Inventory management in a base-stock controlled serial production system with finite storage space

We consider a serial production system controlled by the base-stock policy, in which customer demands must be satisfied immediately or it will be considered lost. Since the exact analysis is impossible for the general system, we present a phase-type approximation for a base-stock controlled serial production system. The numerical results indicate that this approximation provides good estimates for performance measures such as fill rate and mean queue-length distributions of each station. In addition, a cost model is constructed to determine the optimal base-stock level.