The Stackelberg Game Model for Vendor-managed Inventory Systems: A Wholesale Price Versus a Two-part Tariff Contract

Document Type: Research Paper


1 Department of Industrial engineering, Yazd University Yazd Iran

2 Yazd University


This paper investigates the issue of replenishment coordination for a two-echelon supply chain with one manufacturing vendor and multi retailers under vendor-managed inventory mode of operation. The demand is influenced by the retail price and market scale which generally recognized as a Cobb- Douglas demand function in the available studies. Authors developed Stackelberg game theoretic model for examining vendor-managed inventory supply chain performance in terms of combined profit. The aim is to find the wholesale and retail price, the replenishment interval of the retailers, and the fraction backlogging so as to the combined profit of supply chain being optimized. Authors formulates the problem as NLP models while two different contracts including wholesale price and two-part tariff are also being taken into consideration. Using some benchmark data, authors compared and illustrated how such contracts can optimize the performance of VMI-type supply chains. Results from numerical experimental study show that the wholesale price is more benefitting to all supply chain members under specific conditions. Moreover, sensitivity analyses on model’s parameters are performed to assess the impacts of changes on the performance of supply chain.