Application of multidivisional bi-level programming to coordinate pricing and inventory decisions in a multiproduct competitive supply chain

This study concerns the coordination of pricing and inventory decisions in a multiproduct two-stage supply chain that consists of one manufacturer and multiple retailers within a competitive environment. The retailers order some substitutable products from a common manufacturer. It is assumed that channel members have different market power. The purpose of this paper is to coordinate pricing and inventory decisions such that utility of all involved levels (manufacturer and retailers) is met. Hence, a nonlinear multidivisional bi-level programming model is developed. This model considers both retailers and manufacturer when deciding about the pricing and production volume (for manufacturer) or amount of purchase (for retailers). A hybrid of genetic algorithm (GA) and local search method is proposed to solve the nonlinear bi-level model. This model is reduced to a nonlinear programming by replacing the Karush-Kuhn-Tucker (KKT) conditions of followers to the lower level of the model. Then, the obtained single-level model is relaxed to a linear model to achieve an upper bound (UB). Finally, a numerical example is presented to analyze which parameters have more effect on the price, lot size and, consequently, on the profit. Results show that increasing the market scale parameter of the manufacturer increases the profit of the manufacturer, but the market scale parameter of retailers has no effect on the manufacturer's profit, although it increases the retailers' profit.