基于剥夺成本的应急选址-分配p-鲁棒优化研究

doi:10.16381/j.cnki.issn1003-207x.2024.0518

Abstract

Abstract:

Natural disasters pose a great threat to humanity. In order to improve the ability of disaster relief network， it focuses on pre-disaster facilities location and post-disaster capacity allocation and evacuation of disaster victims under uncertain demand. Considering two different types of disaster victims and deprivation costs， a scenario based robust optimization model is developed to minimize the expected total cost. Finally， taking the Sichuan earthquake as a case， numerical experiments and sensitivity analysis are performed to prove the effectiveness of the model and obtain some management insights. The results show that comparing with the deterministic model and stochastic programming model， p-robust optimization model can effectively enhance the cross-scenario robustness of decision-making. In addition， deprivation cost plays an important role in balancing economic benefits and psychological pain in decision-making. Expanding the capacity of emergency reserve warehouse can reduce the risk of shortages. Besides， emphasizing the evacuation of disaster victims can effectively control the deterioration of the disaster and reduce casualties.

Key words: emergency logistics, robust optimization, deprivation cost, location-allocation

CLC Number:

Ling Zhang,Xiaojin Zhuo,Jing Wang. P-robust Optimization of Emergency Location-allocation Problem Considering Deprivation Cost[J]. Chinese Journal of Management Science, 2026, 34(9): 120-132.

Figures/Tables 23

情境	$F s *$	$F s$	$η s$
1	29,115,970	49,633,439	0.7047
2	55,829,022	57,721,268	0.0339
3	82,999,115	139,112,991	0.6761
4	103,691,885	316,140,187	2.0488
5	161,203,789	564,022,240	2.4989(max)
6	279,510,672	683,232,174	1.4444
7	371,226,492	775,481,412	1.0890
8	522,223,069	926,846,338	0.7748

迭代(t)	$η$	$F$
初始化	2.4989	77,513,851
1	2.2490	79,019,162
2	1.6900	83,536,464
3	1.3952	无解

