Benders Decomposition Approach for Generalized Maximal Covering and Partial Set Covering Location Problems

Covering problems constitute a central theme in facility location research. This study extends the classical Maximal Covering Location Problem (MCLP) and Partial Set Covering Location Problem (PSCLP) to their generalized variants, in which each demand point must be simultaneously served by multiple facilities. This generalization captures reliability requirements inherent in applications such as emergency response and robust communication networks. We first present integer programming formulations for both generalized problems, followed by equivalent reformulations that facilitate algorithmic development. Building on these, we design exact Benders decomposition algorithms that exploit structural properties of the problems to achieve enhanced scalability and computational efficiency. Computational experiments on large-scale synthetic instances with up to 200,000 demand points demonstrate that our method attains more than a threefold speedup over CPLEX. We further validate the effectiveness of the proposed approach through experiments on a real-world dataset. In addition, we compare our method with a tabu search heuristic, and the numerical results show that within a fixed time limit, our method is generally able to identify higher-quality feasible solutions. These results collectively demonstrate both the effectiveness and the practical applicability of our approach for large-scale generalized covering problems.