Journal
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
Volume 291, Issue 2, Pages 411-420Publisher
ELSEVIER
DOI: 10.1016/j.ejor.2019.07.070
Keywords
Inventory; Supply chain management; Consignment; Non-negative demand
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Inventory control is a crucial activity in supply chain management, with Vendor Managed Inventory (VMI) and Vendor Managed Inventory with consignment (VMCI) being common techniques. In VMCI, decisions are made in two steps by the vendor and retailer to maximize their expected profits, considering stochastic, additive, and price-sensitive customer demand.
Inventories are ubiquitous in nature and inventory control is a crucial activity undertaken in the supply chain (SC) by a company's management. The Vendor Managed Inventory (VMI) contract has become a common technique for supply chain management (SCM) since the 1980's. In this technique, the decision about how much inventory to hold is made by the vendor. In the paper, we consider VMI with consignment (VMCI). Consignment is a frequently used form of business arrangement, in which the vendor retains the ownership of the inventory and gets paid by the retailer on actual units sold. Under VMCI, decisions are made in two steps. In the first step, the vendor specifies a consignment price and an order quantity with the objective to maximize the vendor's expected profit. In the second step, the retailer chooses a retail price which maximizes the retailer's expected profit. The customer demand is assumed to be stochastic, additive and price-sensitive. Additive uncertainty can produce negative demand realizations, which may occur in adverse market conditions. We prove that in this case an optimal and possibly non-unique solution to VMCI exists. We calculate closed-form formulas for optimal quantities for uniformly distributed demand. Finally, we demonstrate our approach through a numerical example and we show that the imposition of a non-negativity constraint can cause a higher vendor's expected profit. (C) 2019 Elsevier B.V. All rights reserved.
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