A Lagrangean relaxation heuristic for a two-stage capacitated facility location problem with depot size selection

In this paper, we study a variant of the two-stage capacitated facility location problem, a two-stage capacitated facility location problem with depot size selection. This problem is to open plants and depots, select depots' size, determine the product flows from the opened plants to the opened depots and the assignments of the customers to the opened depots for satisfying the customers' demands. The objective is to minimize the sum of the opening costs of the plants and the depots, the handling costs at the depots, the transportation costs and the assignment costs. For the problem, a Lagrangean relaxation heuristic is proposed to find a lower bound and an upper bound. 125 instances are randomly generated and tested to evaluate the performances of the Lagrangean relaxation heuristic. The computational results show that the Lagrangean relaxation heuristic is efficient and effective for our problem.