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.