Continuous-Review (R, nQ) Policies for Inventory Systems with Dual Delivery Modes

Abstract

We study a continuous-review, infinite-horizon inventory system with compound Poisson demand and dual sourcing/delivery modes. Ordering from either source/mode incurs a fixed cost and the expedited mode provides a shorter lead time than the regular mode. As the optimal ordering policy is unknown, while expected to be very complicated, we propose a class of simple policies called single-index (R, nQ) policies—when ordering from each mode, based on the inventory position, the system follows an (R, nQ)-type of policy. We provide an exact procedure to compute the expected long-run average cost. Specifically, we first analyze the steady-state distribution of the inventory position, which is found to be no longer uniform in general as in the classic (R, nQ) inventory system where only one delivery mode is available. We then develop a recursive procedure, which overcomes the order-crossing effect, to determine the steady-state distribution of the inventory level. Two simple heuristics for computing near-optimal policy parameters are provided. For a special case where ordering from the regular mode incurs no fixed cost and follows a base-stock policy, we derive closed-form solution bounds by applying normal approximation. To assess the performance of the single-index (R, nQ) policy, we further study a more complicated class of policies called dual-index (R, nQ) policies and numerically illustrate that the simpler single-index policy performs close to the dual-index policy. Finally, the performance of the single-index policy is also shown comparable to the policy computed via dynamic programming.