{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T16:37:50Z","timestamp":1770223070147,"version":"3.49.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,10,22]],"date-time":"2021-10-22T00:00:00Z","timestamp":1634860800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,10,22]],"date-time":"2021-10-22T00:00:00Z","timestamp":1634860800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The nursing rescheduling problem is a challenging decision-making task in hospitals. However, this decision-making needs to be made in a stochastic setting to meet uncertain demand with insufficient historical data or inaccurate forecasting methods. In this study, a stochastic programming model and a distributionally robust model are developed for the nurse rescheduling problem with multiple rescheduling methods under uncertain demands. We show that these models can be reformulated into an integer program. To illustrate the applicability and validity of the proposed model, a study case is conducted on three joint hospitals in Chengdu, Chongzhou, and Guanghan, Sichuan Province. The results show that the stochastic programming model and the distributionally robust model can reduce the cost by 78.71% and 38.92%, respectively. We also evaluate the benefit of the distributionally robust model against the stochastic model and perform sensitivity analysis on important model parameters to derive some meaningful managerial insights.<\/jats:p>","DOI":"10.1007\/s40747-021-00554-z","type":"journal-article","created":{"date-parts":[[2021,10,22]],"date-time":"2021-10-22T13:05:24Z","timestamp":1634907924000},"page":"4557-4569","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Nursing rescheduling problem with multiple rescheduling methods under uncertainty"],"prefix":"10.1007","volume":"8","author":[{"given":"Zhiren","family":"Long","sequence":"first","affiliation":[]},{"given":"Xianxiu","family":"Wen","sequence":"additional","affiliation":[]},{"given":"Mei","family":"Lan","sequence":"additional","affiliation":[]},{"given":"Yongjian","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,22]]},"reference":[{"key":"554_CR1","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1016\/j.cie.2016.02.023","volume":"96","author":"M Bagheri","year":"2016","unstructured":"Bagheri M, Devin AG, Izanloo A (2016) An application of stochastic programming method for nurse scheduling problem in real word hospital. Comput Ind Eng 96:192\u2013200","journal-title":"Comput Ind Eng"},{"issue":"4","key":"554_CR2","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/s10729-005-4141-9","volume":"8","author":"JF Bard","year":"2005","unstructured":"Bard JF, Purnomo HW (2005) Short-term nurse scheduling in response to daily fluctuations in supply and demand. Health Care Manag Sci 8(4):315\u2013324","journal-title":"Health Care Manag Sci"},{"issue":"2","key":"554_CR3","doi-asserted-by":"publisher","first-page":"548","DOI":"10.1016\/j.ejor.2020.11.002","volume":"292","author":"B Basciftci","year":"2021","unstructured":"Basciftci B, Ahmed S, Shen S (2021) Distributionally robust facility location problem under decision-dependent stochastic demand. Eur J Oper Res 292(2):548\u2013561","journal-title":"Eur J Oper Res"},{"issue":"(2)","key":"554_CR4","first-page":"459","volume":"65","author":"D Bertsimas","year":"2019","unstructured":"Bertsimas D, Sim M, Zhang M (2019) Adaptive distributionally robust optimization. Manag Sci 65((2)):459\u2013954","journal-title":"Manag Sci"},{"key":"554_CR5","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1023\/B:JOSH.0000046076.75950.0b","volume":"7","author":"EK Burke","year":"2004","unstructured":"Burke EK, Causmaecker PD, Berghe GV, Landeghem HV (2004) The state of the art of nurse rostering. J Sched 7:441\u2013499","journal-title":"J Sched"},{"issue":"4","key":"554_CR6","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1080\/19488300.2016.1226211","volume":"6","author":"M Chiaramonte","year":"2016","unstructured":"Chiaramonte M, Caswell D (2016) Rerostering of nurses with intelligent agents and iterated local search. IIE Trans Healthc Syst Eng 6(4):213\u2013222","journal-title":"IIE Trans Healthc Syst Eng"},{"key":"554_CR7","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1016\/j.omega.2015.04.002","volume":"58","author":"M Defraeye","year":"2016","unstructured":"Defraeye M, Nieuwenhuyse IV (2016) Staffing and scheduling under nonstationary demand for service: a literature review. Omega 58:4\u201325","journal-title":"Omega"},{"issue":"3","key":"554_CR8","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1287\/opre.1090.0741","volume":"58","author":"E Delage","year":"2010","unstructured":"Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper Res 58(3):595\u2013612","journal-title":"Oper Res"},{"issue":"1","key":"554_CR9","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0377-2217(03)00095-X","volume":"153","author":"AT Ernst","year":"2004","unstructured":"Ernst AT, Jiang H, Krishnamoorthy M, Sier D (2004) Staff scheduling and rostering: a review of applications, methods and models. Eur J Oper Res 153(1):3\u201327","journal-title":"Eur J Oper Res"},{"issue":"4-part-1","key":"554_CR10","doi-asserted-by":"publisher","first-page":"902","DOI":"10.1287\/opre.1090.0795","volume":"58","author":"J Goh","year":"2010","unstructured":"Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper Res 58(4-part-1):902\u2013917","journal-title":"Oper Res"},{"key":"554_CR11","first-page":"100119","volume":"6","author":"F