Location-Routing Problem of Emergency Facilities under Uncertain Demand by Branch-Price and Cut

This paper studies the location-routing problem of emergency facilities with time window under demand uncertainty. We propose a robust mathematical model in which uncertain requirements are represented by two forms: the support set defined by cardinal constraint set. When the demand value of rescue...

Full description

Saved in:
Bibliographic Details
Main Author: Xuchen Deng
Format: Article
Language:English
Published: Wiley 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/9152989
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832566439564804096
author Xuchen Deng
author_facet Xuchen Deng
author_sort Xuchen Deng
collection DOAJ
description This paper studies the location-routing problem of emergency facilities with time window under demand uncertainty. We propose a robust mathematical model in which uncertain requirements are represented by two forms: the support set defined by cardinal constraint set. When the demand value of rescue point changes in a given definition set, the model can ensure the feasibility of each line. We propose a branch and price cutting algorithm, whose pricing problem is a robust resource-constrained shortest path problem. In addition, we take the Wenchuan Earthquake as an example to verify the practicability of the method. The robust model is simulated under different uncertainty levels and distributions and compared with the scheme obtained by the deterministic problem. The results show that the robust model can run successfully and maintain its robustness, and the robust model provides better protection against demand uncertainty. In addition, we find that cost is more sensitive to uncertainty level than protection level, and our proposed model also allows controlling the robustness level of the solution by adjusting the protection level. In all experiments, the cost of robustness is that the routing cost increases by an average of 13.87%.
format Article
id doaj-art-cb5691466fa848f1b1ac8bf8a1a9dd3c
institution Kabale University
issn 2314-4785
language English
publishDate 2021-01-01
publisher Wiley
record_format Article
series Journal of Mathematics
spelling doaj-art-cb5691466fa848f1b1ac8bf8a1a9dd3c2025-02-03T01:04:11ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/9152989Location-Routing Problem of Emergency Facilities under Uncertain Demand by Branch-Price and CutXuchen Deng0Business SchoolThis paper studies the location-routing problem of emergency facilities with time window under demand uncertainty. We propose a robust mathematical model in which uncertain requirements are represented by two forms: the support set defined by cardinal constraint set. When the demand value of rescue point changes in a given definition set, the model can ensure the feasibility of each line. We propose a branch and price cutting algorithm, whose pricing problem is a robust resource-constrained shortest path problem. In addition, we take the Wenchuan Earthquake as an example to verify the practicability of the method. The robust model is simulated under different uncertainty levels and distributions and compared with the scheme obtained by the deterministic problem. The results show that the robust model can run successfully and maintain its robustness, and the robust model provides better protection against demand uncertainty. In addition, we find that cost is more sensitive to uncertainty level than protection level, and our proposed model also allows controlling the robustness level of the solution by adjusting the protection level. In all experiments, the cost of robustness is that the routing cost increases by an average of 13.87%.http://dx.doi.org/10.1155/2021/9152989
spellingShingle Xuchen Deng
Location-Routing Problem of Emergency Facilities under Uncertain Demand by Branch-Price and Cut
Journal of Mathematics
title Location-Routing Problem of Emergency Facilities under Uncertain Demand by Branch-Price and Cut
title_full Location-Routing Problem of Emergency Facilities under Uncertain Demand by Branch-Price and Cut
title_fullStr Location-Routing Problem of Emergency Facilities under Uncertain Demand by Branch-Price and Cut
title_full_unstemmed Location-Routing Problem of Emergency Facilities under Uncertain Demand by Branch-Price and Cut
title_short Location-Routing Problem of Emergency Facilities under Uncertain Demand by Branch-Price and Cut
title_sort location routing problem of emergency facilities under uncertain demand by branch price and cut
url http://dx.doi.org/10.1155/2021/9152989
work_keys_str_mv AT xuchendeng locationroutingproblemofemergencyfacilitiesunderuncertaindemandbybranchpriceandcut