基于缺货延时双重损失的应急物资配送路径选择研究

doi:10.16381/j.cnki.issn1003-207x.2023.0781

中国管理科学 ›› 2025, Vol. 33 ›› Issue (8): 209-217.doi: 10.16381/j.cnki.issn1003-207x.2023.0781

• • 上一篇

基于缺货延时双重损失的应急物资配送路径选择研究

苏兵¹^,²^,³, 陈相文¹, 张萌¹(), 姬浩¹^,²^,³, 孙璐璐¹, 徐阳¹, 郭清娥¹, Lin Guohui⁴

^1.西安工业大学经济管理学院，陕西西安 710021
^2.陕西省兵工科技创新发展软科学研究基地，陕西西安 710021
^3.陕西高校军民融合科技创新研究中心，陕西西安 710021
^4.阿尔伯塔大学计算机科学系，加拿大埃德蒙顿 T6G 2E8

收稿日期:2023-05-10 修回日期:2024-01-13 出版日期:2025-08-25 发布日期:2025-09-10
通讯作者: 张萌 E-mail:zm890629@sina.com
基金资助:
国家社会科学基金项目(20XGL023);国家自然科学基金项目(72301205);陕西省教育厅重点科研计划项目(23JY037)

Research on Route Selection for Emergency Supply Distribution Based on Dual Losses of Shortage and Delay

Bing Su¹^,²^,³, Xiangwen Chen¹, Meng Zhang¹(), Hao Ji¹^,²^,³, Lulu Sun¹, Yang Xu¹, Qing’e Guo¹, Guohui Lin⁴

^1.School of Economics and Management，Xi’an Technological University，Xi’an 710021，China
^2.Soft Science Base for Ordnance Industry Innovation & Development in Shaanxi Province，Xi’an 710021，China
^3.Civil-Military Integration Science and Technology Innovation Research Center of Shaanxi’s Colleges and Universities，Xi’an 710021，China
^4.Department of Computing Science，University of Alberta，Edmonton T6G 2E8，Alberta，Canada

Received:2023-05-10 Revised:2024-01-13 Online:2025-08-25 Published:2025-09-10
Contact: Meng Zhang E-mail:zm890629@sina.com

摘要/Abstract

摘要：

针对带时间窗的紧缺应急物资配送路径选择问题，综合考虑每个需求点的需求量和配送时间要求，提出需求点最大缺货延时双重损失定义，并以单个需求点最大缺货延时双重损失费用最小为目标，建立应急物资配送路径选择模型。对于配送车辆充足的情形，设计时间复杂性为 $O (n 3)$ 的精确算法 $A *$ 进行求解，其中 $n$ 为需求点数；对于配送车辆不足的情形，设计时间复杂性为 $O (L n 2)$ 的近似算法 $G A *$ 进行求解，其中 $L$ 和 $n$ 分别为车辆数和需求点数，并分析算法 $G A *$ 的近似比。最后结合实例进行分析，验证模型及算法的有效性。

关键词: 应急物资紧缺, 配送时间窗, 路径选择问题, 缺货延时双重损失, 近似算法

Abstract:

Efficient emergency supply distribution after sudden disasters stands as a critical factor in mitigating overall losses. The arrangement of emergency supply distribution encounters two challenges. First， it is difficult to mobilize sufficient emergency supply in a short time after the disaster， resulting in unmet needs of victims and subsequent losses. Second， there exists a pressing demand for timely supply arrivals， and any delays in emergency supply distribution cause further losses. Ensuing equitable access to disaster-stricken individuals necessitates vigilant monitoring of shortages of supply and impediments of distribution at each demand point. It is of great significance to formulate the routing strategy for scarce emergency supply distribution with time windows to reduce dual losses of storage and delay at each demand point as much as possible.In this paper， the problem of determining the optimal routes for emergency supply distribution is studied with the objective of minimizing the maximum dual losses of shortage and delay of each demand point. The premise acknowledges that the emergency supply is scarce and the available vehicles at the distribution center are potentially inadequate. The definition of shortage loss is given based on the shortage ratio， and the definition of delay loss is given based on piecewise penalty function.Further comprehensive consideration of supply shortage and distribution delay of each demand point servers as the foundation of developing a route selection model for emergency supply distribution. The objective of this proposed model is to minimize the maximum dual losses of shortage and delay of each demand point， aiming to avoid critical shortage at any single demand point and ensure adherence to stringent distribution time windows.An in-depth analysis of scenarios regarding supply shortage and distribution delay at each demand point is conducted. It delineates solutions in two distinct cases： sufficient vehicles and insufficient vehicles. In the case with sufficient vehicles， all amounts of supply in the distribution center can be sent to demand points. The routes for emergency supply distribution is initially determined based on the shortest paths from the distribution center to each demand point. Then， the quantities of supply distributed to each demand point is determined by equating the shortage ratio at each demand point， and an algorithm $A *$ is developed accordingly. In the case with insufficient vehicles， it is not possible to send all amounts of supply in the distribution center， and an approximate algorithm $G A *$ is developed to solve the problem in this case.By analyzing the performances of the proposed algorithms， the results demonstrate that algorithm $A *$ is an exact algorithm in the case with sufficient vehicles. Its time complexity is $O (n 3)$ ， where $n$ represents the number of demand points. The results also evaluate the time complexity of the approximate algorithm $G A *$ in the case with insufficient vehicles. Its time complexity is $O (L n 2)$ ， where $L$ denotes the number of vehicles and $n$ represents the number of demand points. Additionally， the approximate ratio of algorithm $G A *$ and the upper and lower bounds of the approximate ratio are also proved.A case study is conducted focusing on the rescue in Luding County， Sichuan Province in September 2022 with a magnitude 6.8 earthquake. The dataset utilized for analysis is based on actual road conditions and related reports from CHINANEWS.COM. The algorithms developed in this paper are used to solve the route selection model for emergency supply distribution with the objective of minimizing the maximum dual losses of shortage and delay of each single demand point. The routing strategy is obtained， and an approximation ratio of 1.32 is yielded when comparing the maximum dual losses of shortage and delay at each single demand point to the result of the optimal solution.By investigating the route selection for emergency supply distribution based on dual losses of shortage and delay， the model developed in this paper aims to prevent the simultaneous occurrence of maximum shortage and delay at a single demand point， thereby enhancing the effectiveness of emergency supply distribution after sudden disasters. The proposed algorithms also provide reference for similar research problems. Future research endeavor will likely focus on building a model that closely mirrors real-world scenarios or refining the algorithm to achieve improved efficacy.

