Constructing Sustainable Humanitarian Relief Equity Allocation-Transportation Problem by Branch-and-Cut Algorithm

An unequitable material allocation scheme will cause secondary disasters and directly affect relief efficiency. Post-disaster relief equity allocation-transportation problem is a key issue in humanitarian logistics. However, existing studies on relief material allocation lack the characterization of...

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Vydáno v:	IEEE transactions on intelligent transportation systems Ročník 26; číslo 10; s. 16418 - 16437
Hlavní autoři:	Wang, Jinpei, Ma, Xiaojuan, Bai, Xuejie, Liu, Yankui
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	IEEE 01.10.2025
Témata:	a posteriori probability bound Allocation-transportation problem branch-and-cut algorithm Costs Disasters Local government mixed integer second-order cone programming Optimization Optimization models Resource management Stochastic processes Sustainable development sustainable humanitarian relief equity Transportation Uncertainty
ISSN:	1524-9050, 1558-0016
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Abstract	An unequitable material allocation scheme will cause secondary disasters and directly affect relief efficiency. Post-disaster relief equity allocation-transportation problem is a key issue in humanitarian logistics. However, existing studies on relief material allocation lack the characterization of equity, and have not considered the hierarchical relationship between two decision-makers and uncertain costs caused by disasters. For this purpose, this paper addresses a satisfaction objective to measure equity, and constructs a bilevel multi-objective distributionally robust (BMDR) method. On the one hand, our work focuses on the hierarchical relationship, with the local government as the upper decision-maker and the affected population as the lower decision-maker. On the other hand, our work constructs chance constraints under ambiguity set to characterize uncertain costs with sub-Gaussian distribution information. In particular, we show that robust optimal solution obtained by our method has not only a priori probability guarantee but also a posteriori probability guarantee. Furthermore, we transform our model into a mixed integer second-order cone programming (MISOCP) model and design a customized branch-and-cut (B&C) algorithm. Finally, some experiments are carried out via a real tornado case in Yancheng. The empirical findings show that the relief scheme obtained by our BMDR model has better out-of-sample performance and an improved posteriori probability bound guarantee, and the proposed algorithm has better solving efficiency. Our method can be used to guide the allocation and transportation of post-disaster relief materials under incomplete cost distribution information and improve the robustness of relief.
AbstractList	An unequitable material allocation scheme will cause secondary disasters and directly affect relief efficiency. Post-disaster relief equity allocation-transportation problem is a key issue in humanitarian logistics. However, existing studies on relief material allocation lack the characterization of equity, and have not considered the hierarchical relationship between two decision-makers and uncertain costs caused by disasters. For this purpose, this paper addresses a satisfaction objective to measure equity, and constructs a bilevel multi-objective distributionally robust (BMDR) method. On the one hand, our work focuses on the hierarchical relationship, with the local government as the upper decision-maker and the affected population as the lower decision-maker. On the other hand, our work constructs chance constraints under ambiguity set to characterize uncertain costs with sub-Gaussian distribution information. In particular, we show that robust optimal solution obtained by our method has not only a priori probability guarantee but also a posteriori probability guarantee. Furthermore, we transform our model into a mixed integer second-order cone programming (MISOCP) model and design a customized branch-and-cut (B&C) algorithm. Finally, some experiments are carried out via a real tornado case in Yancheng. The empirical findings show that the relief scheme obtained by our BMDR model has better out-of-sample performance and an improved posteriori probability bound guarantee, and the proposed algorithm has better solving efficiency. Our method can be used to guide the allocation and transportation of post-disaster relief materials under incomplete cost distribution information and improve the robustness of relief.
Author	Ma, Xiaojuan Liu, Yankui Bai, Xuejie Wang, Jinpei
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SubjectTerms	a posteriori probability bound Allocation-transportation problem branch-and-cut algorithm Costs Disasters Local government mixed integer second-order cone programming Optimization Optimization models Resource management Stochastic processes Sustainable development sustainable humanitarian relief equity Transportation Uncertainty
Title	Constructing Sustainable Humanitarian Relief Equity Allocation-Transportation Problem by Branch-and-Cut Algorithm
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