price changing and inventory sharing in supply chain management

The main task of supply chain management is to balance efficiency and effectiveness. Numerous operational management strategies are used to make a supply chain efficient, one such is inventory management. In this paper, we will consider a particular part of a supply chain consisting comprising a manufacturer and a retailer with the goal of minimizing associated inventory costs. We will focus on an inventory of final products determined as the difference between supply and demand and are expressed as a function of price, inflation rate and change in inflation rate resulting in the possible speculations. The manufacturer’s inventory cost is a function of these same variables, with the retailer’s inventory cost having the same function in addition to the margin. The problem is formulated as a dynamic game to share the speculation problem. The optimization problems to be solved are optimal control theory problems with objective functions in the form of integral functional with the integrand depending on the state function and its first and second derivative.