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Article(id=1149739134903828963, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149739129056969102, articleNumber=1003-3033(2024)03-0222-08, orderNo=null, doi=10.16265/j.cnki.issn1003-3033.2024.03.0625, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1695139200000, receivedDateStr=2023-09-20, revisedDate=1703088000000, revisedDateStr=2023-12-21, acceptedDate=null, acceptedDateStr=null, onlineDate=1752048770881, onlineDateStr=2025-07-09, pubDate=1711555200000, pubDateStr=2024-03-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752048770881, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1752048770881, creator=13701087609, updateTime=1752048770881, updator=13701087609, issue=Issue{id=1149739129056969102, tenantId=1146029695717560320, journalId=1146031787341344770, year='2024', volume='34', issue='3', pageStart='1', pageEnd='252', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1752048769486, creator=13701087609, updateTime=1756468931593, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1168278632783950282, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149739129056969102, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1168278632783950283, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149739129056969102, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=222, endPage=229, ext={EN=ArticleExt(id=1149739135113544175, articleId=1149739134903828963, tenantId=1146029695717560320, journalId=1146031787341344770, language=EN, title=Emergency rescue allocation decision-making based on three-sided matching theory, columnId=1149733268699918866, journalTitle=China Safety Science Journal, columnName=Emergency technology and management, runingTitle=null, highlight=null, articleAbstract=

To address the issues of allocation of emergency rescuers，emergency rescue equipment，and disaster locations in the early stage of emergency rescue under the background of large-scale geological disasters，as well as improve the efficiency and quality of emergency rescue，an emergency rescue allocation decision-making method was proposed based on the three-sided matching theory. Firstly，the selection process among the three parties of emergency rescue was presented as a three-sided matching issue. Then，the multi-attribute preference evaluation information of the matching three parties was standardized，and a multi-attribute comprehensive preference score matrix was proposed. Furthermore，a three-sided matching stable and satisfactory model in the early stage of emergency rescue was developed to maximize system stability and total preference utility. Finally，the performance and accuracy of the proposed model were validated against cases. The results indicated that the proposed model reached reasonable matching between rescuers，emergency rescue equipment，and disaster locations in emergency rescue scenarios due to considering the effects of various parties' preferences on resource allocation. Furthermore，it can contribute to reducing the deployment time of emergency rescue operations and improve emergency efficiency and quality.

, correspAuthors=Gang WU, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Qian GUO, Yike ZHOU, Gang WU), CN=ArticleExt(id=1149739138158609016, articleId=1149739134903828963, tenantId=1146029695717560320, journalId=1146031787341344770, language=CN, title=基于三边匹配理论的应急救援分配决策, columnId=1149733268855108116, journalTitle=中国安全科学学报, columnName=应急技术与管理, runingTitle=null, highlight=null, articleAbstract=

为解决大型地质灾害背景下应急救援初期救援人员、应急救援装备与受灾地点的分配问题，提高应急救援的效率和质量，首先，将应急救援三方主体之间的选择过程描述为三边匹配问题；然后，标准化处理匹配三方主体的多属性偏好评价信息，构造多属性综合偏好得分矩阵，并以系统稳定性和总偏好效用最大化为目标，建立应急救援初期背景下的三边匹配满意稳定模型；最后，通过算例验证模型的可行性和有效性。结果表明：该模型考虑各主体偏好对于资源分配的影响，能实现应急救援背景下救援人员、应急救援装备与受灾地点三方主体的合理匹配，有助于缩短应急救援部署时间，提高应急救援的效率和质量。

, correspAuthors=吴刚, authorNote=null, correspAuthorsNote=
** 吴刚(1972—)，男，四川南江人，博士，教授，主要从事物流与供应链管理等方面的研究。E-mail：。
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郭茜 (1975—)，女，河南南阳人，博士，讲师，主要从事物流管理、项目管理等方面的研究。E-mail：。

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郭茜 (1975—)，女，河南南阳人，博士，讲师，主要从事物流管理、项目管理等方面的研究。E-mail：。

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郭茜 (1975—)，女，河南南阳人，博士，讲师，主要从事物流管理、项目管理等方面的研究。E-mail：。

