A Primal Approach To the Simple Plant Location Problem

TLDR: This work proposes a primal subgradient algorithm to solve the well-known strong linear programming relaxation of the problem, and shows that an optimal solution is discovered with high frequency.

Abstract: The most successful algorithms for solving simple plant location problems are presently dual-based procedures. However, primal procedures have distinct practical advantages (e.g., in sensitivity analysis). We propose a primal subgradient algorithm to solve the well-known strong linear programming relaxation of the problem. Typically this algorithm converges very fast to a point whose objective value is close to the integer optimum and where most of the decision variables have been fixed either to 0 or to 1. To fix the values of the remaining variables we use a greedy-interchange algorithm. Thus we propose thiss approach as a heuristic. Computational experience shows that an optimal solution is discovered with high frequency.