A cross decomposition algorithm for a multiproduct-multitype facility location problem

A generalization of capacitated facility location problem is considered. This problem involves a system with a choice of various facility types where several different products are required by customers. Each facility type offers a different capacity on a particular product with different fixed set-up costs. This is called a multiproduct-multitype facility location problem with a choice of facility types. The solution algorithm developed in this paper unifies Benders decomposition and Lagrangean relaxation into a single framework that involves successive solutions to a Benders (primal) subproblem and a Lagrangean (dual) subproblem. Computational results of this algorithm are quite satisfactory and encouraging.