Formulation and algorithms for the robust maximal covering location problem Amadeu A. Coco a,b,2 , Andréa Cynthia Santos b,4 , Thiago F. Noronha a,3 a DCC, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil b ICD-LOSI, Université de Technologie de Troyes, Troyes, France. Abstract Let N be the line-set and M be the column-set of a matrix {a ij }, such that a ij =1 if line i ∈ N is covered by column j ∈ M , or a ij =0 otherwise. Besides, let b j ≥ 0 be the benefit associated with a column j ∈ M . Given a constant T< |M |, the NP-Hard Maximal Covering Location Problem (MCLP) consists in finding a subset X ⊆ M with the maximum sum of benefits, such that |X |≤ T and every line in N is covered by at least one column in X . In this study, we investigate the min-max regret Maximal Covering Location Problem, a robust counterpart of MCLP, where the benefit of each column is uncertain and modeled as an interval data. The objective is to find a robust solution that minimizes the maximal regret over all possible combinations of values for the columns benefit. This problem has applications in disaster relief. We propose a MILP formulation, an exact and 2-approximation algorithms, and test them using classical instances from the literature. Keywords: Robust optimization, min-max regret, uncertain data, heuristics. 1 This work was partially supported by CNPq, CAPES, and FAPEMIG 2 Email: amadeuac@dcc.ufmg.br 3 Email: tfn@dcc.ufmg.br 4 Email: andrea.duhamel@utt.fr Available online at www.sciencedirect.com Electronic Notes in Discrete Mathematics 64 (2018) 145–154 1571-0653/© 2018 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm https://doi.org/10.1016/j.endm.2018.01.016