An approach for solving maximal covering location problems with fuzzy constraints

Abstract

Several real-world situations can be modeled as maximal covering location problem (MCLP), which is focused on finding the best locations for a certain number of facilities that maximizes the coverage of demand nodes located within a given exact coverage distance (or travel time). In a real scenario, such distance as well as other elements of the location problem can be uncertain or linguistically (vaguely) defined by the decision maker. In this paper, we manage flexibility in the coverage distance through a fuzzy constraint. So, an extension of the original MCLP model is proposed, which is solved by using a parametric approach. Computational experiments have been conducted to analyze how the proposed model can be solved and what kind of information can be obtained to help a potential decision maker to take a more informed decision.

On the fuzzy maximal covering location problem

“…• The FMCLP extends the MCLP recently studied by Guzmán et al [18], in which which uncertain values are considered for distances and the coverage radius, but all other parameters, as well as the allocation decision variables z are crisp. • The FMCLP also extends the gradual covering location problem (GCLP) [9,5,6,4], also known as the general gradual cover decay location problem, which aims at finding a set of p facilities that maximize the total captured demand.…”

“…In fact, the MCLP has already been studied from a fuzzy perspective. In [18] the authors assume flexibility as for the coverage, which is modeled by means of fuzzy constraints, although it is assumed that the remaining input data are precisely known. The authors then apply a parametric approach to transform the fuzzy model into a series of parametric crisp models, which are solved using an iterated local search heuristic.…”

The continuous maximal covering location problem in large-scale natural disaster rescue scenes

“…Constraint (16) indicates that an RT can only be identified as covered when it is covered by a minimum of one CV.…”

“…Corrêa et al (2009) suggested the use of column generation and covering graph approaches to obtain competitive solutions for the probabilistic MCLP instances up to 818 vertices in reasonable computational time. Guzmán et al (2016) used a parametric approach to solve the fuzzy extension of the MCLP model, where they transformed the fuzzy model into several crisp problems using a decision parameter, and then solved the problems using classical optimization techniques. Heuristic algorithms were often applied for solving large scale MCLP problems where exact algorithms are not applicable, such as genetic algorithm (GA) (Zarandi et al, 2011), simulated annealing (SA) (Rabieyan and Esfandiari, 2011), variable neighborhood search (VNS) (Davari et al, 2013), particle swarm optimization (PSO) (Takaci et al, 2012), and hybrid algorithms (Ma et al, 2012;Davari et al, 2013) (2018) studied the maximum k-set coverage problem using the data streaming algorithm.…”

Greedy Reduction Algorithm as the Heuristic Approach in Determining the Temporary Waste Disposal Sites in Sukarami Sub-District, Palembang, Indonesia

“…SCLP nds the optimum number of TWDS to serve all demand points (Jeong, 2017) . MCLP aims to maximize the demand by a limited number of TWDS that can be served in standard time and p-median problem minimizes the distance between TWDS and sorts the routes (Guzmán et al, 2016) . The 𝜌-center problem is the min-max multi-centre problem (Du et al, 2020) .…”