{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T05:56:45Z","timestamp":1770271005011,"version":"3.49.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T00:00:00Z","timestamp":1766361600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T00:00:00Z","timestamp":1766361600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"the Major Program of National Fund of Philosophy and Social Science of China","award":["Number 24ZDA099"],"award-info":[{"award-number":["Number 24ZDA099"]}]},{"name":"the Natural Science Foundation of Hebei Province","award":["number 72471019"],"award-info":[{"award-number":["number 72471019"]}]},{"DOI":"10.13039\/501100014213","name":"Instituto Nacional de Ci\u00eancia e Tecnologia - Oceanografia Integrada e Usos M\u00faltiplos da Plataforma Continental e Oceano Adjacente - Centro de Oceanografia Integrada","doi-asserted-by":"publisher","award":["number 2021ZD0114204"],"award-info":[{"award-number":["number 2021ZD0114204"]}],"id":[{"id":"10.13039\/501100014213","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s10878-025-01380-6","type":"journal-article","created":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T20:23:14Z","timestamp":1766434994000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An integer model for optimizing dynamic allocation of medical supplies during the COVID-19"],"prefix":"10.1007","volume":"51","author":[{"given":"Hongqiang","family":"Fan","sequence":"first","affiliation":[]},{"given":"Shuyao","family":"Duan","sequence":"additional","affiliation":[]},{"given":"Xun","family":"Weng","sequence":"additional","affiliation":[]},{"given":"Jingtian","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Lifen","family":"Yun","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,12,22]]},"reference":[{"key":"1380_CR1","doi-asserted-by":"crossref","unstructured":"Annas S, Pratama MI, Rifandi M et al (2020) Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia. Chaos Solitons Fractals 139:110072","DOI":"10.1016\/j.chaos.2020.110072"},{"issue":"14","key":"1380_CR2","doi-asserted-by":"publisher","first-page":"1191","DOI":"10.1080\/09537287.2018.1542026","volume":"29","author":"B Bodaghi","year":"2018","unstructured":"Bodaghi B, Palaneeswaran E, Abbasi B (2018) Bi-objective multi-resource scheduling problem for emergency relief operations. Prod Plann Control 29(14):1191\u20131206","journal-title":"Prod Plann Control"},{"issue":"3","key":"1380_CR3","doi-asserted-by":"publisher","first-page":"1046","DOI":"10.1016\/j.ejor.2017.08.037","volume":"265","author":"\u0130E B\u00fcy\u00fcktahtak\u0131n","year":"2018","unstructured":"B\u00fcy\u00fcktahtak\u0131n \u0130E, des-Bordes E, K\u0131b\u0131\u015f EY (2018) A new epidemics\u2013logistics model: insights into controlling the Ebola virus disease in West Africa. Eur J Oper Res 265(3):1046\u20131063","journal-title":"Eur J Oper Res"},{"issue":"4","key":"1380_CR4","doi-asserted-by":"publisher","first-page":"1103","DOI":"10.1093\/ije\/dyab106","volume":"50","author":"E Campillo-Funollet","year":"2021","unstructured":"Campillo-Funollet E, Van Yperen J, Allman P et al (2021) Predicting and forecasting the impact of local outbreaks of COVID-19: use of SEIR-D quantitative epidemiological modelling for healthcare demand and capacity. Int J Epidemiol 50(4):1103\u20131113","journal-title":"Int J Epidemiol"},{"key":"1380_CR5","unstructured":"China\u2019s Actions in Combating the COVID-19 Pandemic_ White Paper _ China Government Website [EB\/OL]. https:\/\/www.gov.cn\/zhengce\/2020-06\/07\/content_5517737.htm"},{"issue":"3","key":"1380_CR6","doi-asserted-by":"publisher","first-page":"1106","DOI":"10.1016\/j.ejor.2020.09.052","volume":"291","author":"M Du","year":"2021","unstructured":"Du M, Sai A, Kong N (2021) A data-driven optimization approach for multi-period resource allocation in cholera outbreak control. Eur J Oper Res 291(3):1106\u20131116","journal-title":"Eur J Oper Res"},{"issue":"19","key":"1380_CR7","doi-asserted-by":"publisher","first-page":"10560","DOI":"10.3390\/su131910560","volume":"13","author":"J Geng","year":"2021","unstructured":"Geng J, Hou H, Geng S (2021) Optimization of warehouse location and supplies allocation for emergency rescue under joint government\u2013enterprise cooperation considering disaster victims\u2019 distress perception. Sustainability 13(19):10560","journal-title":"Sustainability"},{"issue":"3","key":"1380_CR8","first-page":"930","volume":"16","author":"Z Ghaffari","year":"2020","unstructured":"Ghaffari Z, Nasiri MM, Bozorgi-Amiri A et al (2020) Emergency supply chain scheduling problem with multiple resources in disaster relief operations. Transp Metr A Transp Sci 16(3):930\u2013956","journal-title":"Transp Metr A Transp Sci"},{"key":"1380_CR9","doi-asserted-by":"publisher","first-page":"1667","DOI":"10.1007\/s11071-020-05743-y","volume":"101","author":"S He","year":"2020","unstructured":"He S, Peng Y, Sun K (2020) SEIR modeling of the COVID-19 and its dynamics. Nonlinear Dyn 101:1667\u20131680","journal-title":"Nonlinear Dyn"},{"key":"1380_CR11","doi-asserted-by":"crossref","unstructured":"Huang YJ, Li CH (2019) Backward bifurcation and stability analysis of a network-based SIS epidemic model with saturated treatment function. Phys A Stat Mech Appl 527:121407","DOI":"10.1016\/j.physa.2019.121407"},{"key":"1380_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.tre.2014.11.007","volume":"75","author":"K Huang","year":"2015","unstructured":"Huang K, Jiang Y, CNY Y et al (2015) Modeling multiple humanitarian objectives in emergency response to large-scale disasters. Transp Res E 75:1\u201317","journal-title":"Transp Res E"},{"key":"1380_CR12","unstructured":"Jiang Y, Han J, Zhu J, Hu L, Luo R (2023) Optimization of dynamic medical supplies distribution considering COVID-19\u2019s diffusion rule. J Saf Environ 23(05):1579\u20131587"},{"key":"1380_CR13","doi-asserted-by":"publisher","first-page":"100126","DOI":"10.1016\/j.dajour.2022.100126","volume":"4","author":"V Khodaee","year":"2022","unstructured":"Khodaee V, Kayvanfar V, Haji A (2022) A humanitarian cold supply chain distribution model with equity consideration: the case of COVID-19 vaccine distribution in the European Union. Decis Analytics J 4:100126","journal-title":"Decis Anal J"},{"issue":"6","key":"1380_CR16","doi-asserted-by":"publisher","first-page":"841","DOI":"10.1057\/jors.2015.105","volume":"67","author":"M Liu","year":"2016","unstructured":"Liu M, Zhang D (2016) A dynamic logistics model for medical resources allocation in an epidemic control with demand forecast updating. J Oper Res Soc 67(6):841\u2013852","journal-title":"J Oper Res Soc"},{"issue":"5","key":"1380_CR15","doi-asserted-by":"publisher","first-page":"748","DOI":"10.1080\/01605682.2019.1582589","volume":"71","author":"M Liu","year":"2020","unstructured":"Liu M, Xu X, Cao J et al (2020) Integrated planning for public health emergencies: a modified model for controlling H1N1 pandemic. J Oper Res Soc 71(5):748\u2013761","journal-title":"J Oper Res Soc"},{"key":"1380_CR14","doi-asserted-by":"publisher","first-page":"102464","DOI":"10.1016\/j.tre.2021.102464","volume":"154","author":"J Liu","year":"2021","unstructured":"Liu J, Bai J, Wu D (2021) Medical supplies scheduling in major public health emergencies. Transp Res E 154:102464","journal-title":"Transp Res E"},{"key":"1380_CR17","unstructured":"Liu M, Du Y, Cao J, Zhang D (2022) Optimization model for allocating emergency budget under the environment of epidemic outbreak. Manag Rev 2022, 34(06):315\u2013324"},{"key":"1380_CR18","unstructured":"Pandemic Exposes Shortcomings China\u2019s Emergency Supplies Reserve System Calls for Reform | Institutional Immunity Series | Jiemian News China [EB\/OL] (2020)"},{"key":"1380_CR19","unstructured":"Q&A How is COVID-19 transmitted? [EB\/OL]. www.who.int. https:\/\/www.who.int\/zh\/news-room\/questions-and-answers\/item\/coronavirus-disease-covid-19-how-is-it-transmitted"},{"key":"1380_CR21","unstructured":"SuQ, Lu S (2022) Optimization model and algorithm for multi-period dynamic emergency medical supplies scheduling. Ind Eng Manag 27(04):50\u201357"},{"issue":"2","key":"1380_CR22","doi-asserted-by":"publisher","first-page":"462","DOI":"10.3390\/jcm9020462","volume":"9","author":"B Tang","year":"2020","unstructured":"Tang B, Wang X, Li Q et al (2020) Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions. J Clin Med 9(2):462","journal-title":"J Clin Med"},{"issue":"2","key":"1380_CR23","doi-asserted-by":"publisher","first-page":"775","DOI":"10.1016\/j.jmaa.2003.11.043","volume":"291","author":"W Wang","year":"2004","unstructured":"Wang W, Ruan S (2004) Bifurcations in an epidemic model with constant removal rate of the infectives. J Math Anal Appl 291(2):775\u2013793","journal-title":"J Math Anal Appl"},{"issue":"3","key":"1380_CR25","doi-asserted-by":"publisher","first-page":"2173","DOI":"10.1007\/s12351-021-00655-0","volume":"22","author":"Y Wang","year":"2022","unstructured":"Wang Y, Sun B (2022) Multiperiod optimal emergency material allocation considering road network damage