Dual Sourcing Policy for a Continuous-Review Stochastic Inventory System

We study a continuous-review inventory system with dual sourcing modes and Brownian motion demand. The regular order is from one supplier at some constant rate with a low unit cost while the expedite order is from the other one with a fixed setup cost and an expensive unit cost. With usual holding/shortage cost, the system's objective is to choose a regular constant order rate and an expedite replenishment policy such that the long-run average cost is minimized. We show that the regular ordering rate must be strictly less than the expected demand rate and an optimal expedite ordering policy is the well-known $(s, S)$ policy. In particular, based on the theoretical analysis, we give a computational algorithm to demonstrate how to find the optimal regular ordering rate $\lambda^*$ and expedite policy parameters $s^*$ and $S^*$ . Finally, using the algorithm, we investigate the effects of system's parameters on the optimal policy parameters and value of dual sourcing by numerical studies.