Toward More Realistic Allocation in Location—Allocation Models: An Interaction Approach

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Abstract
Location—allocation models jointly specify the optimal locations of service facilities and the allocation of patrons to them. Almost without exception, the allocation rule employed in these models has assumed that patrons wish to use the facility at the least travel cost away from them. Spatial interaction theory suggests that a person's travel behaviour is influenced by many other factors, among them differential facility attractiveness and uncertainty about travel costs, and that the least-cost allocation rule is unrealistic. This paper presents a location—allocation model employing an entropy-maximizing interaction model to allocate patrons to facilities. A heuristic solution procedure is proposed and found to be effective and reasonably efficient for small problems. Insofar as travel behaviour in the system is suboptimal, the location—allocation model produces suboptimal solutions. In the interests of providing realistic solutions to real-world problems, however, it is essential that planners accommodate the behaviour of those they plan for, be it normative or not.