C. Samuel Craig*
A Location Allocation Model for Facility Planning
in a Competitive Environment
During the past decade there has been a growing interest in the application of location allocation procedures for solving spatially structured combinatorial problems to determine optimal or desirable facility locations (Scott 1971, 1975; Sheppard 1974; Lea 1978;Leonardi 1981). These methods involve simultaneously selecting facility locations and assigning demand to those facilities to optimize some specified objective criteria. The well known “p-median”and “set covering” problems, for example, belong to this class of spatial optimization methods (Maranzana 1964; Toregas and Revelle 1972; Teitz and Bart 1968; Church and Revelle 1974). Location allocationmodels have been used in planning for: siting warehouses (Geoffrion 1975), corporate receivable collection systems (Cornuejols, Fisher, and Nemhauser 1977, emergency facilities (Toregas and Revelle 1972; Revelle et al. 1977), rural services (Fisher and Rushton 1977), urban public facilities (Revelle and Church 1977), retail facilities (Coelho and Wilson 1976; Zeller, Achabal, and Brown 1980) toname some. The ongoing interest in location allocation models reflects their flexibility in dealing with a variety of planning situations. While a large literature on location allocation models now exists, as Hakimi (1981)notes, existing models deal exclusively with noncompetitive situations. The effect of competitive facilities on locational performance is either ignored or assumed to be easilypredictable. Ignoring the competitive environment might not be a drawback for public facility locations, but the application of location allocation models to many private sector problems requires us to consider competition explicitly. In a competitive environment a location deemed desirable initially may become undesirable as competitors locate additional facilities in order to achieve their ownobjectives. It is necessary, therefore, to find facility locations that not only improve performance in the short run, but also protect performance from future competitive encroachment. The Hotelling spatial duopoly model of two vendors on a beach (Hotelling 1929) has been the basis of a number of studies on spatial competition. The problem has
*The authors wish to thank two anonymous reviewers andSara McLafTerty of Columbia University for helpful comments.
Avijit Ghosh is assistant professor, and C . Samuel Craig is associate professor, Graduate School of Business Administration, New York University. GeographicaZAnaZysis, Vol. 16, No. 1 (Jan. 1984) Q 1984 Ohio State University Press Submitted 3/83. Revised version accepted 8/83.
40 I Geographical Analysis
been extended to considermore than two participants (Shaked 1975; Eaton and Lipsey 1975) and reformulated as well into a game theoretic framework (Stevens 1961). Starting basically with Hotelling’s assumptions, Teitz (1968)determined the equilibrium locations of multiple firms operated by duopolists. For a linear market with uniform distribution of consumers, he developed the relationship between market share and theshare of outlets operated by each duopolist. More recently, Presscott and Visscher (1977) have presented a series of four models to study the locational organization in a linear market in which firms enter in sequence and use foresight in choosing their locations. Similarly, Eaton and Lipsey (1979) demonstrated how the adoption of market preemption strategies by early entrants affects’ long-runspatial equilibrium. Although these models are rich in their theoretical insights about spatial competition and have greatly enhanced our understanding of locational interdependence, they provide very little guidance for developing practical planning approaches to facility location in competitive environments. The purpose of this paper is to develop a location allocation model that deals explicitly...