Joint optimization of production, transportation and pricing policies of complementary products in a supply chain

•Joint optimization of production, inventory, transportation and pricing policies in a two-stage supply chain is obtained.•Exact algorithms are presented using mathematical and convexity analysis to solve mixed integer nonlinear models.•The purchasing price between supply chain members can be used as a coordination mechanism.•The profit of centralized SC is more stable compared to decentralized SC when the dependency rate of products changes.

In this paper, we consider the joint optimization of production, inventory, transportation and pricing policies in a multi-product two-stage supply chain. The products are complementary and their demands are not only dependent on their own price but also on their complementary product price. Mathematical model of the problem is presented in both centralized and decentralized supply chains. Exact algorithms are presented using mathematical and convexity analysis to solve mixed integer nonlinear models. Numerical studies show that the profit of centralized supply chain is more stable compared to decentralized supply chain when the dependency rate of products changes.