Dynamic supply chain design with inventory

In this paper, we deal with a facility location problem where we build new facilities or close down already existing facilities at two different distribution levels over a given time horizon. In addition, we allow to carry over stock in warehouses between consecutive periods. Our model intends to minimize the total costs, including transportation and inventory holding costs for products as well as fixed and operating costs for facilities. After formulating the problem, we propose a Lagrangian approach which relaxes the constraints connecting the distribution levels. A procedure is developed to solve the resulting, independent subproblems and, based on this solution, to construct a feasible solution for the original problem.