On the fuzzy maximal covering location problem

Abstract

In this paper studies the maximal covering location problem, assuming imprecise knowledge of all data involved. The considered problem is modeled from a fuzzy perspective producing suitable fuzzy Pareto solutions. Some properties of the fuzzy model are studied, which validate the equivalent mixed-binary linear multiobjective formulation proposed. A solution algorithm is developed, based on the augmented weighted Tchebycheff method, which produces solutions of guaranteed Pareto optimality. The effectiveness of the algorithm has been tested with a series of computational experiments, whose numerical results are presented and analyzed.

Minmax regret maximal covering location problems with edge demands

“…Since there are m edges, r(x, y) has m addends, each one being a piecewise linear function with a constant number of pieces for each y ∈ P P and e ∈ E, (Theorem 3). Therefore, the optimal location of the facility with the objective of minimising the maximal regret is x ⋆ = [1, 2], 2 3 and the regret is r(x ⋆ ) = 13 9 . To highlight the usefulness of our max-regret approach, we also compute the optimal location for a deterministic version of the problem.…”

“…The gradual covering location problem is a generalized version of MCLP where the coverage area is divided in two sectors, one where the demand of nodes within it is completely covered and the other one where the demand is partially covered. An alternative way of considering uncertainty for the discrete MCLP is to use a fuzzy framework, as shown in Arana-Jiménez et al [2].…”

A Note on Two-Stage Fuzzy Location Problems Under VaR Criterion With Irregular Fuzzy Variables

“…For instance, Zhou and Liu [4] and Hosseininezhad et al [5] respectively discussed the capacitated location-allocation problem with fuzzy demands in discrete and continuous spaces. Arana-Jiménez et al [6] studied the maximal covering location problem, assuming all involved data to be imprecise knowledge and thus being presented as fuzzy numbers. In these studies, credibility and possibility measures, as well as chance constraint, fuzzy simulation, and α-cut methods, were usually adopted to formulate and solve the location problem.…”

Extended Maximal Covering Location and Vehicle Routing Problems in Designing Smartphone Waste Collection Channels: A Case Study of Yogyakarta Province, Indonesia

“…Several researchers have developed MCLPs. For example, Davari et al [31] developed a MCLP with fuzzy travel times; Arana-Jiménez et al [32] developed a fuzzy MCLP; Vatsa and Jayaswal ( [33,34]) modeled a capacitated multiperiod MCLP with server uncertainty; and Cordeau et al [9] introduced the MCLP algorithm to determine a subset of facilities, maximizing customer requests by considering budget constraints. A continuous MCLP was also developed by Yang et al [35] to optimize a continuous location of the cellular network's communication centers for natural disaster rescue.…”