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Research on post-earthquake emergency material allocation considering psychological pain of victims[J]. China Safety Science Journal, 2022, 32(11): 200-207., articleTitle=Research on post-earthquake emergency material allocation considering psychological pain of victims, refAbstract=null), Reference(id=1168130101855134075, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2019, volume=29, issue=12, pageStart=137, pageEnd=143, url=null, language=null, rfNumber=[2], rfOrder=2, authorNames=吕伟, 李志红, 冯满满, journalName=中国安全科学学报, refType=null, unstructuredReference=吕伟, 李志红, 冯满满, 等. 考虑资源和时间窗约束的应急物资调配模型[J]. 中国安全科学学报, 2019, 29(12): 137-143., articleTitle=考虑资源和时间窗约束的应急物资调配模型, refAbstract=null), Reference(id=1168130101939020156, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2019, volume=29, issue=12, pageStart=137, pageEnd=143, url=null, language=null, rfNumber=[2], rfOrder=3, authorNames=LYU Wei, LI Zhihong, FENG Manman, journalName=China Safety Science Journal, refType=null, unstructuredReference=LYU Wei, LI Zhihong, FENG Manman, et al. Emergency material allocation in consideration of resource and time window constraints[J]. China Safety Science Journal, 2019, 29(12): 137-143., articleTitle=Emergency material allocation in consideration of resource and time window constraints, refAbstract=null), Reference(id=1168130102052266365, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2022, volume=32, issue=1, pageStart=172, pageEnd=179, url=null, language=null, rfNumber=[3], rfOrder=4, authorNames=宋英华, 白明轩, 马亚萍, journalName=中国安全科学学报, refType=null, unstructuredReference=宋英华, 白明轩, 马亚萍, 等. 考虑区域灾情分级的应急物资公平调度优化模型[J]. 中国安全科学学报, 2022, 32(1): 172-179., articleTitle=考虑区域灾情分级的应急物资公平调度优化模型, refAbstract=null), Reference(id=1168130102098403710, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2022, volume=32, issue=1, pageStart=172, pageEnd=179, url=null, language=null, rfNumber=[3], rfOrder=5, authorNames=SONG Yinghua, BAI Mingxuan, MA Yaping, journalName=China Safety Science Journal, refType=null, unstructuredReference=SONG Yinghua, BAI Mingxuan, MA Yaping, et al. Optimal model for fair dispatch of emergency materials considering regional disaster classification[J]. China Safety Science Journal, 2022, 32(1): 172-179., articleTitle=Optimal model for fair dispatch of emergency materials considering regional disaster classification, refAbstract=null), Reference(id=1168130102161318271, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2023, volume=33, issue=11, pageStart=206, pageEnd=213, url=null, language=null, rfNumber=[4], rfOrder=6, authorNames=张民波, 钟子逸, 闫瑾, journalName=中国安全科学学报, refType=null, unstructuredReference=张民波, 钟子逸, 闫瑾, 等. 考虑生物危险源扩散的疫区应急物资调配模型[J]. 中国安全科学学报, 2023, 33(11): 206-213., articleTitle=考虑生物危险源扩散的疫区应急物资调配模型, refAbstract=null), Reference(id=1168130102220038528, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2023, volume=33, issue=11, pageStart=206, pageEnd=213, url=null, language=null, rfNumber=[4], rfOrder=7, authorNames=ZHANG Minbo, ZHONG Ziyi, YAN Jin, journalName=China Safety Science Journal, refType=null, unstructuredReference=ZHANG Minbo, ZHONG Ziyi, YAN Jin, et al. Model of emergency supplies allocation in epidemic areas considering spread of biohazard diffusion[J]. China Safety Science Journal, 2023, 33(11): 206-213., articleTitle=Model of emergency supplies allocation in epidemic areas considering spread of biohazard diffusion, refAbstract=null), Reference(id=1168130102266175873, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2019, volume=29, issue=1, pageStart=180, pageEnd=186, url=null, language=null, rfNumber=[5], rfOrder=8, authorNames=杨琴, 陈金铭, 刘桔, journalName=中国安全科学学报, refType=null, unstructuredReference=杨琴, 陈金铭, 刘桔, 等. 基于双边匹配决策的应急救助人员任务分配[J]. 中国安全科学学报, 2019, 29(1): 180-186., articleTitle=基于双边匹配决策的应急救助人员任务分配, refAbstract=null), Reference(id=1168130102312313218, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2019, volume=29, issue=1, pageStart=180, pageEnd=186, url=null, language=null, rfNumber=[5], rfOrder=9, authorNames=YANG Qin, CHEN Jinming, LIU Ju, journalName=China Safety Science Journal, refType=null, unstructuredReference=YANG Qin, CHEN Jinming, LIU Ju, et al. Task allocation of emergency rescue workers based on bilateral matching decision[J]. China Safety Science Journal, 2019, 29(1): 180-186., articleTitle=Task allocation of emergency rescue workers based on bilateral matching decision, refAbstract=null), Reference(id=1168130102362644867, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=1962, volume=69, issue=1, pageStart=9, pageEnd=15, url=null, language=null, rfNumber=[6], rfOrder=10, authorNames=GALE D, SHAPLEY L S, journalName=The American Mathematical Monthly, refType=null, unstructuredReference=GALE D, SHAPLEY L S. College admissions and the stability of marriage[J]. The American Mathematical Monthly, 1962, 69(1): 9-15., articleTitle=College admissions and the stability of marriage, refAbstract=null), Reference(id=1168130102421365124, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=1984, volume=92, issue=6, pageStart=991, pageEnd=1016, url=null, language=null, rfNumber=[7], rfOrder=11, authorNames=ROTH A E, journalName=Journal of Political Economy, refType=null, unstructuredReference=ROTH A E. The evolution of the labor market for medical interns and residents: a case study in game theory[J]. Journal of Political Economy, 1984, 92(6): 991-1016., articleTitle=The evolution of the labor market for medical interns and residents: a case study in game theory, refAbstract=null), Reference(id=1168130102471696773, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2017, volume=26, issue=7, pageStart=104, pageEnd=109, url=null, language=null, rfNumber=[8], rfOrder=12, authorNames=赵晓冬, 臧誉琪, 孙微, journalName=运筹与管理, refType=null, unstructuredReference=赵晓冬, 臧誉琪, 孙微. 基于区间犹豫模糊信息双向投影技术的双边匹配决策方法[J]. 运筹与管理, 2017, 26(7): 104-109., articleTitle=基于区间犹豫模糊信息双向投影技术的双边匹配决策方法, refAbstract=null), Reference(id=1168130102522028422, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2017, volume=26, issue=7, pageStart=104, pageEnd=109, url=null, language=null, rfNumber=[8], rfOrder=13, authorNames=ZHAO Xiaodong, ZANG Yuqi, SUN Wei, journalName=Operations Research and Management Science, refType=null, unstructuredReference=ZHAO Xiaodong, ZANG Yuqi, SUN Wei. Two-sided matching decision method with interval-valued hesitant fuzzy information based on bidirectional projection method[J]. Operations Research and Management Science, 2017, 26(7):104-109., articleTitle=Two-sided matching decision method with interval-valued hesitant fuzzy information based on bidirectional projection method, refAbstract=null), Reference(id=1168130102580748679, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2019, volume=39, issue=7, pageStart=1752, pageEnd=1762, url=null, language=null, rfNumber=[9], rfOrder=14, authorNames=袁铎宁, 姜艳萍, journalName=系统工程理论与实践, refType=null, unstructuredReference=袁铎宁, 姜艳萍. 择期手术患者与手术医生的稳定双边匹配模型[J]. 系统工程理论与实践, 2019, 39(7): 1752-1762., articleTitle=择期手术患者与手术医生的稳定双边匹配模型, refAbstract=null), Reference(id=1168130102664634760, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2019, volume=39, issue=7, pageStart=1752, pageEnd=1762, url=null, language=null, rfNumber=[9], rfOrder=15, authorNames=YUAN Duoning, JIANG Yanping, journalName=Systems Engineering-Theory & Practice, refType=null, unstructuredReference=YUAN Duoning, JIANG Yanping. Stable two-sided matching model between selective operation patients and surgeons[J]. Systems Engineering-Theory & Practice, 2019, 39(7): 1752-1762., articleTitle=Stable two-sided matching model between selective operation patients and surgeons, refAbstract=null), Reference(id=1168130102710772105, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2016, volume=124, issue=5, pageStart=1235, pageEnd=1268, url=null, language=null, rfNumber=[10], rfOrder=16, authorNames=AZEVEDO E M, LESHNO J D, journalName=Journal of Political Economy, refType=null, unstructuredReference=AZEVEDO E M, LESHNO J D. A supply and demand framework for two-sided matching markets[J]. Journal of Political Economy, 2016, 124(5): 1235-1268., articleTitle=A supply and demand framework for two-sided matching markets, refAbstract=null), Reference(id=1168130102790463882, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2016, volume=7, issue=2, pageStart=449, pageEnd=482, url=null, language=null, rfNumber=[11], rfOrder=17, authorNames=ECHENIQUE F, WILSON A J, YARIV L, journalName=Quantitative Economics, refType=null, unstructuredReference=ECHENIQUE F, WILSON A J, YARIV L. Clearinghouses for two-sided matching: an experimental study[J]. Quantitative Economics, 2016, 7(2): 449-482., articleTitle=Clearinghouses for two-sided matching: an experimental study, refAbstract=null), Reference(id=1168130102928875915, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2023, volume=23, issue=5, pageStart=1568, pageEnd=1578, url=null, language=null, rfNumber=[12], rfOrder=18, authorNames=喇蕊芳, 薛芳明, 白鹏飞, journalName=安全与环境学报, refType=null, unstructuredReference=喇蕊芳, 薛芳明, 白鹏飞, 等. 基于“情景-任务”的重特大地质灾害救援装备调配优化[J]. 安全与环境学报, 2023, 23(5): 1568-1578., articleTitle=基于“情景-任务”的重特大地质灾害救援装备调配优化, refAbstract=null), Reference(id=1168130103029539212, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2023, volume=23, issue=5, pageStart=1568, pageEnd=1578, url=null, language=null, rfNumber=[12], rfOrder=19, authorNames=LA Ruifang, XUE Fangming, BAI Pengfei, journalName=Journal of Safety and Environment, refType=null, unstructuredReference=LA Ruifang, XUE Fangming, BAI Pengfei, et al. Optimizing the rescue equipment allocation of major geological disasters based on "scenario-task"[J]. Journal of Safety and Environment, 2023, 23(5): 1568-1578., articleTitle=Optimizing the rescue equipment allocation of major geological disasters based on "scenario-task", refAbstract=null), Reference(id=1168130103142785421, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=1991, volume=4, issue=2, pageStart=245, pageEnd=252, url=null, language=null, rfNumber=[13], rfOrder=20, authorNames=CHENG N G, DANIEL S H, journalName=SIAM Journal on Discrete Mathematics, refType=null, unstructuredReference=CHENG N G, DANIEL S H. Three-dimensional stable matching problems[J]. SIAM Journal on Discrete Mathematics, 1991, 4(2): 245-252., articleTitle=Three-dimensional stable matching problems, refAbstract=null), Reference(id=1168130103218282894, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2021, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[14], rfOrder=21, authorNames=杨洋, journalName=具有独立非循环偏好结构的三边匹配方法及应用研究, refType=null, unstructuredReference=杨洋. 具有独立非循环偏好结构的三边匹配方法及应用研究[D]. 秦皇岛: 燕山大学, 2021., articleTitle=null, refAbstract=null), Reference(id=1168130103310557583, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, doi=null, pmid=null, pmcid=null, year=2021, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[14], rfOrder=22, authorNames=YANG Yang, journalName=Research on decision method and application for three-sided matching with independent acyclic preference structure, refType=null, unstructuredReference=YANG Yang. Research on decision method and application for three-sided matching with independent acyclic preference structure[D]. Qinhuangdao: Yanshan University, 2021., articleTitle=null, refAbstract=null)], funds=[Fund(id=1168130101427315064, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, awardId=2020-RK00-00071-ZF, language=CN, fundingSource=成都市科技项目(2020-RK00-00071-ZF), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1168130096687751494, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, xref=1, ext=[AuthorCompanyExt(id=1168130096691945799, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, companyId=1168130096687751494, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1 School of Transportation and Logistics，Southwest Jiaotong University，Chengdu Sichuan 611756，China), AuthorCompanyExt(id=1168130096696140104, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, companyId=1168130096687751494, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1 西南交通大学 交通运输与物流学院，四川 成都 611756)]), AuthorCompany(id=1168130096788414793, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, xref=2, ext=[AuthorCompanyExt(id=1168130096792609098, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, companyId=1168130096788414793, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2 Tangshan Institute，Southwest Jiaotong University，Tangshan Hebei 063000，China), AuthorCompanyExt(id=1168130096796803403, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, companyId=1168130096788414793, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2 西南交通大学 唐山研究院，河北 唐山 063000)])], figs=[ArticleFig(id=1168130098361278826, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=EN, label=Fig.1, caption=Relationship of emergency rescue three-sided matching, figureFileSmall=yjs4L5Hs1tylFVPq4qO8VA==, figureFileBig=EdOn6x+7XnbCqodfjc+Xrg==, tableContent=null), ArticleFig(id=1168130098415804779, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=CN, label=图1, caption=应急救援三边匹配关系, figureFileSmall=yjs4L5Hs1tylFVPq4qO8VA==, figureFileBig=EdOn6x+7XnbCqodfjc+Xrg==, tableContent=null), ArticleFig(id=1168130098470330732, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=EN, label=Tab.1, caption=

