Coordinating Pricing and Ordering Decisions in a Multi-Echelon Pharmacological Supply Chain under Different Market Power using Game Theory

The importance of supply chains in pharmacological industry is remarkable so that nowadays many pharmacological supply chains have an effective and critical role for supplying and distributing drugs in health area. So, this study studies a three-echelon pharmacological supply chain contained multi-distributor of raw materials, a pharmaceutical factory, and multi-drug distributors companies such that distributors of raw material, order raw materials of some drugs to own suppliers and sell them to the pharmaceutical factory. Then it transmutes raw materials to the several finished products and sells them to the some drug distributors companies. There are several types of raw materials and finished products.
Here, it is supposed that the market powers of partners are different. So, the Stackelberg game among the members of the chain is deemed to analyze the coordination behavior of the members of the proposed chain. The aim of the research is to maximize the total profit of supply chain by employing the optimal pricing and ordering decision policies where the order quantities of the distributors and the selling prices of pharmaceutical factory (manufacturer) and the distributors are the decision variables. Besides, the closed form solutions of the decision variables are presented. At the end, numerical example and some sensitivity analysis are presented.