Dual-based heuristics for a hierarchical covering location problem

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.