Analysis of Serial Supply Chains with a Service Constraint

We consider an N -stage serial supply chain with random demand, and study the problem of minimizing average inventory-holding cost subject to a pre-specified fill-rate constraint. Since the form of the optimal policy is unknown, we focus on base-stock policies. We present a bottom-up recursive procedure for policy evaluation and develop bounds on the optimal basestock levels. Using these bounds, an efficient algorithm is devised to compute the optimal base-stock policy. We also discuss the connection between the service-constrained model and the model using a backorder cost. Based on this connection, we construct a simple, closed-form heuristic, which can be obtained from solving 2N separate newsvendor models with the original problem data. Numerical results indicate that the heuristic is quite effective. Examining the expressions of the heuristic allows us to gain various managerial insights, such as 1) how the optimal base-stock levels change when system parameters change, and 2) which stage is the most effective stage for process improvement. Finally, we discuss how to implement the optimal policy in a decentralized control environment.