A multi-item multi-echelon inventory system with quantity-based order consolidation

The efficient management of a distribution system requires coordination between transportation planning and inventory control. Small and frequent shipments can reduce inventory levels while maintaining high customer service levels, but they increase unit transportation costs due to inappropriate utilization of the vehicles and more handling costs. On the other hand shipment consolidation policies reduce unit shipping cost because of economies of scale but they require higher inventory levels to maintain high service levels. Hence, it is of considerable interest to understand the trade-off between shipment consolidation policies and inventory levels. In this paper we consider a distribution network under a quantity based shipment consolidation policy, which means that all orders for a particular destination are held and shipped when a predetermined weight or volume is reached. The studied system is a divergent multi-item multi-echelon network with stochastic demand at the lowest echelon. The stockpoints are controlled by continuous review (s,Q) installation stock policies where the replenishment leadtime is dependent on the shipment consolidation policy. We derive approximations for the first two moments of the leadtimes, the reorder levels, the average inventory levels and the service levels which enables the evaluation of the relevant performance characteristics as well as the allocation of safety stocks for given target service levels. In a numerical study we test our approximations using computer simulation and we illustrate that the estimated service and inventory levels are close to the actual ones.