Optimal and heuristic algorithms for the multi-location dynamic transshipment problem with fixed transshipment costs

We consider centrally controlled multi-location systems, which coordinate their replenishment strategies through the use of transshipments. In a dynamic deterministic demand environment the problem is characterized by several locations, each of which has known demand for a single product for each period in a given finite horizon. We consider replenishment, transshipment and inventory holding costs at each location, where the first two have location-dependent fixed, as well as linear components, and the third is linear and identical to all locations. We prove that the resulting dynamic transshipment problem is NP-hard, identify a special structure which is satisfied by an optimal solution and develop, based on this structure, an exponential time algorithm to solve the problem optimally. In addition, we develop a heuristic algorithm, based on partitioning the time horizon, which is capable of solving larger instances than the optimal solution. Our computational tests demonstrate that the heuristic performs extremely well.