A new hybrid approach to discrete multiple facility location problem

Locating certain facilities in predetermined sites is named the multiple facility location problems (MFLP). The objective of these kinds of problems is locating facilities to serve a given set of customers so that candidate sites and requirements are known. When the new facility sites have to be selected from a given set of candidate sites, the mentioned location problem becomes a discrete multiple facility location problem (DMFLP). In this paper, a special approach of DMFLP is considered where different multiple facilities have to be placed (location decision) and also customers have to be assigned to these facilities (allocation or assignment). The mathematical model of the proposed problem is developed, and with respect to the complexity of solving the mathematical model, especially in large scale, a new hybrid approach is proposed based on tabu search algorithm to solve the problem at each scale. Computational results on several randomly generated problems in comparison with a new proposed lower bound obtained from Lagrangian relaxation indicate that the proposed hybrid approach is both accurate and efficient.