A Closed-Loop Supply Chain Equilibrium Model with Random and Price-Sensitive Demand and Return

This paper proposes a decentralized closed-loop supply chain network model consisting of raw material suppliers, manufacturers, retailers, and recovery centers. We assume that the demands for the product and the corresponding returns are random and price-sensitive. Retailers and recovery centers face penalties associated with shortage demand and supply, respectively. We derive the optimality conditions of the various decision-makers, and establish that the governing equilibrium conditions can be formulated as a finite-dimensional variational inequality problem. The qualitative properties of the solution to the variational inequality are discussed. Numerical examples are provided to illustrate the effects of demand and return uncertainties on quantity shipments and prices.