Optimal Control of Serial, Multi-Echelon Inventory/Production Systems with Periodic Batching

We consider a single-item, periodic-review, serial, multi-echelon inventory system, with linear inventory holding and penalty costs. In order to facilitate shipment consolidation and capacity planning, we assume the system has implemented periodic batching: each stage is allowed to order at given equidistant times. Further, for each stage except the most downstream one, the reorder interval is assumed to be an integer multiple of the reorder interval of the next downstream stage. This reflects the fact that the further upstream in a supply chain, the higher setup times and costs tend to be, and thus stronger batching is desired. Our model with periodic batching is a direct generalization of the serial, multi-echelon model of Clark and Scarf (1960). For this generalized model, we prove the optimality of basestock policies, we derive Newsboy-type characterizations for the optimal basestock levels, and we describe an efficient exact solution procedure for the case with mixed Erlang demands. Finally, we present extensions to assembly systems and to systems with a modified fill rate constraint instead of backorder costs. Subject classification: Inventory/Production: Multi-echelon, stochastic demand, periodic batching, opti-