A multiperiod two‐echelon multicommodity capacitated plant location problem

In this paper we deal with a facility location problem where one desires to establish facilities at two different distribution levels by selecting the time periods. Our model intends to minimize the total cost for meeting demands for all the products specified over the planning horizon at various customer locations while satisfying the capacity requirements of the production plants and intermediate warehouses. We address this problem by means of a formulation as a mixed integer programming problem. A Lagrangean relaxation is proposed to solve the problem, together with a heuristic procedure that constructs feasible solutions of the original problem from the solutions at the lower bounds obtained by the relaxed problems. Computational tests are provided showing the good performance of this approach for a wide range of problems.