An optimal algorithm for the multiproduct capacitated facility location problem with a choice of facility type

Consider a generalization of the multiproduct capacitated facility location problem in which each facility capacity has to be chosen from a given set of admissible levels. The objective is to select a set of facilities to open, along with their capacities, and to assign customer demands to them so as to minimize the total cost. In this model, in addition to a fixed cost for opening a facility, a fixed cost is incurred for each product that a facility is equipped to produce. Also, transportation costs are incurred for satisfying each customer’s requirement for a particular product at each chosen facility. Benders’ decomposition provides a natural partitioning of this model which defines a master problem for selecting a set of open facilities and equipment (or machines) and a subproblem in which the optimal assignment of demand to a specific facility is determined. A solution algorithm based on Bender’s decomposition is developed, implemented and applied to a numerical example to discuss the behavior of the cutting planes generated in Benders’ decomposition. Computational results of this algorithm are quite satisfactory and encouraging.