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

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 generally recognized as a Cobb- Douglas demand function in the available studies. The authors developed a Stackelberg game theoretic model for examining vendor-managed inventory supply chain performance in terms of combined profit. The aim was 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. The problem was formulated as NLP models while two different contracts including wholesale price and two-part tariff were also taken into consideration. Using some benchmark data, the authors compared such contracts and illustrated how they can optimize the performance of VMI-type supply chains. Results of the numerical experimental study show that the wholesale price is more beneficial to all supply chain members under specific conditions. Sensitivity analyses of the model’s parameters are also performed to assess the impacts of changes on the performance of supply chain.