Vendor and retailer managed consignment inventory with additive price–dependent demand

Abstract

Consignment is the shifting of the inventory ownership to the supplier. In this form of business arrangement the supplier places goods at a customer’s location without receiving payment, until the goods are sold. We consider a single period supply chain model, where the supplier contracts with the retailer. Market demand for the product is price–dependent and uncertain. The supplier decides the consignment price and the retailer chooses the retail price for each unit sold. Two arrangements called retailer managed consignment inventory (RMCI), and vendor managed consignment inventory (VMCI) are studied. The only difference between these arrangements is that under RMCI contract the retailer is allowed to choose the service level, and under VMCI contract the supplier decides about this service level. In our paper we give the optimal solutions for the retail price, the service level and the consignment price in closed–form, which maximize the expected profit of the retailer or the supplier under both consignment regimes. We consider the additive demand linearly dependent on price. We also illustrate the solutions by a numerical example, which explains the general results well.