Preference value of rescuers' group for rescue equipment group

, figureFileSmall=null, figureFileBig=null, tableContent=
Dp(ai，bj) b1 b2
D1 D2 D3 D4 D5 D6 D1 D2 D3 D4 D5 D6
a1 3 4 5 7 4 4 4 1 6 4 3 5
a2 6 9 6 4 2 3 7 3 3 6 5 4
a3 5 7 4 5 6 5 9 7 4 3 8 8
a4 4 5 7 8 7 9 3 6 5 2 4 3
Dp(ai，bj) b3 b4
D1 D2 D3 D4 D5 D6 D1 D2 D3 D4 D5 D6
a1 8 4 3 4 6 3 2 4 5 3 3 4
a2 4 6 7 3 4 6 6 3 9 5 2 7
a3 6 8 2 5 9 5 7 6 4 7 8 2
a4 5 6 6 7 5 7 4 2 3 4 5 5
), ArticleFig(id=1168130098533245293, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=CN, label=表1, caption=

救援人员组对救援装备组的偏好值

, figureFileSmall=null, figureFileBig=null, tableContent=
Dp(ai，bj) b1 b2
D1 D2 D3 D4 D5 D6 D1 D2 D3 D4 D5 D6
a1 3 4 5 7 4 4 4 1 6 4 3 5
a2 6 9 6 4 2 3 7 3 3 6 5 4
a3 5 7 4 5 6 5 9 7 4 3 8 8
a4 4 5 7 8 7 9 3 6 5 2 4 3
Dp(ai，bj) b3 b4
D1 D2 D3 D4 D5 D6 D1 D2 D3 D4 D5 D6
a1 8 4 3 4 6 3 2 4 5 3 3 4
a2 4 6 7 3 4 6 6 3 9 5 2 7
a3 6 8 2 5 9 5 7 6 4 7 8 2
a4 5 6 6 7 5 7 4 2 3 4 5 5
), ArticleFig(id=1168130098638102894, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=EN, label=Tab.2, caption=

Preference value of rescuers' group for disaster location

, figureFileSmall=null, figureFileBig=null, tableContent=
Eq(ai，ck) c1 c2 c3
E1 E2 E3 E4 E1 E2 E3 E4 E1 E2 E3 E4
a1 3 9 5 4 4 4 7 5 3 4 5 7
a2 7 4 8 3 8 6 3 4 5 7 4 9
a3 4 5 6 5 6 6 5 3 6 3 8 8
a4 6 7 3 6 5 4 2 6 4 5 5 6
Eq(ai，ck) c4 c5
E1 E2 E3 E4 E1 E2 E3 E4
a1 7 2 2 5 5 4 5 7
a2 4 7 8 3 4 9 4 5
a3 6 3 5 9 4 6 8 6
a4 4 5 3 4 8 6 4 3
), ArticleFig(id=1168130098709406063, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=CN, label=表2, caption=

救援人员组对受灾地点的偏好值

, figureFileSmall=null, figureFileBig=null, tableContent=
Eq(ai，ck) c1 c2 c3
E1 E2 E3 E4 E1 E2 E3 E4 E1 E2 E3 E4
a1 3 9 5 4 4 4 7 5 3 4 5 7
a2 7 4 8 3 8 6 3 4 5 7 4 9
a3 4 5 6 5 6 6 5 3 6 3 8 8
a4 6 7 3 6 5 4 2 6 4 5 5 6
Eq(ai，ck) c4 c5
E1 E2 E3 E4 E1 E2 E3 E4
a1 7 2 2 5 5 4 5 7
a2 4 7 8 3 4 9 4 5
a3 6 3 5 9 4 6 8 6
a4 4 5 3 4 8 6 4 3
), ArticleFig(id=1168130100634591600, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=EN, label=Tab.3, caption=

Preference value of rescue equipment group for disaster location

, figureFileSmall=null, figureFileBig=null, tableContent=
Ft(bj，ck) c1 c2 c3
F1 F2 F3 F4 F5 F1 F2 F3 F4 F5 F1 F2 F3 F4 F5
b1 3 7 6 2 6 4 4 2 3 2 4 4 7 4 3
b2 4 6 2 3 7 8 3 7 5 5 8 6 3 6 9
b3 8 2 3 7 2 5 7 6 6 8 4 7 8 3 4
b4 5 3 4 7 4 3 5 4 3 1 3 2 4 5 6
Ft(bj，ck) c4 c5
F1 F2 F3 F4 F5 F1 F2 F3 F4 F5
b1 6 8 4 5 5 6 3 8 4 2
b2 8 5 6 2 1 3 6 2 5 7
b3 4 7 4 7 2 8 7 6 7 1
b4 3 4 2 3 6 5 2 4 3 4
), ArticleFig(id=1168130100735254897, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=CN, label=表3, caption=