References 34

[1]	Y´anez-Sandivari L， Cort´es C E， Rey P A. Humanitarian logistics and emergencies management： New perspectives to a sociotechnical problem and its optimization approach management［J］. International Journal of Disaster Risk Reduction， 2021， 52： 1-19.
[2]	袁涛，蔡佳，郑磊，等. 考虑道路损毁情况的应急物流LRP研究［J］. 铁道运输与经济， 2021， 43（9）： 30-37.
	Yuan T， Cai J， Zheng L， et al. LRP study of emergency logistics considering road damage［J］. Railway Transport and Economy， 2021， 43（9）： 30-37.
[3]	Sanci E， Daskin M S. An integer L-shaped algorithm for the integrated location and network restoration problem in disaster relief［J］. Transportation Research Part B： Methodological， 2021， 145： 152-184.
[4]	周愉峰，陈娜，李志，等. 考虑设施中断情景的震后救援初期应急物流网络优化设计［J］. 运筹与管理， 2020， 29（6）： 107-112.
	Zhou Y F， Chen N， Li Z， et al. Optimization design of emergency logistics network considering facility disruption scenarios during the early stage of post-earthquake relief［J］. Operations Research and Management Science， 2020， 29（6）： 107-112.
[5]	张聆晔，吕靖，梁孝，等. 考虑多事故点的海上重大事故应急物资优化调度［J］. 系统工程， 2021， 39（4）： 103-114.
	Zhang L Y， Lv J， Liang X， et al. Optimal scheduling of emergency supplies for major maritime accidents considering multiple demand sites［J］. Systems Engineering， 2021， 39（4）： 103-114.
[6]	赵建有，韩万里，郑文捷，等. 重大突发公共卫生事件下城市应急医疗物资配送［J］. 交通运输工程学报， 2020， 20（3）： 168-177.
	Zhao J Y， Han W L， Zheng W J， et al. Distribution of emergency medical supplies in cities under major public health emergency［J］.Journal of Traffic and Transportation Engineering， 2020， 20（3）： 168-177.
[7]	Yang Y， Yin Y， Wang D， et al. Distributionally robust multi-period location-allocation with multiple resources and capacity levels in humanitarian logistics［J］. European Journal of Operational Research， 2023， 305（3）： 1042-1062.
[8]	Shaw L， Das S K， Roy S K. Location-allocation problem for resource distribution under uncertainty in disaster relief operations［J］. Socio-Economic Planning Sciences， 2022， 82（8）： 101-232.
[9]	Panchalee P， Huynh V N， Sarunya K. A multi-objective optimization model for shelter location-allocation in response to humanitarian relief logistics［J］. The Asian Journal of Shipping and Logistics， 2021， 37（2）： 149-156.
[10]	Zhong S P， Cheng R， Jiang Y， et al. Risk-averse optimization of disaster relief facility location and vehicle routing under stochastic demand［J］. Transportation Research Part E： Logistics and Transportation Review， 2020， 141： 102015.
[11]	薛星群，王旭坪，韩涛，等. 考虑通行约束和运力限制的灾后应急物资联合调度优化研究［J］. 中国管理科学， 2020， 28（3）： 21-30.
	Xue X Q， Wang X P， Han T， et al. Study on joint dispatch optimization of emergency materials considering traffic constraints and capacity limits［J］. Chinese Journal of Management Science， 2020， 28（3）： 21-30.
[12]	Liu C， Qian Y H. Optimal allocation of material dispatch in emergency events using multi-objective constraint for vehicular networks［J］. Wireless Networks， 2022， 28（8）： 3715-3727.
[13]	Eriskin L， Karatas M. Applying robust optimization to the shelter location-allocation problem： A case study for Istanbul［J］. Annals of Operations Research， 2022，339： 1589-1635.
[14]	Wang X F， Paul J A. Robust optimization for hurricane preparedness［J］. International Journal Of Production Economics， 2020， 221 （13）： 107464 .
[15]	陈刚，付江月. 灾后不确定需求下应急医疗移动医院鲁棒选址问题研究［J］. 中国管理科学， 2021， 29（9）： 213-223.
	Chen G， Fu J Y. Emergency medical mobile hospital robust location problem in post-disaster under demand uncertainty［J］. Chinese Journal of Management Science， 2021，29（9）： 213-223.
[16]	Zhang J， Long D Z， Li Y. A reliable emergency logistics network for COVID-19 considering the uncertain time-varying demands［J］. Transportation Research Part E： Logistics and Transportation Review， 2023， 172： 103087.
[17]	Wang D， Yang K， Yang L X. Risk-averse two-stage distributionally robust optimization for logistics planning in disaster relief management［J］. International Journal of Production Research， 2021，6（2）： 668-691.
[18]	赖志柱，王铮，戈冬梅，等.多目标应急物流中心选址的鲁棒优化模型［J］.运筹与管理，2020，29（5）： 74-83.
	Lai Z Z， Wang Z， Ge D M， et al. A multi-objective robust optimization model for emergency logistics center location［J］. Operations Research and Management Science，2020，29（5）： 74-83.
[19]	Haghjoo N， Tavakkoli-Moghaddam R， Shahmoradi-Moghadam H， et al. Reliable blood supply chain network design with facility disruption： A real world application［J］. Engineering Applications of Artificial Intelligence， 2020， 90： 103493.
[20]	Sun H， Li J， Wang T， et al. A novel scenario-based robust bi-objective optimization model for humanitarian logistics network under risk of disruptions［J］. Transportation Research Part E： Logistics and Transportation Review， 2022， 157： 102578.
[21]	Snyder L V.Facility location under uncertainty： A review［J］. IIE-Transactions，2006，38（7）：547-564.
[22]	Snyder L V， Daskin M S. Stochastic p-robust location problems［J］. IISE Transactions， 2006， 38（11）： 971-985.
[23]	Paul J A， Wang X F. Robust location-allocation network design for earthquake preparedness［J］. Transportation Research Part B： Methodological， 2019，119：139-155.
[24]	周愉峰，李志，刘思峰.基于随机p-鲁棒优化的国家血液战略储备库选址-库存模型［J］.中国管理科学，2018，26（10）：52-63.
	Zhou Y F， Li Z， Liu S F. Location-inventory model of national blood strategic reserves based on p-stochastic optimization method［J］. Chinese Journal of Management Science，2018，26（10）：52-63.
[25]	商丽媛，谭清美.多分配枢纽站集覆盖问题的随机p-鲁棒优化模型及算法［J］.控制与决策，2014，29（8）：1517-1521.
	Shang L Y， Tan Q M. Stochastic p-robust optimization model and algorithm of multiple allocation hub set covering problem［J］.Control and Decision，2014，29（8）：1517-1521.
[26]	Long S J， Zhang D Z， Li S Y， et al. Two stage multi-objective stochastic model on patient transfer and relief distribution in lockdown area of COVID-19［J］. International Journal of Environmental Research and Public Health， 2023， 20（3）： 1765.
[27]	Vahdani B， Veysmoradi D， Mousavi S M， et al. Planning for relief distribution， victim evacuation， redistricting and service sharing under uncertainty［J］. Socio-Economic Planning Sciences， 2022， 80： 101158.
[28]	Ghasemi P， Khalili-Damghani K， Hafezalkotob A， et al. Stochastic optimization model for distribution and evacuation planning （A case study of Tehran earthquake）［J］. Socio-economic Planning Sciences， 2020， 71： 100745.
[29]	Haeri A， Hosseini-Motlagh S M， Samani M R G， et al. A bi-level programming approach for improving relief logistics operations： A real case in Kermanshah earthquake［J］. Computers & Industrial Engineering， 2020， 145： 106532.
[30]	Zhu L， Gong Y， Xu Y， Gu J. Emergency relief routing models for injured victims considering equity and priority［J］. Annals of Operations Research， 2019，283（1）， 1573-1606.
[31]	Song Y H， Huang X， Ma Y P， et al. Emergency resource allocation considering psychological pain effect of disaster victims Under multi-dimensional fairness measurement［J］. Journal of Safety Science and Technology， 2021， 17（4）： 47-53.
[32]	朱莉，曹杰，顾珺，等. 公平缓解灾民创伤下的应急物资动态调配研究［J］. 系统工程理论与实践， 2020， 40（9）： 2427-2437.
	Zhu L， Cao J， Gu J， et al. Dynamic emergency supply distribution considering fair mitigation of victim suffering［J］. Systems Engineering-Theory & Practice， 2020， 40（9）： 2427-2437.
[33]	曲冲冲，田歆，刘淑芹，等.考虑灾民恐慌心理影响的应急资源配置优化研究［J］. 系统工程学报， 2021， 36（6）： 721-730.
	Qu C C， Tian X， Liu S Q， et al. Research on emergency resource allocation considering the psychological panic spread［J］. Journal of Systems Engineering， 2021，36 （6）： 721-730.
[34]	Ni W， Shu J， Song M. Location and emergency inventory pre-positioning for disaster response operations： Min-max robust model and a case study of yushu earthquake［J］.Production And Operations Management， 2018， 27（1）： 160-183.