and risk under uncertain conditions. Oper Res Int Journal 22(3):2173\u20132208","journal-title":"Oper Res Int Journal"},{"key":"1380_CR24","doi-asserted-by":"publisher","first-page":"107041","DOI":"10.1016\/j.knosys.2021.107041","volume":"223","author":"Y Wang","year":"2021","unstructured":"Wang Y, Peng S, Xu M (2021) Emergency logistics network design based on space\u2013time resource configuration. Knowl Based Syst 223:107041","journal-title":"Knowl Based Syst"},{"issue":"2","key":"1380_CR26","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1016\/j.ejor.2016.03.052","volume":"254","author":"C Wanying","year":"2016","unstructured":"Wanying C, Alain G, Angel R (2016) Modeling the logistics response to a bioterrorist anthrax attack. Eur J Oper Res 254(2):458\u2013471","journal-title":"Eur J Oper Res"},{"key":"1380_CR27","unstructured":"Weekly epidemiological update on COVID- 19-17 August 2023[EB\/OL]. www.who.int. 2023-08-17. https:\/\/www.who.int\/publications\/m\/item\/weekly-epidemiological-update-on-covid-19---17-august-2023"},{"key":"1380_CR28","unstructured":"World Health Organization. Coronavirus disease (COVID-19)[EB\/OL] (2023) -08-09 https:\/\/www.who.int\/news-room\/fact-sheets\/detail\/coronavirus-disease-(covid-19)"},{"issue":"10225","key":"1380_CR29","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1016\/S0140-6736(20)30260-9","volume":"395","author":"JT Wu","year":"2020","unstructured":"Wu JT, Leung K, Leung GM (2020) Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, china: a modelling study. Lancet 395(10225):689\u2013697","journal-title":"Lancet"},{"key":"1380_CR30","unstructured":"Yan YAN, Xiaolai MA (2023) Air freight route planning based on transshipment under air alliance. J Beijing Univ Aeronaut Astronaut , 49(01):115\u2013127"},{"issue":"3","key":"1380_CR31","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s10729-021-09559-z","volume":"24","author":"X Yin","year":"2021","unstructured":"Yin X, B\u00fcy\u00fcktahtak\u0131n \u0130E (2021) A multi-stage stochastic programming approach to epidemic resource allocation with equity considerations. Health Care Manag Sci 24(3):597\u2013622","journal-title":"Health Care Manag Sci"},{"key":"1380_CR20","unstructured":"Yinghua SONG, Yinghui SONG, Chaoxin LI, Zhe WANG (2020) Emergency supplies distribution model considering psychological impact of supplies damage. China Saf Sci J 2020, 30(07):173\u2013179"},{"key":"1380_CR32","doi-asserted-by":"publisher","first-page":"1145","DOI":"10.1016\/j.cie.2019.02.003","volume":"135","author":"J Zhang","year":"2019","unstructured":"Zhang J, Liu H, Yu G et al (2019) A three-stage and multi-objective stochastic programming model to improve the sustainable rescue ability by considering secondary disasters in emergency logistics. Comput Ind Eng 135:1145\u20131154","journal-title":"Comput Ind Eng"},{"key":"1380_CR33","unstructured":"Zhou L, Huang P, Dai Y, Song H (2023) Research on coordinated dispatching of emergency materials in the initial stage of outburst epidemic with the coupling of regional mutual rescue and external rescue. Chin J Manag Sci 1\u201311"},{"key":"1380_CR34","unstructured":"Zhu L, Cao J, Gu J, Zheng Y (2020) Dynamic emergency supply distribution considering fair mitigation of victim suffering. Syst Engineering-Theory Pract 40(09):2427\u20132437"},{"issue":"03","key":"1380_CR35","first-page":"109","volume":"58","author":"C Zhuang","year":"2023","unstructured":"Zhuang C, Zhang K (2023) Optimization of material allocation under public health events based on SEIR model. J Shandong Univ (Nat Sci) 58(03):109\u2013120","journal-title":"J Shandong Univ (Nat Sci)"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-025-01380-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-025-01380-6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-025-01380-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T08:53:57Z","timestamp":1769849637000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-025-01380-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,22]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["1380"],"URL":"https:\/\/doi.org\/10.1007\/s10878-025-01380-6","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"value":"1382-6905","type":"print"},{"value":"1573-2886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,22]]},"assertion":[{"value":"6 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 November 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 December 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"4"}}