Continuous Review Inventory Model with Dynamic Choice of Two Freight Modes with Fixed Costs

We analyze a continuous review (Q, r) stochastic inventory model in which orders placed with a make-to-order manufacturer can be shipped via two alternative freight modes differing in lead time and costs. The costs of placing an order and using each freight mode consist of fixed components and hence exhibit economies of scale. We derive an optimal policy for using the two freight modes for shipping each order. This freight-mode decision is delayed until manufacturing is complete and the optimal policy uses information about the demand incurred in the meantime. Furthermore, given that the two freight modes are used optimally for shipping each order, we solve our model for reorder point and order quantity that minimizes cost. We analyze the cost savings achieved from postponing the freight-mode decision and provide analytical and numerical comparisons between the solutions to our two-freight model and single-freight models. Finally, we illustrate the properties of the solution to our model using an extensive set of numerical examples.