救援装备组对受灾地点的偏好值

, figureFileSmall=null, figureFileBig=null, tableContent=
Ft(bj，ck) c1 c2 c3
F1 F2 F3 F4 F5 F1 F2 F3 F4 F5 F1 F2 F3 F4 F5
b1 3 7 6 2 6 4 4 2 3 2 4 4 7 4 3
b2 4 6 2 3 7 8 3 7 5 5 8 6 3 6 9
b3 8 2 3 7 2 5 7 6 6 8 4 7 8 3 4
b4 5 3 4 7 4 3 5 4 3 1 3 2 4 5 6
Ft(bj，ck) c4 c5
F1 F2 F3 F4 F5 F1 F2 F3 F4 F5
b1 6 8 4 5 5 6 3 8 4 2
b2 8 5 6 2 1 3 6 2 5 7
b3 4 7 4 7 2 8 7 6 7 1
b4 3 4 2 3 6 5 2 4 3 4
), ArticleFig(id=1168130100861084018, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=EN, label=Tab.4, caption=

Standardized preference value of rescuers' group for rescue equipment group

, figureFileSmall=null, figureFileBig=null, tableContent=
D ¯ p ( a i ， b j ) b1 b2
D1 D2 D3 D4 D5 D6 D1 D2 D3 D4 D5 D6
a1 0.167 1.000 0.667 1.000 0.333 0.500 0.333 0.000 1.000 0.250 0.000 0.000
a2 0.667 1.000 0.500 0.333 0.000 1.000 1.000 0.000 0.000 1.000 1.000 0.750
a3 0.000 0.500 1.000 0.500 0.000 0.500 1.000 0.500 1.000 0.000 0.667 0.000
a4 0.500 0.750 1.000 1.000 1.000 0.000 0.000 1.000 0.500 0.000 0.000 1.000
D ¯ p ( a i ， b j ) b3 b4
D1 D2 D3 D4 D5 D6 D1 D2 D3 D4 D5 D6
a1 1.000 1.000 0.000 0.250 1.000 1.000 0.000 1.000 0.667 0.000 0.000 0.500
a2 0.000 0.500 0.667 0.000 0.667 0.250 0.667 0.000 1.000 0.667 0.000 0.000
a3 0.250 1.000 0.000 0.500 1.000 0.500 0.500 0.000 1.000 1.000 0.667 1.000
a4 1.000 1.000 0.750 0.833 0.333 0.333 0.500 0.000 0.000 0.333 0.333 0.667
), ArticleFig(id=1168130100936581491, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=CN, label=表4, caption=

救援人员组对救援装备组的标准化偏好值

, figureFileSmall=null, figureFileBig=null, tableContent=
D ¯ p ( a i ， b j ) b1 b2
D1 D2 D3 D4 D5 D6 D1 D2 D3 D4 D5 D6
a1 0.167 1.000 0.667 1.000 0.333 0.500 0.333 0.000 1.000 0.250 0.000 0.000
a2 0.667 1.000 0.500 0.333 0.000 1.000 1.000 0.000 0.000 1.000 1.000 0.750
a3 0.000 0.500 1.000 0.500 0.000 0.500 1.000 0.500 1.000 0.000 0.667 0.000
a4 0.500 0.750 1.000 1.000 1.000 0.000 0.000 1.000 0.500 0.000 0.000 1.000
D ¯ p ( a i ， b j ) b3 b4
D1 D2 D3 D4 D5 D6 D1 D2 D3 D4 D5 D6
a1 1.000 1.000 0.000 0.250 1.000 1.000 0.000 1.000 0.667 0.000 0.000 0.500
a2 0.000 0.500 0.667 0.000 0.667 0.250 0.667 0.000 1.000 0.667 0.000 0.000
a3 0.250 1.000 0.000 0.500 1.000 0.500 0.500 0.000 1.000 1.000 0.667 1.000
a4 1.000 1.000 0.750 0.833 0.333 0.333 0.500 0.000 0.000 0.333 0.333 0.667
), ArticleFig(id=1168130101016273268, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=EN, label=Tab.5, caption=

Standardized preference value for disaster location for rescuers' group

, figureFileSmall=null, figureFileBig=null, tableContent=
E q ¯ ( a i ， c k ) c1 c2 c3
E1 E2 E3 E4 E1 E2 E3 E4 E1 E2 E3 E4
a1 1.000 0.000 0.400 1.000 0.750 0.714 0.000 0.667 1.000 0.714 0.400 0.000
a2 0.250 1.000 0.000 1.000 0.000 0.600 1.000 0.833 0.750 0.400 0.800 0.000
a3 1.000 0.333 0.667 0.667 0.000 0.000 1.000 1.000 0.000 1.000 0.000 0.167
a4 0.500 0.000 0.667 0.000 0.750 1.000 1.000 0.000 1.000 0.667 0.000 0.000
E q ¯ ( a i ， c k ) c4 c5
E1 E2 E3 E4 E1 E2 E3 E4
a1 0.000 1.000 1.000 0.667 0.500 0.714 0.400 0.000
a2 1.000 0.400 0.000 1.000 1.000 0.000 0.800 0.667
a3 0.000 1.000 1.000 0.000 1.000 0.000 0.000 0.500
a4 1.000 0.667 0.667 0.667 0.000 0.333 0.333 1.000
), ArticleFig(id=1168130101100159349, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=CN, label=表5, caption=

救援人员组对受灾地点的标准化偏好值

, figureFileSmall=null, figureFileBig=null, tableContent=
E q ¯ ( a i ， c k ) c1 c2 c3
E1 E2 E3 E4 E1 E2 E3 E4 E1 E2 E3 E4
a1 1.000 0.000 0.400 1.000 0.750 0.714 0.000 0.667 1.000 0.714 0.400 0.000
a2 0.250 1.000 0.000 1.000 0.000 0.600 1.000 0.833 0.750 0.400 0.800 0.000
a3 1.000 0.333 0.667 0.667 0.000 0.000 1.000 1.000 0.000 1.000 0.000 0.167
a4 0.500 0.000 0.667 0.000 0.750 1.000 1.000 0.000 1.000 0.667 0.000 0.000
E q ¯ ( a i ， c k ) c4 c5
E1 E2 E3 E4 E1 E2 E3 E4
a1 0.000 1.000 1.000 0.667 0.500 0.714 0.400 0.000
a2 1.000 0.400 0.000 1.000 1.000 0.000 0.800 0.667
a3 0.000 1.000 1.000 0.000 1.000 0.000 0.000 0.500
a4 1.000 0.667 0.667 0.667 0.000 0.333 0.333 1.000
), ArticleFig(id=1168130101163073910, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149739134903828963, language=EN, label=Tab.6, caption=

Standardized preference value of rescue equipment group for disaster location

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F t ¯ ( b j ， c k ) c1 c2 c3
F1 F2 F3 F4 F5 F1 F2 F3 F4 F5 F1 F2 F3
b1 1.000 0.200 0.333 1.000 0.000 0.667 0.800 1.000 0.667 1.000 0.667 0.800 0.167
b2 0.800 0.000 1.000 0.750 0.250 0.000 1.000 0.000 0.250 0.500 0.000 0.000 0.800
b3 0.000 1.000 1.000 0.000 0.857 0.750 0.000 0.400 0.250 0.000 1.000 0.000 0.000
b4 0.000 0.667 0.000 0.000 0.400 1.000 0.000 0.000 1.000 1.000 1.000 1.000 0.000
F t ¯ ( b j ， c k ) c3 c4 c5
F4 F5 F1 F2 F3 F4 F5 F1 F2 F3 F4 F5
b1 0.333 0.750 0.000 0.000 0.667 0.000 0.250 0.000 1.000 0.000 0.333 1.000
b2 0.000 0.000 0.000 0.333 0.200 1.000 1.000 1.000 0.000 1.000 0.250 0.250
b3 1.000 0.571 1.000 0.000 0.800 0.000 0.857 0.000 0.000 0.400 0.000 1.000
b4 0.500 0.000 1.000 0.333 1.000 1.000 0.000 0.000 1.000 0.000 1.000 0.400
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救援装备组对受灾地点的标准化偏好值

