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...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9152989 |
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| _version_ | 1832566439564804096 |
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| 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 |