A Langrangean heuristic for a modular capacitated location problem

This paper considers the Modular Capacitated Location Problem (MCLP) which consists of finding the location and capacity of the facilities, to serve a set of customers at a minimum total cost. Each customer has an associated demand and the capacity of each potential location must be chosen from a finite and discrete set of available capacities. Practical applications of this problem can be found in the location of warehouses, schools, health care services or other types of public services. For the MCLP different mixed integer linear programming models are proposed. The authors develop upper and lower bounds on the problem's optimal value and present computational results with randomly generated test problems.