This article considers the base station deployment problem in a wireless network. The natural formulation of this problem usually leads to numerical and memory issues, preventing users from dealing with real‐world cases. We provide a compact reformulation that allows us to get beyond the drawbacks of the natural formulation. Tests are done on ten instances derived from realistic LTE scenarios. The computational results show that the proposed reformulation enables mixed‐integer programming solvers to provide an optimal solution in a short amount of time.

This paper analyzes the performance of five well-known off-the-shelf optimization solvers on a set of mixed-integer conic programs proposed for the congested capacitated facility location problem. We aim to compare the computational efficiency of the solvers and examine the solution strategies they adopt when solving instances with different sizes and complexity. The solvers we compare are Gurobi, Cplex, Mosek, Xpress, and Scip. We run extensive numerical tests on a testbed of 30 instances from the literature. Our results show that Mosek and Gurobi are the most competitive solvers, as they achieve better time and gap performance, solving most instances within the time limit. Mosek outperforms Gurobi in large-size problems and provides more accurate solutions in terms of feasibility. Xpress solves to optimality about half of the instances tested within the time limit, and in this half, it achieves performance similar to that of Gurobi and Mosek. Cplex and Scip emerge as the least competitive solvers. The results provide guidelines on how each solver behaves on this class of problems and highlight the importance of choosing a solver suited to the problem type.

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