A joint economic lot-sizing model for the hospital's supplier with capacitated warehouse constraint

In a vertically integrated supply chain of healthcare groups such as Chang Gung memorial hospitals in Taiwan, the vendor of special medical items and the hospitals are owned by the same business conglomerate; besides, warehouse capacity is one of the scarcest resources that greatly affect the inventory control policies. Taking the vendor's limited warehouse capacity into account, this article first proposes a generic joint economic lot sizing (JELS) model in determining the optimal production and shipment policy for a two-layer supply chain. The vendor manufactures the requested products in lots and delivers them in batches to the buyer with partial shipment policy. A threshold value which defines those existing JELS problems as a special case of our proposed model, while the manufacturer's warehouse capacity exceeds it, is attained. Finally, a numerical example is used to characterize the optimal production and replenishment lot-size decisions for the supply chain.