Dealing with edge length modifications in the maximal covering location problem on networks.

M. Baldomero Naranjo, J. Kalcsics, A. M. Rodríguez-Chía

In this work, we focus our research on the upgrading version of the maximal covering location problem with edge length modifications.
Let G = (V, E) be an undirected network with node set V, edge set E, and non-negative node weights. For each edge, we are given its current length and an upper bound on the maximal reduction of its length. Moreover, we are given the cost per unit of reduction for each edge, which can be different for each edge, and a total budget for reductions. The upgrading maximal covering location problem with edge length modifications aims at reducing the length of the edges in such a way that the maximal coverage is maximized, subject to the given budget for reductions. In this work, we formulate the problem as a mixed-integer program and we develop some strategies for making the formulation solvable in a shorter time. The performance of the proposed resolution method will be tested on a set of networks.

Keywords: Covering problems, networks, upgrading problems

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