Periodic Review Inventory Management with Contingent Use of Two Freight Modes with Fixed Costs

We study a stochastic inventory model of a firm, that sources the product from a make-to-order manufacturer, and can ship orders by a combination of two freight modes. The two freight modes differ in lead-times, and each has a fixed and a quantity proportional cost for each use. The ordering decisions are made periodically; however, the inventory holding and back-order penalty costs are incurred continuously in time. The decision of how to allocate units between the two freight modes utilizes information about demand during the completion of manufacturing. We derive the optimal freight mode allocation policy and show that the optimal ordering policy is not an (s,S) policy in general. We provide bounds for the optimal policy and perform a stationary analysis of the model assuming an (s,S) policy. We show that the best (s,S) policy achieves time average probability of being in-stock equal to the ratio of penalty cost rate and the sum of penalty cost rate and holding cost rate. We carry-out extensive numerical investigations of the properties of the optimal ordering policy and its benefits over the single freight policy, and show that the performance of best (s,S) policy is comparable to the optimal policy in most cases.