Modeling Facility Location Problems as Generalized Assignment Problems

A variety of well-known facility location and location-allocation models are shown to be equivalent to, and therefore solvable as, generalized assignment problems (GAP's). (The GAP is a 0-1 programming model in which it is desired to minimize the cost of assigning n tasks to a subset of m agents. Each task must be assigned to one agent, but each agent is limited only by the amount of a resource, e.g., time, available to him and the fact that the amount of resource required by a task depends on both the task and the agent performing it.) The facility location models considered are divided into public and private sector models. In the public sector, both p-median and capacity constrained p-median problems are treated (In the p-median problem exactly p of n sites must be selected to provide service to all n. Each site has an associated weight, e.g., its population, and it is desired to minimize the weighted average distance between the n sites and their respective service sites. The capacity constrained p-median problem differs only in that there is an upper limit on the sum of the weights of the sites served by each service site.) In the private sector we consider both capacitated and uncapacitated warehouse location problems in which each customer's demands must be satisfied by a single warehouse. In addition, we show how certain types of constraints limiting the site and capacity combinations allowed can be incorporated into these models through their treatment as GAP's. An existing algorithm for the GAP is modified to take advantage of the special structure of these facility location problems, and computational results are reported.