Dual-based heuristics for a hierarchical covering location problem

Authors:
Luis Gonzalo Acosta Espejo;Roberto D. Galvão;Brian Boffey
Affiliations:
Prog. Eng. Produção, COPPE/UFRJ, Caixa Postal 68507, 21945-970, Rio de Janeiro, Brazil;Prog. Eng. Produção, COPPE/UFRJ, Caixa Postal 68507, 21945-970, Rio de Janeiro, Brazil;Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 3BX, England, UK
Venue:
Computers and Operations Research
Year:
2003

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Abstract

A 2-level hierarchical extension of the maximal covering location problem is considered and an effective method for its solution developed. A combined Lagrangean-surrogate (L-S) relaxation is defined which reduces to a 0-1 knapsack problem. Tests were carried out using a subgradient-based heuristic incorporating the L-S relaxation, with the resulting knapsack problems being solved both with and without the integrality constraints relaxed. Results were obtained for test problems available in the literature ranging from 55-node to 700-node networks. These were compared, where possible, with exact results obtained using CPLEX. It was found that computing times were reasonable.