A Threshold-Satisfying Competitive Location Model

In this paper we consider a location model based on the threshold concept. We find the best location such that the probability of revenue falling short of the threshold is minimized. This objective is appropriate when a firm will not survive if its revenue falls below a known threshold. A new store is to be located. Demand is not deterministic but rather has a statistical distribution. We seek the location at which the probability that the revenue (expressed as market share attracted by the new store) is below a given threshold is minimized. The model is formulated and solved, and computational results are given.     

On the Logit Approach to Competitive Facility Location

The random utility model in competitive facility location is one approach for estimating the market share captured by a retail facility in a competitive environment. However, it requires extensive computational effort for finding the optimal location for a new facility because its objective function is based on a k -dimensional integral. In this paper we show that the random utility model can be approximated by a logit model. The proportion of the buying power at a demand point that is attracted to the new facility can be approximated by a logit function of the distance to it. This approximation demonstrates that using the logit function of the distance for estimating the market share is theoretically founded in the random utility model. A simplified random utility model is defined and approximated by a logit function. An iterative Weiszfeld-type algorithm is designed to find the best location for a new facility using the logit model. Computational experiments show that the logit approximation yields a good location solution to the random utility model.     

Optimal Facility Location in a One-Dimensional Spatial Market

This paper analyzes properties of the optimal spatial arrangement of what may be interpreted as a class of public facilities. Optimality is defined as cost minimization. Three different optimality criteria are considered, and for each, the necessary and, sufficient conditions, market area size, and production levels, are derived. The relationship between optimal production levels and number of facilities needed is also considered. Next the results of implementing various pricing strategies are analyzed with emphasis given to marginal and uniform pricing. It is shown that, given certain conditions, all facilities incur operating deficits, given marginal pricing. Estimates on the level of the deficits are derived in terms of location rents. Finally, in the appendix, several important results from other studies are derived as special cases of the basic model.     

Equity and Efficiency in Public Facility Location

In designing a system of urban public service centers, planners should consider both equity and efficiency effects in selecting the size of each center and the spacing between centers. The paper establishes theoretical and operational concepts for evaluating equity and efficiency, as affected by size and spacing alternatives. No objective means exists for determining the relative importance of equity and efficiency, so the decision, ultimately, is subjective. However, theoretical, empirical and simulation evidence indicate that equity is more sensitive than efficiency to the selection of size and spacing, within a wide range of alternatives. This suggests that the equity criterion is important in the design of public service systems, and deserves more attention in the public facility location literature than it has received in the past.     

A Model of Contiguity for Spatial Unit Allocation

We consider a problem of allocating spatial units (SUs) to particular uses to form "regions" according to specified criteria, which is here called "spatial unit allocation." Contiguity—the quality of a single region being connected—is one of the most frequently required criteria for this problem. This is also one that is difficult to model in algebraic terms for algorithmic solution. The purpose of this article is to propose a new exact formulation of contiguity that can be incorporated into any mixed integer programming model for SU allocation. The resulting model guarantees to enforce contiguity regardless of other included criteria such as compactness. Computational results suggest that problems involving a single region and fewer than about 200 SUs are optimally solved in fairly reasonable time, but that larger problems must rely on heuristics for approximate solutions. It is also found that a problem of any size can be formulated in a more tractable form when a fixed number of SUs are to be selected or when a certain SU is selected in advance.     

A Model for Location of Capacitated Alternative-Fuel Stations

Increased interest in alternative fuels is attributable, in part, to rising oil prices and increasing concern about global warming. A lack of a refueling infrastructure, however, has inhibited the adoption of alternative-fuel vehicles. Little economic incentive exists to mass-produce alternative-fuel vehicles until a network of stations exists that can refuel a reasonable number of trips. The flow refueling location model (FRLM) was developed to minimize the investment necessary to create a refueling infrastructure by optimizing the location of fueling stations. The original uncapacitated FRLM assumes that the presence of a refueling station is sufficient to serve all flows passing through a node, regardless of their volume. This article introduces the capacitated flow refueling location model that limits the number of vehicles refueled at each station. It also introduces a modified objective function maximizing vehicle-miles traveled instead of trips, applies both models to an intercity network for Arizona, and formulates several other extensions.     

Optimal Timing and Location in Competitive Markets

The choice of a good location strategy is one of the most crucial decisions facing a retailer. While a number of recent articles have addressed the issue of site selection, the related issue of optimal timing and preemption has been largely ignored. In this paper, we present an integrated location allocation model that allows a retailer to formulate an overall location strategy by addressing the questions of how many stores to open, where to open them, and when to open them. In addition, the model explicitly incorporates demand growth scenarios and takes into account the dynamics of competitive actions. As an illustration of its use, the model is applied to a simple yet realistic decision scenario.     

The Theory of Welfare Considerations in Public Facility Location Problems

The paper provides a general theoretical framework for analyzing the locational choice of public facilities from the point of view of social welfare. Spatial interactions of individuals and economies to scale in the public sector are taken into account, and that, in turn, adds another dimension to the set of alternatives facing the decision maker. His choice has to be made by considering size as well as space alternatives for the provision of the public service. The paper presents a theoretical structure for ranking those alternatives.     

Errors Caused by Rounded Data in Two Simple Facility Location Problems

As a rule, data to be used in locational analysis are either rounded up or rounded down. Therefore, error is incurred if such location data are used. The objective of this paper is to examine location error and cost error due to rounding in unweighted minisum and minimax problems in one-dimensional continuous space. Several conclusions on rounding effects are obtained by examining the respective mean-squared errors. First, rounding tends to exert more serious influence on the minisum problem than on the minimax problem. Second, in both location problems, the location error shows a pattern that is the inverse of that of the cost error.     

Aboriginal Participation in Environment Planning

The efforts to involve Aboriginal people in the development of a management plan for a newly created World Heritage Area (WHA) in northern Queensland are examined. Although the management agency expended considerable effort to encourage the participation of local Aboriginal people the program was flawed and served to marginalise some Aboriginal groups from the management of their traditional lands. The management agency failed to understand the nature of contemporary and traditional Aboriginal social organisation. Insensitivity to the diverse nature of Aboriginal social organisation, and ignorance of the complexity of Aboriginal representation, rendered the interests of some groups with traditional interests invisible to the management agency. Because the management agency uncritically accepted the claims to a mandate for regional representation by one Aboriginal lobby group, this group was able to assume a dominant position in liaising with the management agency.     

A Model for the Integration of Health and Nutrition Planning

The authors wish to thank UNICEF for sponsoring this study; Mr Rolv Moltu for suggestions during its preparation; and Mr A. Izmirlioglu who performed the computations for this final version in the University of Pittsburgh Computer Center.     

A Dynamic Location-Allocation Model for Evaluating the Spatial Impacts for Just-in-Time Planning

This paper presents an interperiod network storage location-allocation (INSLA) model to solve the just-in-time production planning problem. The model is extended to a multiobjective problem in which trade-offs between delivery time and transportation costs are analyzed. The results for a hypothetical problem show that in an attempt to reduce inventories on the part of the primary purchaser of raw materials, the possibility exists for less than optimal behavior in the system.