Replenishment and transshipment in periodic-review systems with a fixed order cost

Small businesses with many stocking locations face high ordering costs and imbalanced inventories. To address those challenges, we consider an inventory system of multiple retailers: each has Poisson demand and backorders are permitted. They order together periodically and there is an opportunity to transship available inventory between retailers in each order cycle. Each order incurs a fixed cost, and there is a variable transshipping cost, a holding cost for inventory, and a penalty cost for backorders. The system aims to determine a feasible ordering and transshipping plan which minimizes the long-run average total cost over time. We provide an analytical approach to evaluating costs, construct bounds to search for the optimal order interval, order-up-to level, and timing of transshipment, and determine the amounts to transship based on a marginal cost. Our numerical studies find that, first, the optimal order interval is between that in the no-transshipment case and an EOQ-like calculation. Second, the optimal timing of transshipments is in the middle of an order cycle or a little later. Third, the optimal order interval and timing of transshipments are insensitive to the introduction of differences between retailers. Fourth, transshipment effectively reduces costs, especially when transshipment costs are low or different between retailers. These findings can simplify the task of cost optimization in complex inventory systems and develop practical measures to further reduce costs.