Sample average approximation approach to multi-location transshipment problem with capacitated production

We consider a supply chain, which consists of N stocking locations and one supplier. The locations may be coordinated through replenishment strategies and lateral transshipments, i.e., transfer of a product among locations at the same echelon level. The supplier has limited production capacity. Therefore, the total amount of product supplied to the N locations is limited in each time period. When total replenishment orders exceed total supply, not all locations will be able to attain their base stock values. Therefore, different allocation rules are considered to specify how the supplier rations its limited capacity among the locations. We team up the modeling flexibility of simulation with sample path optimization to address the multi-location transshipment problem. We solve the sample average approximation problem by random search and by gradient search. With this numerical approach, we can study problems with non-identical costs and correlated demand structures.