Region-rejection based heuristics for the capacitated multi-source Weber problem
Computers and Operations Research
Computers and Operations Research
A review of recent advances in global optimization
Journal of Global Optimization
A guided reactive GRASP for the capacitated multi-source Weber problem
Computers and Operations Research
Computers and Operations Research
Journal of Global Optimization
Heuristics for the single source capacitated multi-facility Weber problem
Computers and Industrial Engineering
Beam search heuristics for the single and multi-commodity capacitated Multi-facility Weber Problems
Computers and Operations Research
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In this paper, we study the capacitated Euclidean andlpdistance location-allocation problems. There exists no global optimization algorithm that has been developed and tested for this class of problems, aside from a total enumeration approach. Beginning with the Euclidean distance problem, we design a branch-and-bound algorithm based on a partitioning of the allocation space that finitely converges to a global optimum for this nonconvex problem. For deriving lower bounds at node subproblems in this partial enumeration scheme, we employ two types of procedures. The first approach computes a lower bound via a projected location space subproblem. The second approach derives a significantly enhanced lower bound by using a Reformulation-Linearization Technique (RLT) to transform an equivalent representation of the original nonconvex problem into a higher dimensional linear programming relaxation. In addition, certain cut-set inequalities are generated in the allocation space, and objective function based cuts are derived in the location space to further tighten the lower bounding relaxation. The RLT procedure is then extended to the generallpdistance problem, forp 1. Computational experience is provided on a set of test problems to investigate both the projected location space and the RLT-lower bounding schemes. The results indicate that the proposed global optimization approach using the RLT-based scheme offers a promising viable solution procedure. In fact, among the problems solved, for the only two test instances available in the literature for the Euclidean distance case, we report significantly improved solutions.