, figureFileSmall=null, figureFileBig=null, tableContent=
F t ¯ ( b j ， c k ) c1 c2 c3
F1 F2 F3 F4 F5 F1 F2 F3 F4 F5 F1 F2 F3
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b2 0.800 0.000 1.000 0.750 0.250 0.000 1.000 0.000 0.250 0.500 0.000 0.000 0.800
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b4 0.000 0.667 0.000 0.000 0.400 1.000 0.000 0.000 1.000 1.000 1.000 1.000 0.000
F t ¯ ( b j ， c k ) c3 c4 c5
F4 F5 F1 F2 F3 F4 F5 F1 F2 F3 F4 F5
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b2 0.000 0.000 0.000 0.333 0.200 1.000 1.000 1.000 0.000 1.000 0.250 0.250
b3 1.000 0.571 1.000 0.000 0.800 0.000 0.857 0.000 0.000 0.400 0.000 1.000
b4 0.500 0.000 1.000 0.333 1.000 1.000 0.000 0.000 1.000 0.000 1.000 0.400
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基于三边匹配理论的应急救援分配决策
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郭茜 1 , 周伊可 2 , 吴刚 1, 2, **
中国安全科学学报 | 应急技术与管理 2024,34(3): 222-229
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中国安全科学学报 | 应急技术与管理 2024, 34(3): 222-229
基于三边匹配理论的应急救援分配决策
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郭茜1 , 周伊可2, 吴刚1, 2, **
作者信息
  • 1 西南交通大学 交通运输与物流学院，四川 成都 611756
  • 2 西南交通大学 唐山研究院，河北 唐山 063000

    • 郭茜 (1975—)，女，河南南阳人，博士，讲师，主要从事物流管理、项目管理等方面的研究。E-mail：。

通讯作者:

** 吴刚(1972—)，男，四川南江人，博士，教授，主要从事物流与供应链管理等方面的研究。E-mail：。
Emergency rescue allocation decision-making based on three-sided matching theory
Qian GUO1 , Yike ZHOU2, Gang WU1, 2, **
Affiliations
  • 1 School of Transportation and Logistics，Southwest Jiaotong University，Chengdu Sichuan 611756，China
  • 2 Tangshan Institute，Southwest Jiaotong University，Tangshan Hebei 063000，China
出版时间: 2024-03-28 doi: 10.16265/j.cnki.issn1003-3033.2024.03.0625
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摘要
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为解决大型地质灾害背景下应急救援初期救援人员、应急救援装备与受灾地点的分配问题，提高应急救援的效率和质量，首先，将应急救援三方主体之间的选择过程描述为三边匹配问题；然后，标准化处理匹配三方主体的多属性偏好评价信息，构造多属性综合偏好得分矩阵，并以系统稳定性和总偏好效用最大化为目标，建立应急救援初期背景下的三边匹配满意稳定模型；最后，通过算例验证模型的可行性和有效性。结果表明：该模型考虑各主体偏好对于资源分配的影响，能实现应急救援背景下救援人员、应急救援装备与受灾地点三方主体的合理匹配，有助于缩短应急救援部署时间，提高应急救援的效率和质量。

应急救援  /  三边匹配  /  分配决策  /  偏好值  /  满意稳定匹配模型

To address the issues of allocation of emergency rescuers，emergency rescue equipment，and disaster locations in the early stage of emergency rescue under the background of large-scale geological disasters，as well as improve the efficiency and quality of emergency rescue，an emergency rescue allocation decision-making method was proposed based on the three-sided matching theory. Firstly，the selection process among the three parties of emergency rescue was presented as a three-sided matching issue. Then，the multi-attribute preference evaluation information of the matching three parties was standardized，and a multi-attribute comprehensive preference score matrix was proposed. Furthermore，a three-sided matching stable and satisfactory model in the early stage of emergency rescue was developed to maximize system stability and total preference utility. Finally，the performance and accuracy of the proposed model were validated against cases. The results indicated that the proposed model reached reasonable matching between rescuers，emergency rescue equipment，and disaster locations in emergency rescue scenarios due to considering the effects of various parties' preferences on resource allocation. Furthermore，it can contribute to reducing the deployment time of emergency rescue operations and improve emergency efficiency and quality.

