Edge covering with continuous location along the network
The set covering problem is to find the minimum cardinality set of locations to site the facilities which cover all of the demand points in the network. In this classical problem, it is assumed that the potential facility locations and the demand points are limited to the set of vertices. Although t...
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doaj-ba308e4feb724892929bd149e8b74af92020-11-25T03:15:05ZengGrowing ScienceInternational Journal of Industrial Engineering Computations1923-29261923-29342020-06-0111462764210.5267/j.ijiec.2020.4.002Edge covering with continuous location along the network Kayhan AlamatsazAli Aghadavoudi Jolfaei Mehdi IranpoorThe set covering problem is to find the minimum cardinality set of locations to site the facilities which cover all of the demand points in the network. In this classical problem, it is assumed that the potential facility locations and the demand points are limited to the set of vertices. Although this problem has some applications, there are some covering problems in which the facilities can be located along the edges and the demand exists on the edges, too. For instance, in the public service environment the demand (population) is distributed along the streets. In addition, in many applications (like bus stops), the facilities are not limited to be located at the vertices (intersections), rather they are allowed to be located along the edges (streets). For the first time, this paper develops a novel integer programming formulation for the set covering problem wherein the demand and facility locations lie continuously along the edges. In order to find good solutions in a reasonable time, a matheuristic algorithm is developed which iteratively adds dummy vertices along the edges and solves a simpler problem which does not allow non-nodal facility locations. Finally, a Benders decomposition reformulation of the problem is developed and the lower bounds generated by the Benders algorithm are used to evaluate the quality of the heuristic solutions. Numerical results show that the Benders lower bounds are tight and the matheuristic algorithm generates good quality solutions in short time.http://www.growingscience.com/ijiec/Vol11/IJIEC_2020_8.pdfedge coveringunrestricted facility locationmathematical formulationbenders decompositionmatheuristic |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Kayhan Alamatsaz Ali Aghadavoudi Jolfaei Mehdi Iranpoor |
spellingShingle |
Kayhan Alamatsaz Ali Aghadavoudi Jolfaei Mehdi Iranpoor Edge covering with continuous location along the network International Journal of Industrial Engineering Computations edge covering unrestricted facility location mathematical formulation benders decomposition matheuristic |
author_facet |
Kayhan Alamatsaz Ali Aghadavoudi Jolfaei Mehdi Iranpoor |
author_sort |
Kayhan Alamatsaz |
title |
Edge covering with continuous location along the network |
title_short |
Edge covering with continuous location along the network |
title_full |
Edge covering with continuous location along the network |
title_fullStr |
Edge covering with continuous location along the network |
title_full_unstemmed |
Edge covering with continuous location along the network |
title_sort |
edge covering with continuous location along the network |
publisher |
Growing Science |
series |
International Journal of Industrial Engineering Computations |
issn |
1923-2926 1923-2934 |
publishDate |
2020-06-01 |
description |
The set covering problem is to find the minimum cardinality set of locations to site the facilities which cover all of the demand points in the network. In this classical problem, it is assumed that the potential facility locations and the demand points are limited to the set of vertices. Although this problem has some applications, there are some covering problems in which the facilities can be located along the edges and the demand exists on the edges, too. For instance, in the public service environment the demand (population) is distributed along the streets. In addition, in many applications (like bus stops), the facilities are not limited to be located at the vertices (intersections), rather they are allowed to be located along the edges (streets). For the first time, this paper develops a novel integer programming formulation for the set covering problem wherein the demand and facility locations lie continuously along the edges. In order to find good solutions in a reasonable time, a matheuristic algorithm is developed which iteratively adds dummy vertices along the edges and solves a simpler problem which does not allow non-nodal facility locations. Finally, a Benders decomposition reformulation of the problem is developed and the lower bounds generated by the Benders algorithm are used to evaluate the quality of the heuristic solutions. Numerical results show that the Benders lower bounds are tight and the matheuristic algorithm generates good quality solutions in short time. |
topic |
edge covering unrestricted facility location mathematical formulation benders decomposition matheuristic |
url |
http://www.growingscience.com/ijiec/Vol11/IJIEC_2020_8.pdf |
work_keys_str_mv |
AT kayhanalamatsaz edgecoveringwithcontinuouslocationalongthenetwork AT aliaghadavoudijolfaei edgecoveringwithcontinuouslocationalongthenetwork AT mehdiiranpoor edgecoveringwithcontinuouslocationalongthenetwork |
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