Optimal Policies for Multi-Echelon Inventory Problems with Batch Ordering

Abstract
In many production/distribution systems, materials flow from one stage to another in fixed lot sizes. For example, a retailer orders a full truckload from a manufacturer to qualify for a quantity discount; a factory has a material handling system that moves full containers of parts from one production stage to the next. In this paper, we derive optimal policies for multi-stage serial and assembly systems where materials flow in fixed batches. The optimal policies have a simple structure, and their parameters can be easily determined. This research extends the multi-echelon inventory theory in several ways. It generalizes the Clark-Scarf model by allowing batch transfers of inventories. Rosling (1989) shows that assembly systems can be interpreted as serial systems under the assumption that there are no setup costs. We show that the series interpretation still holds when materials flow in fixed batches which satisfy a certain regularity condition. Finally, Veinott (1965) identifies an optimal policy for a single-location inventory system with batch ordering. This paper generalizes his result to multi-echelon settings.