Lagrangian relaxation heuristics for the uncapacitated single-source multi-product facility location problem

Facility location problem is one of the strategic logistical drivers within the supply chain which is a hard to solve optimization problem. In this study, we focus on the uncapacitated single-source multi-product production/distribution facility location problem with the presence of set-up cost. To efficiently tackle this decision problem, two Lagrangian-based heuristics are proposed one of which incorporates integer cuts to strengthen the formulation. Local search operators are also embedded within these methods to improve the upper bounds as the search progresses. Three sets of instances with various characteristics are generated and used to evaluate the performance of the proposed algorithms. Encouraging results are obtained when assessed against an ILP formulation using CPLEX. The latter is used for generating optimal solutions for small size instances and also as a means for producing upper and lower bounds for larger ones when restricted by a limited amount of execution time.