Inventory replenishment and inbound shipment scheduling under a minimum replenishment policy

An effective supply system for a vendor-managed inventory (VMI) warehouse requires collaboration between a supplier and a customer, and coordination between production and distribution functions. We study a dynamic lot-sizing model for production and inbound transportation to the VMI warehouse under a policy, based on mutual benefit of the supplier and the customer, that each replenishment quantity should be no less than a predetermined minimum size. To take advantage of economies of scale in replenishment operations as well as in shipment consolidation operations, the problem in this study assumes a concave replenishment cost structure in general for which optimal algorithms are presented. By computational experiments, we show that the most important parameter on the system is the minimum replenishment quantity. We also show that the minimum replenishment policy is successful only when large-size demands are guaranteed based on collaborations.