Multi-Location Transshipment Problem with Capacitated Transportation

The authors consider coordination among stocking locations through replenishment strategies that take explicitly into consideration transshipments, that is, transfer of a product among locations at the same echelon level. They incorporate transportation capacity such that transshipment quantities between stocking locations are bounded due to transportation media or the location's transshipment policy. They model different cases of transshipment capacity as a capacitated network flow problem embedded in a stochastic optimization problem. Under the assumption of instantaneous transshipments, they develop a solution procedure based on infinitesimal perturbation analysis to solve the stochastic optimization problem, where the objective is to find the policy that minimizes the expected total cost of inventory, shortage, and transshipments. Such a numerical approach provides the flexibility to solve complex problems. Investigating two problem settings, they show the impact of transshipment capacity between stocking locations on system behavior. They observe that transportation capacity constraints not only increase total cost, but also modify the inventory distribution throughout the network.