sites for facilities, especially in the public sector, the issue of equity is becoming increasingly important. Beginning with the work of Mumphreys et al. (1971), McAllister (1976), and Savas (1978), a substantial literature has developed that incorporates equity in facility siting decision models. Despite this level of interest, however, there has been little agreement in these models as to how equity should be measured. Further, except for some recent works, there has generally been little comparison of alternative measures, or assesment of their relative value, let alone any consensus on the best measure(s) to use. Perhaps even more surprising is the great number and variety of measures employed. The motivation for this paper is to address these problems and provide for researchers a base from which issues of equity can be included in facility siting models. More specifically, we seek to review the equity literature as it pertains to facility location, assemble the set of measures that have been developed, and introduce a framework and common notation for organizing them. We also will discuss approaches that can be used to select an appropriate measure of equity.

An efficient tabu search procedure for the p-Median Problem

Abstract In this paper we present a new solution heuristic for the p-Median Problem. The algorithm is based on tabu search principles, and uses short term and long term memory, as well as strategic oscillation and random tabu list sizes. Our proposed procedure is compared with two other move heuristics: a well-known interchange heuristic and a recent hybrid heuristic. In computational tests on networks ranging in size up to 500 nodes the new heuristic is found to be superior with respect to the quality of solutions produced.

The median tour and maximal covering tour problems: Formulations and heuristics

Abstract In this paper, the authors introduce two bicriterion routing problems: the median tour problem (MTP) and the maximal covering tour problem (MCTP). In both problems the tour must visit only p of the n nodes on the network. In addition, both problems have as one of their objectives the minimization of total tour length. The second objective in both problems maximizes access to the tour for the nodes not directly on it. In the MTP, the access objective is the minimization of the total travel distance necessary for demand at the nodes to reach their nearest stop on the tour. In the MCTP, the access objective is to maximize the total demand within some prespecified maximal travel distance from a tour stop. It is shown that the MCTP may be viewed as a special case of the MTP; consequently, solution procedures developed for the MTP may also be employed to solve the MCTP. Unfortunately, both problems are NP-hard. In addition, the number of efficient solutions may grow exponentially with the number of nodes in the particular problem instance. Consequently a heuristic procedure is developed to generate a good approximation of the efficient frontier. Not only does this approximation provide the decision marker with insight into the magnitudes of the inherent tradeoffs between the two objectives, but it also provides him or her with a set of feasible options to consider. Computational experience, on a realistically scaled problem, is provided. Applications of the problems include the design of mobile service delivery systems (e.g. healthcare delivery in rural areas of developing countries), bi-modal transportation systems (e.g. overnight mail delivery), and distributed computer networks, among others.

Some models for fire protection locational decisions

Abstract A number of new location models which utilize the notion of coverage were developed in a study of the Baltimore City Fire Protection system. These models augment the typical analysis to include: • - Multiple performance criteria such as population and property value coverage, • - Relocation of a given number of existing facilities, and • - Allocation of equipment to facilities.

Heuristic concentration and Tabu search: A head to head comparison

Earlier this year two papers applying the metaheuristics Tabu search (TS) and Heuristic concentration (HC) to the p-median problem were published in consecutive volumes of this journal. Here we apply the method of HC to some of the data sets which were used for computational experience in the paper on TS. For these examples, which we regard as being of a particularly challenging character, HC discovers the superior solution (superior to TS) in about 95% of the cases, and, where the optimal solution is known, the optimal solution in about 80% of the cases. No general conclusion on the relative times for the two approaches can be drawn.

An approach to the display and analysis of multiobjective problems

Abstract In all operations research applications, the problem of implementation rests on the information conveyed to the decision maker. The presentation of results is a critical link in the success of a project. An ineffective transfer of information will reduce the chance of decision maker acceptance. This final step in the analysis is particularly difficult in multiobjective analyses, where the amount of relevent information increases with each performance measure. This paper will describe an alternative to the typical graphical approach to multiobjective display, which is adaptable to any number of objectives. A real world example is given and some theoretical insights are developed.

Design and implementation of decision support systems in the public sector

This article examines the implications of utilizing decision support systems (DSS) in the public sector based on a DSS developed and implemented for a community mental health system. The DSS includes a multiple objective (goal programming) allocation model and encompasses a multiple party decision process. The experiences and insights acquired during the development and implementation of this DSS are relevant to public sector decision support in general. The importance of a DSS as a process-support aid rather than a product-oriented aid (i.e., simply providing answers) and the interaction of system architecture and the chosen design strategy are key insights. In particular, the distinction between model-oriented and data-oriented DSS does not appear to be appropriate. The public sector decision makers concern with issues of equity requires the ability to operate in a higher dimensional framework than the typical spreadsheet model and there is a critical need for communication support.

A gamma heuristic for the p-median problem

Heuristic concentration (HC) is a two-stage metaheuristic that can be applied to a wide variety of combinatorial problems. It is particularly suited to location problems in which the number of facilities is given in advance. In such settings, the first stage of HC repeatedly applies some random-start interchange (or other) heuristic to produce a number of alternative facility configurations. A subset of the best of these alternatives is collected and the union of the facility sites in them is called a concentration set (CS). Among the component elements of the CS are likely to be included those sites which are members of the optimal solution. In earlier studies the second stage of HC has consisted of an exact procedure to extract the best possible solution from the CS. In this paper we demonstrate, for the p-median problem, the use of two sequentially active heuristics in the second stage of HC. That is, we offer two additional layers of heuristics to improve solutions which are found in the first stage of HC. Thus we are describing a variant of the HC metaheuristic consisting of three layers of heuristics which are utilized in sequence. We propose for this procedure the name of Gamma Heuristic.

The capacitated maximal covering location problem with backup service

The maximal covering location problem has been shown to be a useful tool in siting emergency services. In this paper we expand the model along two dimensions — workload capacities on facilities and the allocation of multiple levels of backup or prioritized service for all demand points. In emergency service facility location decisions such as ambulance sitting, when all of a facilitys resources are needed to meet each call for service and the demand cannot be queued, the need for a backup unit may be required. This need is especially significant in areas of high demand. These areas also will often result in excessive workload for some facilities. Effective siting decisions, therefore, must address both the need for a backup response facility for each demand point and a reasonable limit on each facilitys workload. In this paper, we develop a model which captures these concerns as well as present an efficient solution procedure using Lagrangian relaxation. Results of extensive computational experiments are presented to demonstrate the viability of the approach.