Multi-location transshipment problem with capacitated production and lost sales

We consider coordination among stocking locations through replenishment strategies that explicitly take into account lateral transshipments, i.e., transfer of a product among locations at the same echelon level. The basic contribution of our research is the incorporation of supply capacity into the traditional emergency transshipment model. We formulate the capacitated production case as a network flow problem embedded in a stochastic optimization problem. We develop a solution procedure based on infinitesimal perturbation analysis (IPA) to solve the stochastic optimization problem numerically. We analyze the impact on system behavior and on stocking locations' performance when the supplier may fail to fulfill all the replenishment orders and the unmet demand is lost. We find that depending on the production capacity, system behavior can vary drastically. Moreover, in a production-inventory system, we find evidence that either capacity flexibility (i.e., extra production) or transshipment flexibility is required to maintain a certain level of service.