emergency rescue  /  three-sided matching  /  allocation decision  /  preference value  /  stable and satisfactory matching model
郭茜, 周伊可, 吴刚. 基于三边匹配理论的应急救援分配决策. 中国安全科学学报, 2024 , 34 (3) : 222 -229 . DOI: 10.16265/j.cnki.issn1003-3033.2024.03.0625
Qian GUO, Yike ZHOU, Gang WU. Emergency rescue allocation decision-making based on three-sided matching theory[J]. China Safety Science Journal, 2024 , 34 (3) : 222 -229 . DOI: 10.16265/j.cnki.issn1003-3033.2024.03.0625
正文
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0 引言
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突发地质灾害后的应急救援初期，救援人员与装备设施等应急资源匮乏[1]，受灾点的需求远大于供给。如何在有限时间内，实现受灾地点人员、装备的合理分配，保障救援的效率和质量，是应急管理领域研究的重点问题之一。
针对应急资源调度，诸多学者研究了不同灾情条件下救援物资的分配与运输问题，如吕伟等[2]以最大化时间满意度和需求满意度为目标，兼顾救援过程中的公平性原则，构建了考虑综合时间窗约束的应急物资分配与路径规划模型；宋英华等[3]以最小化调度时间和最大化应急物资分配公平性为目标，构建了考虑差异化灾情分级的应急物资公平调度优化模型；张民波等[4]以最小化配送时间、最小化疫区物资未满足程度为目标，构建了传染性生物危险源扩散后疫区应急物资选址—分配模型。除救援物资外，人员和装备也是应急救援中的重要资源，是救援行动成功的重要保障。人员对于任务的选择具有一定偏好性，不能像物资一样被动调运。为此，杨琴等[5]考虑了人员与受灾点之间的双向选择问题，根据双方在多个评价指标下的心理感知，构建了感知契合度、接受度函数，以最大化感知契合度和接受度为目标，建立双边匹配决策模型，实现了人员与任务的合理匹配。现有研究在物资分配与运输问题上，实现了应急物资的合理调配及人员和任务的合理匹配，但是，多数研究均未考虑应急救援装备高价值、稀缺性、异质性等特点，且忽略了应急救援背景下装备、人员、受灾点三方主体的匹配需求。
鉴于此，笔者拟引入三边匹配决策理论，以大型地质灾害爆发后的应急救援初期为研究背景，将救援人员、救援装备、受灾点作为参与匹配决策的三方独立主体，依据主体之间的偏好评价信息，建立最大化主体总满意度的三边匹配决策满意稳定模型，在多属性指标体系下实现主体之间的满意稳定匹配，并通过算例验证模型的可行性和有效性，以期有效提升应急救援调度管理水平。
1 基于三边匹配理论的问题描述
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三边匹配理论是匹配决策理论的拓展[6⇓-8]，是决策者根据三边主体的偏好评价信息，以满意、稳定、公平等指标为决策目标，寻求最优匹配的过程[9⇓-11]。
以大型地质灾害发生后的应急救援初期为背景，该时期的首要任务是确定受灾地点的个数、具体位置以及受灾严重程度，合理调配所有的应急救援人员和救援装备，以提高受灾民众的存活率[12]。因此，救援人员、救援装备、受灾地点三方主体之间的快速合理匹配十分必要。
基于三边匹配理论，设应急救援人员组集合为A={a1，a2，…，ai，…，an}，ai为第i组应急救援人员组，i∈I，I={1，2，…，n}，n为应急救援人员组的总数量，1≤n<l，l为受灾地点的总数量；应急救援装备组集合为B={b1，b2，…，bj，…，bm}，bj为第j组应急救援装备组，j∈J，J={1，2，…，m}，m为应急救援装备组的总数量，1≤m<l;受灾地点构成的集合为C={c1，c2，…，ck，…，cl}，ck为第k处受灾地点，k∈K，K={1，2，…，l}。
三方主体间的偏好评价信息是匹配决策的依据。在大型地质灾害发生后的救援初期，救援人员组评价应急救援装备组的可靠性、恶劣天气适应性、极端地形适应性、作业效率、设备质量、能耗等多方面的偏好，并评价受灾地点的受灾程度、救援任务量、人员伤亡情况、二者距离等多方面的偏好；同时，由于救援初期装备紧缺，应急救援装备组从受灾地气象恶劣程度、地理环境恶劣程度、塌方程度、受灾人数、二者距离等多方面评价受灾地点的偏好。此时，三方主体均以独立形式对其他方各主体单独作出偏好评价，且3个偏好边未构成循环关系[13]。因此，应急救援人员组、应急救援装备组、受灾地点构成基于多指标综合评价下的三边独立非循环匹配系统，如图1所示。
综上所述，文中所解决的主要问题如下：在多指标评价体系下，基于应急救援人员组、应急救援装备组、受灾地点三方主体间的评价得分信息，从系统偏好最优和三方主体间关系最稳定的视角，寻找最大化系统偏好以及满足系统稳定性需求的最优满意稳定匹配方案。
2 应急救援分配决策模型构建
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2.1 多指标评价体系下的综合偏好得分矩阵
设应急救援人员组对应急救援装备组的评价指标集为D={D1，D2，…，Dp，…，Dh}，指标Dp的属性权重为wp，p=1，2，…，h，h为应急救援人员组对应急救援装备组评价指标的总数量；应急救援人员组对受灾地点的评价集为E={E1，E2，…，Eq，…，Es}，指标Eq的属性权重为ηq，q=1，2，…，s，s为应急救援人员组对受灾地点评价指标的总数量；应急救援装备组对受灾地点的评价指标集为F={F1，F2，…，Ft，…，Fr}，指标Ft的属性权重为λt，t=1，2，…，r，r为应急救援装备组对受灾地点评价指标的总数量。设在多指标体系下，应急救援人员组ai对应急救援装备组bj在评价指标Dp上的得分为Dp(ai，bj);应急救援人员组ai对受灾地点ck在评价指标Eq上的得分为Eq(ai，ck);应急救援装备组bj对受灾地点ck在评价指标Ft上的得分为Ft(bj，ck)。
为消除不同量纲和评价尺度对匹配结果的影响，采用Min-max方法标准化处理偏好评价信息。上述体系的指标分为2大类：效益型属性和成本型属性，其偏好属性值计算如下：
$overline{D}_{p}\left(a_{i}，b_{j}\right)=\left\{\begin{array}{l} \frac{D_{p}\left(a_{i}，b_{j}\right)-\min _{j \in J}\left\{D_{p}\left(a_{i}，b_{j}\right)\right\}}{\max _{j \in J}\left\{D_{p}\left(a_{i}，b_{j}\right)\right\}-\min _{j \in J}\left\{D_{p}\left(a_{i}，b_{j}\right)\right\}}，\\ D_{p} \text { 为效益型属性 } \\ \frac{\max _{j \in J} D_{p}\left(a_{i}，b_{j}\right)-D_{p}\left(a_{i}，b_{j}\right)}{\max _{j \in J}\left\{D_{p}\left(a_{i}，b_{j}\right)\right\}-\min _{j \in J}\left\{D_{p}\left(a_{i}，b_{j}\right)\right\}}，\\ D_{p} \text { 为成本型属性 } \end{array}\right.$
$\overline{E}_{q}\left(a_{i}，c_{k}\right)=\left\{\begin{array}{l} \frac{E_{q}\left(a_{i}，c_{k}\right)-\min _{k \in K}\left\{E_{q}\left(a_{i}，c_{k}\right)\right\}}{\max _{k \in k}\left\{E_{q}\left(a_{i}，c_{k}\right)\right\}-\min _{k \in K}\left\{E_{q}\left(a_{i}，c_{k}\right)\right\}}，\\ E_{q} \text { 为效益型属性 } \\ \frac{\max _{k \in K} E_{q}\left(a_{i}，c_{k}\right)-E_{q}\left(a_{i}，c_{k}\right)}{\max _{k \in K}\left\{E_{q}\left(a_{i}，c_{k}\right)\right\}-\min _{k \in K}\left\{E_{q}\left(a_{i}，c_{k}\right)\right\}}，\\ E_{q} \text { 为成本型属性 } \end{array}\right.$
$\overline{F}_{t}\left(b_{j}，c_{k}\right)=\left\{\begin{array}{l} \frac{F_{t}\left(b_{j}，c_{k}\right)-\min _{k \in K}\left\{F_{t}\left(b_{j}，c_{k}\right)\right\}}{\max _{k \in K}\left\{F_{t}\left(b_{j}，c_{k}\right)\right\}-\min _{k \in K}\left\{F_{t}\left(b_{j}，c_{k}\right)\right\}}，\\ F_{t} \text { 为效益型属性 } \\ \frac{\max _{k \in K} F_{t}\left(b_{j}，c_{k}\right)-F_{t}\left(b_{j}，c_{k}\right)}{\max _{k \in K}\left\{F_{t}\left(b_{j}，c_{k}\right)\right\}-\min _{k \in K}\left\{F_{t}\left(b_{j}，c_{k}\right)\right\}}，\\ F_{t} \text { 为成本型属性 } \end{array}\right.$
