M/M/1 Subcontracting Model

Optimal Control of a Dual Service Rate M/M/1 Production-Inventory Model
James R. Bradley, The Johnson School, Cornell University

Although the optimal policy structures of many dual-source inventory problems have been determined, these results do not allow for the study of the optimal policy values, and the resulting performance as the model parameters vary. We present a simple model that provides for such an analysis for a dual-source problem when demand is stochastic, and the base manufacturing capacity and the capacity of the alternate source are both limited. Specifically, we assume that the processing times at the primary manufacturing resource and the secondary resource are exponentially distributed. \ We make two technical contributions. First, we prove the structure of the optimal stationary control policy for our M/M/1 dual-source model. Second, we derive an exact closed-form expression for the optimal base stock, which to our knowledge is the first closed-form solution for a dual-source model. \ We also gain considerable practical insight into the effectiveness of a second source through a numerical study in which the optimal policies for the capacity level, inventory, and procurement from the second source are computed.