A game theoretical for coordination of pricing, recycling, and green product decisions in the supply chain

Abstract

In order to increase profit of supply chain there are many powerful coordination tools such as: pricing, advertising, inventory management products and etc. Also, nowadays green products paid attention to the manufacturers, therefore effort has been made in this paper to study, through the non-cooperative game theory, a multi-product competitive 3-echelon supply chain with a specified demand function. The supply chain involves one manufacturer and multiple suppliers and retailers, in which the latter two compete horizontally while keeping the Nash equilibrium, but all the three compete vertically while maintaining the Stackelberg equilibrium based on the assumption that, in the market, the manufacturer is stronger. Aiming at coordinating the company's ordering, pricing, and green product decisions, the followers' KKT (Karush–Kuhn–Tucker) conditions are replaced by the model's lower level (i.e. a one-level nonlinear programming model is obtained from a bi-level one). Parameters that are more effective on the demand, price, and profit are determined through a numerical example. According to obtained results, if the retailers' market competition is increased, their profit will increase, but an increase in the suppliers' market competition will reduce theirs; the results also show that, with increasing competition in the market, the overall supply chain profit will increase.