A bi-level programming approach to coordinating pricing and ordering decisions in a multi-channel supply chain

This paper investigates the Stackelberg equilibrium for pricing and ordering decisions in a multi-channel supply chain. We study a situation where a manufacturer is going to open a direct online channel in addition to n existing traditional retail channels. It is assumed that the manufacturer is the leader and the retailers are the followers. The situation has a hierarchical nature and is formulated as a bi-level programming problem. The upper level problem is a mathematical model dealing with decisions of the manufacturer, while the lower level is a Nash equilibrium model determining the retail prices and order quantities by formulating the competition between the physical retailers. We consider a price-sensitive linear demand model with an additive uncertain part and analyze the optimal decisions for each sales channel. To enable supply chain coordination, we propose a particular revenue-sharing contract. This contract enables the retailers to set pricing and ordering policies that are equivalent to those in an integrated supply chain.  Finally, we examine the impact of the model parameters on the equilibrium with a comprehensive numerical study.