多指标评价体系下的三边匹配系统中，设应急救援人员组集合A中主体ai对应急救援装备组集合B中主体bj方向的主体综合偏好得分为 S A B → ( a i ， b j );应急救援人员组集合A中主体ai对受灾地点集合C中主体ck方向的主体综合偏好得分为 S A C → ( a i ， c k );应急救援装备组集合B中主体bj对受灾地点集合C中主体ck方向的主体综合偏好得分为 S B C → ( b j ， c k )。其中，
S A B → ( a i ， b j ) = ∑ p = 1 h D p ¯ ( a i ， b j ) w p
S A C → ( a i ， c k ) = ∑ q = 1 s E q ¯ ( a i ， c k ) η q
S B C → ( b j ， c k ) = ∑ t = 1 r F t ¯ ( b j ， c k ) λ t
应急救援人员组集合A对应急救援装备组集合B的主体综合偏好得分矩阵为 S A B →;应急救援人员组集合A对受灾地点集合C的主体综合偏好得分矩阵为 S A C →;应急救援装备组集合B对受灾地点集合C的主体综合偏好得分矩阵为 S B C →。其中，
S A B → = S A B → ( a i ， b j ) n × m
S A C → = S A C → ( a i ， c k ) n × l
S B C → = S B C → ( b j ， c k ) m × l
其中，i∈I，I={1，2，…，n};j∈J，J={1，2，…，m};k∈K，K={1，2，…，l}。
2.2 三边匹配满意稳定条件
在三边匹配系统中，由救援人员、救援装备、受灾地点三方主体构成的有序组(ai，bj，ck)∈A×B×C称为匹配组。由全体匹配组构成的集合，称为该匹配系统的一个匹配，设为M [13]。设N(M，x)为匹配M中由x构成的匹配组的个数，N(M，x)={0，1}，其中，x∈A∪B∪C，N(M，x)=0表示x尚处于闲置状态，在M中尚未与其他边的主体匹配成组；N(M，x)=1 表示x已与其他边的主体匹配成组[13]。设Ω=A×B×C，对于三边独立非循环匹配M，若Ω中存在M之外的匹配组(ai，bj，ck)∈Ω-M满足条件如下：
S A B → ( a i ， b j ) ≥ S A B → a i ， M A B → ( a i )
S A C → ( a i ， c k ) ≥ S A C → a i ， M A C → ( a i )
S A B → ( a i ， b j ) - S A B → a i ， M A B → ( a i ) 2 + S A C → ( a i ， c k ) - S A C → a i ， M A C → ( a i ) 2 ≠ 0
S B C → ( b j ， c k ) > S B C → b j ， M B C → ( b j )
N ( M ， c k ) = 0
则称匹配组(ai，bj，ck)为匹配M的一个阻塞组[14]。对于精确偏好值信息下的三边独立非循环匹配M，若∀(ai，bj，ck)∈Ω-M均不同时满足式(10)—式(14)，则M不存在阻塞组，此时称M为稳定匹配[14]，即救援人员、救援装备、受灾地点三方主体构成匹配不存在阻塞组，达到稳定匹配。
2.3 应急救援三边匹配模型构建
2.3.1 三边匹配模型假设
1) 应急救援初期救援人员和应急救援装备紧缺，不能满足所有受灾地点的需要，因此，受灾地点对于救援人员、救援装备无选择权。
2) 该模型为一对一匹配，即应急救援人员组、应急救援装备组与受灾地点为一一对应关系。
3) 应急救援人员组集合A中各主体均由国家专业救援人员组成，具备操作各种救援设备的能力。
4) 各主体对于匹配结果完全接受，即不考虑主体心理行为。
2.3.2 应急救援三边满意稳定匹配模型
基于三方主体对于系统总体偏好得分最优和稳定性2方面的匹配需求，建立三边独立非循环满意稳定匹配模型如下：
m a x z = w 1 ∑ i = 1 n ∑ j = 1 m ∑ k = 1 l u i j x i j k + w 2 ∑ i = 1 n ∑ j = 1 m ∑ k = 1 l v i k x i j k + w 3 ∑ i = 1 n ∑ j = 1 m ∑ k = 1 l w j k x i j k
s . t . ∑ j = 1 m ∑ k = 1 l x i j k ≤ 1 ， i = 1，2 ， … ， n .
∑ i = 1 n ∑ k = 1 l x i j k ≤ 1 ， j = 1，2 ， … ， m .
∑ i = 1 n ∑ j = 1 m x i j k ≤ 1 ， k = 1，2 ， … ， l .
x i j k = { 0，1 } ， i ∈ I ; j ∈ J ; k ∈ K .
∑ i = 1 n ∑ j = 1 m ∑ k = 1 l x i j k = m i n { n ， m ， l } ， i ∈ I ， j ∈ J ， k ∈ K .
x i j k + ∑ k ' = 1 l ∑ j ' ： u i j ' > u i j x i j ' k ' + ∑ j ″ = 1 m ∑ k ″ ： v i k ″ > v i k x i j ″ k ″ + ∑ j ' ≠ j u i j ' = u i j 　 ∑ k ″ ≠ k v i k ″ = v i k x i j ' k ″ + ∑ i ' = 1 n 　 ∑ k ‴ ： w j k ‴ ≥ w j k x i ' j k ‴ + ∑ i ″ = 1 n ∑ j ‴ = 1 m x i ″ j ‴ k ≥ 1
其中， u i j = S A B → ( a i ， b j ) ， v i k = S A C → ( a i ， c k ) ， w j k = S B C → ( b j ， c k )。
式(15)为目标函数，表示满意稳定匹配模型以参与匹配的三方总体偏好得分最大化为目标。式(16)—式(18)分别为集合A、B、C中任意一个主体在匹配M中至多结成一个匹配组；式(19)xijk=0为ai，bj，ck三者在M中未能结成一个匹配组，即(ai，bj，ck)∉M，xijk=1为ai，bj，ck三者在M中结成一个匹配组，即(ai，bj，ck)∈M;式(20)为匹配M中所包含的匹配组个数，等于集合A、B、C中的最小主体数；式(21)为对匹配稳定性的约束条件，即满足该式的匹配M不存在阻塞组。
3 应急救援分配决策数值算例
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以我国西南地区某地发生的大型地质灾害为例，灾害发生后地方政府紧急部署救灾工作，集结多方救援力量，并成立应急救援指挥中心，组织开展救援行动。指挥中心紧急募集到的无人机、机器人、推土机、挖掘装备等救援装备，其型号、性能、工作效率及救援能力存在差异，且无法满足所有受灾地的实际需求，指挥中心将这些现有装备分组。此外，已有部分国家专业救援人员抵达救援指挥部，集结成若干救援小队。采用文中所建立的应急救援三边满意稳定匹配模型，快速匹配装备组、救援小队与受灾地。
应急救援指挥中心在第一时间收集匹配所需的三方主体间偏好评价信息。设应急救援人员组集合A={a1，a2，a3，a4}，应急救援装备组集合为B={b1，b2，b3，b4}，受灾地点的集合为C={c1，c2，…，c5}。救援人员组就可靠性D1、恶劣天气适应性D2、极端地形适应性D3、作业效率D4、设备质量D5、能耗D6，对应急救援装备组评价，相应指标权重分别为w1=0.2、w2=0.1、w3=0.2、w4=0.2、w5=0.15、w6=0.15。同样地，救援人员组就受灾程度E1、救援任务量E2、人员伤亡情况E3、二者距离E4，对受灾地点评价，相应的指标权重分别为η1=0.2、η2=0.35、η3=0.35、η4=0.1。
救援装备组就受灾地气象恶劣程度F1、地理环境恶劣程度F2、塌方程度F3、受灾人数F4、二者距离F5对受灾地点评价，相应指标权重分别为λ1=0.3、λ2=0.3、λ3=0.15、λ4=0.15、λ5=0.1。由此，应急救援人员组、应急救援装备组、受灾地点构成了三边独立非循环偏好，各方主体认识的主观性、复杂性造成了在同一属性偏好上的差异，3个偏好方向的主体偏好值见表1—表3。
依据表1—表3中的精确偏好值信息，分别根据式(1)—式(3)标准化处理3个偏好方向上主体的精确偏好值，获得3个偏好方向上主体的标准化精确值 D ¯ p ( a i ， b j ) 、 E ¯ q ( a i ， c k ) 、 F ¯ t ( b j ， c k )，见表4—表6。
分别根据式(4)—式(6)，计算3个偏好方向上的各主体综合偏好得分 S A B → ( a i ， b j ) 、 S A C → ( a i ， c k ) 、 S B C → ( b j ， c k )，从而获得3个偏好方向上各主体的综合偏好得分矩阵 S A B → 、 S A C →和 S B C →分别为：
S A B → = 0 . 592 0 . 317 0 . 650 0 . 308 0 . 550 0 . 663 0 . 321 0 . 467 0 . 425 0 . 550 0 . 475 0 . 750 0 . 725 0 . 350 0 . 717 0 . 317 S A C → = 0 . 440 0 . 467 0 . 590 0 . 767 0 . 490 0 . 500 0 . 643 0 . 570 0 . 440 0 . 547 0 . 617 0 . 450 0 . 367 0 . 700 0 . 250 0 . 334 0 . 850 0 . 434 0 . 734 0 . 333 S B C → = 0 . 560 0 . 790 0 . 590 0 . 125 0 . 450 0 . 528 0 . 388 0 . 120 0 . 380 0 . 513 0 . 536 0 . 323 0 . 507 0 . 506 0 . 160 0 . 240 0 . 550 0 . 675 0 . 700 0 . 490
设置3个偏好方向的满意度权重分别为w1=0.3、w2=0.4、w3=0.3，根据式(15)确定该算例的满意稳定匹配模型的目标函数为 m a x z = 0.3 ∑ i = 1 4 ∑ j = 1 4 ∑ k = 1 5 u i j x i j k + 0.4 ∑ i = 1 4 ∑ j = 1 4 ∑ k = 1 5 v i k x i j k + 0.3 ∑ i = 1 4 ∑ j = 1 4 ∑ k = 1 5 w j k x i j k，使用Matlab软件求解该满意稳定匹配模型，解得x133=x225=x344=x412=1，其余xijk=0，从而得到三边满意稳定匹配方案为{(a1，b3，c3)，(a2，b2，c5)，(a3，b4，c4)，(a4，b1，c2)}。
