A Branch-and-Cut algorithm for the Single Source Capacitated Facility Location problem

Several Mixed Integer Linear Programming problems present a formulation based on a great number of knapsack constraints. Problems widely addressed in literature with this structure are, among others, Generalized Assignment, Multiple Knapsack, Bin Packing, Capacitated P-median and Single Source Capacitated Facility Location. In general knapsack constraints make these problems very hard to solve. The state of the art on these problems requires to use approaches besed on Lagrangean Relaxation or decomposition approaches like Dantzig-Wolfe and Column Generation tenchniques. In this paper, we present an approach based on the generation of general cutting planes of the polyhedron associated with each knapsack constraints. This approach yields a lower bound for the LP-relaxation that is the same obtained by the Dantzig-Wolfe decomposition and henceforth stronger than the LP-relaxation. We use this approach in the solution of the Single Source Capacitated Facility Location problem (SSCFLP) using a Branch-and-Cut algorithm. Computational experience is reported on a large set of test instances available in literature.