The Multiperiod Location-Allocation Problem with Relocation of Facilities

A dynamic or multiperiod location-allocation formulation is developed from the static problem of locating G facilities among M possible sites to serve N demand points. This dynamic model provides a tool for analyzing tradeoffs among present values of static distribution costs in each period and costs of relocating facilities. The objective is to specify the plan for facility locations and relocations and for attendant allocations of demands which minimize these costs. Two methods of solution are presented. First, a mixed-integer programming approach is used to solve sample problems. From computational results reported for structurally-similar problems, it seems that efficient general purpose codes for this method would be capable of solving problems with at least 5 periods, 5 potential sites, and 15 demand points. The second method, dynamic programming, is capable of increasing the size of problems that are computationally feasible. The dynamic programming approach is quite attractive when the relative values of G and M restrict the state space to a manageable size and constraints on the extent of location changes in each period limit the number of alternate decisions. Possible extensions of the model and solution procedures are discussed.