地震情境	1	2	3	4	5	6	7	8
震级	M＜5	5≤M＜5.5	5.5≤M＜6	6≤M＜6.5	6.5≤M＜7	7≤M＜7.5	7.5≤M＜8	M≥8
概率	0.6576	0.2003	0.0940	0.0309	0.0120	0.0041	0.0008	0.0003

需求点编号	需求点	常住人口（万人）
1	汶川县	8.3
2	绵竹市	43.9
3	北川县	17.41
4	什邡市	40.68
5	绵阳市	223.29
6	平武县	12.64
7	德阳市	127.55
8	青川县	15.6
9	茂县	9.54

情境	迭代（t）
情境	1	2
1	1.1353	1.4431
2	0.2569	0.3759
3	0.1097	0.0081
4	1.0840	0.7704
5	1.8778	1.5502
6	1.0861	0.8965
7	0.8183	0.6767
8	0.5824	0.4806

模型	系统总成本	应急物资储备库的建设成本	医疗物资供应商的固定成本	医院的开放成本	应急物资的预置成本	医疗物资的采购成本	应急物资储备库数量	医疗物资供应商数量	医院开放数量
随机规划模型	77513831	24000000	200000	15500000	537535	988500	2	3	2
p-鲁棒模型	83536464	36300000	320000	23800000	806302	1499100	3	4	3

成本		情境
成本		1	2	3	4	5	6	7	8
灾前	建设成本	20,170,000	40,530,000	60,300,000	73,920,000	95,470,000	95,470,000	95,470,000	95,470,000
灾前	预置成本	538,566	1,125,226	1,739,979	2,342,528	3,345,500	3,345,500	3,345,464	3,345,500
灾后	建设成本	6,000,000	11,700,000	16,700,000	22,200,000	29,200,000	29,200,000	29,200,000	29,200,000
	物资运输成本	303,286	650,686	966,693	1,402,382	1,772,826	1,772,826	1,772,769	1,772,828
	灾民运输成本	62,464	116,005	181,282	251,482	337,453	331,905	330,587	328,143
	剥夺成本	2,041,654	1,707,105	3,111,161	3,575,493	4,927,010	3,845,441	3,613,672	3,096,598
	惩罚成本	0	0	0	0	26,151,000	145,545,000	237,494,000	389,010,000
总成本		29,115,970	55,829,022	82,999,115	103,691,885	161,203,789	279,510,672	371,226,492	522,223,069

