Continuous Time Control of Make-to-Stock Production Systems

This study considers the problem of production control and stock rationing in a make-to-stock production system with multiple servers parallel production channels--, and several customer classes that generate independent Poisson demands. At decision epochs, in conjunction with the stock allocation decision, the control specifies whether to increase the number of operational servers or not. We both study the cases of exponential and Erlangian processing times and model the respective systems as M /M /s and M /Ek /s make-to-stock queues. We characterize properties of the optimal cost function, and of the optimal production and rationing policies. We show that the optimal production policy is a state-dependent base-stock policy, and the optimal rationing policy is of state-dependent threshold type. Furthermore, we propose a dynamic rationing policy for the systems with uncapacitated replenishment channels. The proposed policy utilizes the information on the status of the outstanding replenishment orders. This work constitutes a significant extension of the literature in the area of control of make-to-stock queues, which considers only a single server.