Key words: scarcer emergency supply, distribution time windows, route selection problem, dual losses of shortage and delay, approximation algorithm

中图分类号:

U116

苏兵, 陈相文, 张萌, 姬浩, 孙璐璐, 徐阳, 郭清娥, Lin Guohui. 基于缺货延时双重损失的应急物资配送路径选择研究[J]. 中国管理科学, 2025, 33(8): 209-217.

Bing Su, Xiangwen Chen, Meng Zhang, Hao Ji, Lulu Sun, Yang Xu, Qing’e Guo, Guohui Lin. Research on Route Selection for Emergency Supply Distribution Based on Dual Losses of Shortage and Delay[J]. Chinese Journal of Management Science, 2025, 33(8): 209-217.

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需求点	需求量(万件)	ST_i	MT_i	D_i	需求点	需求量(万件)	ST_i	MT_i	D_i
v₁	0.69	208	220	14	v₁₅	0.71	254	262	13
v₂	0.74	222	229	12	v₁₆	0.31	219	225	15
v₃	0.52	217	222	14	v₁₇	1.63	213	223	13
v₄	0.40	185	197	12	v₁₈	0.03	155	168	10
v₅	0.05	238	251	12	v₁₉	2.61	201	208	14
v₆	0.25	247	258	10	v₂₀	0.70	187	201	13
v₇	0.70	229	237	14	v₂₁	1.41	179	186	11
v₈	2.18	161	165	14	v₂₂	0.54	191	200	14
v₉	0.85	177	186	12	v₂₃	3.10	171	174	15
v₁₀	1.00	183	192	11	v₂₄	0.31	189	192	14
v₁₁	0.47	145	153	14	v₂₅	1.44	122	126	12
v₁₂	2.03	191	193	13	v₂₆	0.25	84	92	10
v₁₃	0.30	594	596	13	v₂₇	0.39	49	53	13
v₁₄	0.10	299	308	14

车辆1	车辆2	车辆3	车辆4	车辆5
y_23,1=1.64	y_18,2=0.01	y_1,3=0.23	y_12,4=1.07	y_14,5=0.05
y_24,1=0.16	y_19,2=0.84	y_2,3=0.25	y_13,4=0.16	y_15,5=0.38
y_26,1=0.13	y_20,2=0.22	y_4,3=0.13		y_16,5=0.16
	y_21,2=0.46	y_6,3=0.08		y_17,5=0.86
	y_25,2=0.13	y_8,3=0.73
		y_9,3=0.29
		y_11,3=0.16
		y_27,3=0.13

需求点	缺货量	缺货比例	缺货惩罚费用	延时损失	延时惩罚费用	单个需求点最大缺货延时双重损失费用
v₁	0.46	0.67	67	8	40	107
v₂	0.49	0.66	66	5	25	91
v₃	0.52	1.00	100	14	70	170
v₄	0.27	0.68	68	9	45	113
v₅	0.05	1.00	100	8	40	140
v₆	0.17	0.68	68	7	35	103
v₇	0.70	1.00	100	6	30	130
v₈	1.45	0.67	67	14	70	137
v₉	0.56	0.66	66	7	35	101
v₁₀	1.00	1.00	100	6	30	130
v₁₁	0.31	0.66	66	7	35	101
v₁₂	0.96	0.47	47	13	65	112
v₁₃	0.14	0.47	47	13	65	112
v₁₄	0.05	0.50	50	8	40	90
v₁₅	0.33	0.46	46	5	25	71
v₁₆	0.15	0.48	48	15	75	123
v₁₇	0.77	0.47	47	6	30	77
v₁₈	0.02	0.67	67	10	50	117
v₁₉	1.77	0.68	68	14	70	138
v₂₀	0.48	0.69	69	10	50	119
v₂₁	0.95	0.67	67	11	55	122
v₂₂	0.54	1.00	100	14	70	170
v₂₃	1.46	0.47	47	15	75	122
v₂₄	0.15	0.48	48	14	70	118
v₂₅	0.97	0.67	67	12	60	127
v₂₆	0.12	0.48	48	10	50	98
v₂₇	0.26	0.67	67	13	65	132

基于缺货延时双重损失的应急物资配送路径选择研究

Research on Route Selection for Emergency Supply Distribution Based on Dual Losses of Shortage and Delay

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