A Goal Programming Approach for a Fuzzy SingleSource Capacitated Facility Location Problem In this paper, we present a new mixedinteger linear goal programming (MILGP) model for a fuzzy singlesource capacitated facility location problem (FSSCFLP), in which demands are considered as triangular fuzzy values and capacity of facilities are fuzzy constraints. At first, the basic fuzzy model for the given problem is presented. Then, utilizing goal programming (GP) approach and fuzzy principals the proposed MILGP model is introduced. Accordingly, considering a certain acceptable deviation from capacities and demands, the cost of selecting facilities and serving the demand points is minimized. Finally, to investigate the effectiveness of the presented model some largesized problems generated randomly and all of them are solved globally in a reasonable time.

Solving Capacitated Facility Location Problem Using Lagrangian Decomposition and Volume Algorithm In this research, we will focus on one variant of the problem: the capacitated facility location problem (CFLP). In many formulations of the CFLP, it is assumed that each demand point can be supplied by only one open facility, which is the simplest case of the problem. We consider the case where each demand point can be supplied by more than one open facility. We first investigate a Lagrangian relaxation approach. Then, we illustrate in the problem decomposition how to introduce tighter constraints, which solve the CFLP faster while achieving a better quality solution as well. At the same time, we apply the volume algorithm to improve both the lower and the upper bound on the optimum solution of the original problem for the large problem size.