An algorithm for the capacitated, multi-commodity multi-period facility location problem

There are substantial number of exact and heuristic solution methods proposed for solving the facilities location problems. This paper develops an algorithm to solve the capacitated, multi-commodity, multi-period (dynamic), multi-stage facility location problem. The literature on such composite facility location problem is still sparse. The proposed algorithm consists of two parts: in the first part branch and bound is used to generate a list of candidate solutions for each period and then dynamic programming is used to find the optimal sequence of configurations over the multi-period planning horizon. Bounds commonly known in the location literature as delta and omega are used extensively to effectively reduce the total number of transshipment subproblems needed to be solved. The proposed algorithm is particularly effective when the facility reopening and closing costs are relatively significant in the multi-period problem. An example problem is included to illustrate the proposed solution procedure.