上述分析结果表明：第1组应急救援人员、第3组应急救援装备应分配至第3处受灾地点，第2组应急救援人员、第2组应急救援装备应分配至第5处受灾地点，第3组应急救援人员、第4组应急救援装备应分配至第4处受灾地点，第4组应急救援人员、第1组应急救援装备应分配至第2处受灾地点。此外，还可以通过改变主体偏好信息以及偏好方向的满意度权重，以适应不同的应急救援条件，灵活满足应急救援三方主体的匹配需求。与文献[5]实现受灾群众与救助人员的双边匹配决策方法相比，文中考虑了救援装备高价值、异质性等特性，所建立的三边匹配模型能够生成满意稳定的人员—装备—受灾地分配决策方案，更为全面地指导应急救援资源的部署。
4 结论
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1) 文中所建三边匹配应急救援决策分配模型能够实现大型地质灾害背景下应急救援初期救援人员组、应急救援装备组、受灾地点三方主体间的独立非循环满意稳定匹配，符合灾害发生后匹配决策主体众多且主体间偏好关系复杂的实际情况，能够使有限资源得到合理匹配，有助于提升应急资源调度水平。
2) 模型假设中限定救援人员均为国家专业救援人员，然而，在实际救灾中，各类社会救援队伍也是救援行动的中坚力量，其救援能力存在一定差异。如何将救援人员的异质性融入分配决策模型中，是未来研究需要解决的问题。
3) 未来研究中，应进一步考虑主体对于匹配结果的有限妥协性、不完全接受性、共情心理等因素。此外，考虑到应急救援初期受灾地点情况的不确定性，灾情不断变化情况下的三边匹配问题，也是需要进一步探索的方向。
基金
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  • 成都市科技项目(2020-RK00-00071-ZF)
文献
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参考文献 引证文献
排序方式：
[1]
高鹏飞, 刘方翔, 黄建华, 等. 考虑灾民心理痛苦的震后应急物资调配问题研究[J]. 中国安全科学学报, 2022, 32(11): 200-207.
GAO Pengfei, LIU Fangxiang, HUANG Jianhua, et al. Research on post-earthquake emergency material allocation considering psychological pain of victims[J]. China Safety Science Journal, 2022, 32(11): 200-207.
[2]
吕伟, 李志红, 冯满满, 等. 考虑资源和时间窗约束的应急物资调配模型[J]. 中国安全科学学报, 2019, 29(12): 137-143.
LYU Wei, LI Zhihong, FENG Manman, et al. Emergency material allocation in consideration of resource and time window constraints[J]. China Safety Science Journal, 2019, 29(12): 137-143.
[3]
宋英华, 白明轩, 马亚萍, 等. 考虑区域灾情分级的应急物资公平调度优化模型[J]. 中国安全科学学报, 2022, 32(1): 172-179.
SONG Yinghua, BAI Mingxuan, MA Yaping, et al. Optimal model for fair dispatch of emergency materials considering regional disaster classification[J]. China Safety Science Journal, 2022, 32(1): 172-179.
[4]
张民波, 钟子逸, 闫瑾, 等. 考虑生物危险源扩散的疫区应急物资调配模型[J]. 中国安全科学学报, 2023, 33(11): 206-213.
ZHANG Minbo, ZHONG Ziyi, YAN Jin, et al. Model of emergency supplies allocation in epidemic areas considering spread of biohazard diffusion[J]. China Safety Science Journal, 2023, 33(11): 206-213.
[5]
杨琴, 陈金铭, 刘桔, 等. 基于双边匹配决策的应急救助人员任务分配[J]. 中国安全科学学报, 2019, 29(1): 180-186.
YANG Qin, CHEN Jinming, LIU Ju, et al. Task allocation of emergency rescue workers based on bilateral matching decision[J]. China Safety Science Journal, 2019, 29(1): 180-186.
[6]
GALE D, SHAPLEY L S. College admissions and the stability of marriage[J]. The American Mathematical Monthly, 1962, 69(1): 9-15.
[7]
ROTH A E. The evolution of the labor market for medical interns and residents: a case study in game theory[J]. Journal of Political Economy, 1984, 92(6): 991-1016.
[8]
赵晓冬, 臧誉琪, 孙微. 基于区间犹豫模糊信息双向投影技术的双边匹配决策方法[J]. 运筹与管理, 2017, 26(7): 104-109.
ZHAO Xiaodong, ZANG Yuqi, SUN Wei. Two-sided matching decision method with interval-valued hesitant fuzzy information based on bidirectional projection method[J]. Operations Research and Management Science, 2017, 26(7):104-109.
[9]
袁铎宁, 姜艳萍. 择期手术患者与手术医生的稳定双边匹配模型[J]. 系统工程理论与实践, 2019, 39(7): 1752-1762.
YUAN Duoning, JIANG Yanping. Stable two-sided matching model between selective operation patients and surgeons[J]. Systems Engineering-Theory & Practice, 2019, 39(7): 1752-1762.
[10]
AZEVEDO E M, LESHNO J D. A supply and demand framework for two-sided matching markets[J]. Journal of Political Economy, 2016, 124(5): 1235-1268.
[11]
ECHENIQUE F, WILSON A J, YARIV L. Clearinghouses for two-sided matching: an experimental study[J]. Quantitative Economics, 2016, 7(2): 449-482.
[12]
喇蕊芳, 薛芳明, 白鹏飞, 等. 基于“情景-任务”的重特大地质灾害救援装备调配优化[J]. 安全与环境学报, 2023, 23(5): 1568-1578.
LA Ruifang, XUE Fangming, BAI Pengfei, et al. Optimizing the rescue equipment allocation of major geological disasters based on "scenario-task"[J]. Journal of Safety and Environment, 2023, 23(5): 1568-1578.
[13]
CHENG N G, DANIEL S H. Three-dimensional stable matching problems[J]. SIAM Journal on Discrete Mathematics, 1991, 4(2): 245-252.
[14]
杨洋. 具有独立非循环偏好结构的三边匹配方法及应用研究[D]. 秦皇岛: 燕山大学, 2021.
YANG Yang. Research on decision method and application for three-sided matching with independent acyclic preference structure[D]. Qinhuangdao: Yanshan University, 2021.
2024年第34卷第3期
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doi: 10.16265/j.cnki.issn1003-3033.2024.03.0625
  • 接收时间：2023-09-20
  • 首发时间：2025-07-09
  • 出版时间：2024-03-28
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  • 收稿日期：2023-09-20
  • 修回日期：2023-12-21
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成都市科技项目(2020-RK00-00071-ZF)
作者信息
    1 西南交通大学 交通运输与物流学院，四川 成都 611756
    2 西南交通大学 唐山研究院，河北 唐山 063000

通讯作者:

** 吴刚(1972—)，男，四川南江人，博士，教授，主要从事物流与供应链管理等方面的研究。E-mail：。
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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