P-robust Optimization of Emergency Location-allocation Problem Considering Deprivation Cost

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 23

References 34

Related Articles 15

Metrics

Comments

Recommended 0

变量	-75%	-50%	-25%	0	25%	50%	75%
应急物资储备库数量（个）	4	4	3	3	3	3	2
储备库建设成本（%）	35.81	35.81	0.00	0.00	0.00	0.00	-33.88
应急物资储备数量（%）	-67.34	-33.33	-24.91	0.00	25.68	50.98	67.59
应急物资储备成本（%）	-66.03	-33.33	-26.00	0.00	18.00	40.00	67.89
总成本（%）	63.61	23.05	2.77	0.00	-8.86	-10.09	-17.73

[1]	Zongyu Yao, Lihui Zhang, Yifei Li, Yafan Fu. Robust Optimization Approach for Repetitive Project Scheduling [J]. Chinese Journal of Management Science, 2026, 34(7): 206-217.
[2]	Yu Fan, Xihui Wang. Construction and Analysis of Emergency Logistics Decision-Making Models Based on Deprivation Theory in Different Scenarios of Disasters [J]. Chinese Journal of Management Science, 2026, 34(3): 114-121.
[3]	Xuelong Chen, Zirui Wang, Miaomiao Li. Research on Agent Conflict Resolution Method for Multi-period Emergency Resource Allocation [J]. Chinese Journal of Management Science, 2026, 34(3): 226-241.
[4]	Lifang Peng, Nannan Zhao. Location-routing Problem Considering Psychological Cost in Emergency Logistics [J]. Chinese Journal of Management Science, 2026, 34(1): 234-243.
[5]	Mingli Yuan, Ruozhen Qiu, Yue Sun. An Affinely Adjustable Robust Optimization Model for Prouction-Inventory Planning Problem with Demand and Lead Time Uncertainties [J]. Chinese Journal of Management Science, 2025, 33(9): 97-108.
[6]	Jianfang Shao, Yu Fan, Xihui Wang, Liang Liang. The Impact of Emergency Supplies Quantitative Differences and Social Factors on the Fair Perceptions of Victims: An Empirical Study [J]. Chinese Journal of Management Science, 2025, 33(8): 189-197.
[7]	Yanqiu Liu, Jihui Hu. Research on Emergency Logistics Path Optimization Based on Hybrid Artificial Fish Swarm Algorithm [J]. Chinese Journal of Management Science, 2025, 33(8): 198-208.
[8]	Wenqiang Dai, Danyang Li. Robust Guaranteed Delivery and Allocation Optimization for Online Display Advertising with Covariate-based Information [J]. Chinese Journal of Management Science, 2025, 33(8): 230-237.
[9]	Jing Li, Ada Che. Distributionally Robust Optimization on Emergency Facility Location and Relief Supply Distribution Considering Household Reserves [J]. Chinese Journal of Management Science, 2025, 33(5): 268-279.
[10]	Wenqiang Dai, Xiaoyue Zhang, Lin Chen. Emergency Evacuation Route Planning under Uncertain Road Stability Coefficient [J]. Chinese Journal of Management Science, 2025, 33(4): 204-212.
[11]	Shuangsong Xu, Kanglin Liu. Hub-and-spoke Network Optimization Method of China Railway Highspeed Express Based on Distriutionally Robust Optimization [J]. Chinese Journal of Management Science, 2025, 33(3): 231-238.
[12]	Ling Zhang, Jinpeng Li, Shengqun Chen. Research on Distributed Robust Optimization Scheme of Emergency Blood Supply Network Configuration Based on Data Driven [J]. Chinese Journal of Management Science, 2025, 33(2): 131-140.
[13]	Ziqing Zhang, Lin Wang, Sirui Wang, Jinlong Zhang. The Location of Post-harvest Grain Service Centers Considering Two Service Capabilities and Benders Decomposition Algorithm [J]. Chinese Journal of Management Science, 2025, 33(2): 141-149.
[14]	Fang Guo, Runliu Niu, Zhihong Huang. Robust Optimization of Procurement and Routing Strategy of Multi-period Multimodal Transport in Uncertain Environment [J]. Chinese Journal of Management Science, 2025, 33(11): 103-113.
[15]	Jinfeng Sun, Hongxi Sheng, Xiangpei Hu. Production Decision-making Optimization and Emission Behavioral Analysis under Emission Permits Price Uncertainty [J]. Chinese Journal of Management Science, 2025, 33(11): 65-80.