He","year":"2019","unstructured":"He F, Chaussalet T, Qu R (2019) Controlling understaffing with conditional value-at-risk constraint for an integrated nurse scheduling problem under patient demand uncertainty. Oper Res Perspect 6:100119","journal-title":"Oper Res Perspect"},{"issue":"3","key":"554_CR12","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1016\/j.ejor.2012.11.029","volume":"226","author":"VDB Jorne","year":"2013","unstructured":"Jorne VDB, Jeroen B, Philippe DB, Erik D, Liesje DB (2013) Personnel scheduling: a literature review. Eur J Oper Res 226(3):367\u2013385","journal-title":"Eur J Oper Res"},{"issue":"3","key":"554_CR13","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1287\/opre.2013.1158","volume":"61","author":"Q Kong","year":"2013","unstructured":"Kong Q, Lee C-Y, Teo C-P, Zheng Zhichao (2013) Scheduling arrivals to a stochastic service delivery system using copositive cones. Oper Res 61(3):711\u2013726","journal-title":"Oper Res"},{"key":"554_CR14","doi-asserted-by":"publisher","first-page":"1431","DOI":"10.1287\/opre.2015.1421","volume":"63","author":"K Kim","year":"2014","unstructured":"Kim K, Mehrotra S (2014) A two-stage stochastic integer programming approach to integrated staffing and scheduling with application to nurse management. Oper Res 63:1431\u20131451","journal-title":"Oper Res"},{"key":"554_CR15","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.trb.2018.11.012","volume":"119","author":"K Liu","year":"2019","unstructured":"Liu K, Li Q, Zhang Z (2019) Distributionally robust optimization of an emergency medical service station location and sizing problem with joint chance constraints. Transport Res Part B Methodol 119:79\u2013101","journal-title":"Transport Res Part B Methodol"},{"issue":"4","key":"554_CR16","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1287\/msom.2015.0541","volume":"17","author":"M Lu","year":"2015","unstructured":"Lu M, Ran L, Shen ZM (2015) Reliable facility location design under uncertain correlated disruptions. Manuf Serv Oper Manag 17(4):445\u2013455","journal-title":"Manuf Serv Oper Manag"},{"issue":"2","key":"554_CR17","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1016\/j.omega.2012.01.002","volume":"41","author":"B Maenhout","year":"2013","unstructured":"Maenhout B, Vanhoucke M (2013) An integrated nurse staffing and scheduling analysis for longer-term nursing staff allocation problems. Omega 41(2):485\u2013499","journal-title":"Omega"},{"issue":"2","key":"554_CR18","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1287\/mnsc.2013.1881","volume":"61","author":"H-Y Mak","year":"2015","unstructured":"Mak H-Y, Rong Y, Zhang J (2015) Appointment scheduling with limited distributional information. Manag Sci 61(2):316\u2013334","journal-title":"Manag Sci"},{"key":"554_CR19","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1023\/A:1022907212477","volume":"119","author":"M Moz","year":"2003","unstructured":"Moz M, Pato MV (2003) An integer multicommodity flow model applied to the rerostering of nurse schedules. Ann Oper Res 119:285\u2013301","journal-title":"Ann Oper Res"},{"key":"554_CR20","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1023\/B:ANOR.0000019104.39239.ed","volume":"128","author":"M Moz","year":"2004","unstructured":"Moz M, Pato MV (2004) Solving the problem of rerostering nurse schedules with hard constraints: new multicommodity flow models. Ann Oper Res 128:179\u2013197","journal-title":"Ann Oper Res"},{"issue":"2","key":"554_CR21","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1287\/mnsc.2015.2353","volume":"63","author":"J Qi","year":"2016","unstructured":"Qi J (2016) Mitigating delays and unfairness in appointment systems. Manag Sci 63(2):566\u2013583","journal-title":"Manag Sci"},{"issue":"3","key":"554_CR22","doi-asserted-by":"publisher","first-page":"995","DOI":"10.1016\/j.ejor.2020.09.026","volume":"291","author":"A Saif","year":"2020","unstructured":"Saif A, Delage E (2020) Data-driven distributionally robust capacitated facility location problem. Eur J Oper Res 291(3):995\u20131007","journal-title":"Eur J Oper Res"},{"issue":"2","key":"554_CR23","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1016\/j.ejor.2019.11.039","volume":"283","author":"KS Shehadeh","year":"2020","unstructured":"Shehadeh KS, Cohn AEM, Jiang R (2020) A distributionally robust optimization approach for outpatient colonoscopy scheduling. Eur J Oper Res 283(2):549\u2013561","journal-title":"Eur J Oper Res"},{"key":"554_CR24","doi-asserted-by":"publisher","first-page":"101840","DOI":"10.1016\/j.tre.2020.101840","volume":"134","author":"C Wang","year":"2020","unstructured":"Wang C, Chen S, Talley W (2020) A distributionally robust optimization for blood supply network considering disasters. Transport Res Part E Logist Transport Rev 134:101840","journal-title":"Transport Res Part E Logist Transport Rev"},{"issue":"8","key":"554_CR25","doi-asserted-by":"publisher","first-page":"102332","DOI":"10.1016\/j.tre.2021.102332","volume":"149","author":"W Wang","year":"2021","unstructured":"Wang W, Yang K, Yang L, Gao Z (2021) Two-stage distributionally robust programming based on worst-case mean-CVaR criterion and application to disaster relief management. Transport Res Part E Logist Transport Rev 149(8):102332","journal-title":"Transport Res Part E Logist Transport Rev"},{"issue":"2","key":"554_CR26","doi-asserted-by":"publisher","first-page":"740","DOI":"10.1016\/j.ejor.2018.08.037","volume":"273","author":"Y Wang","year":"2019","unstructured":"Wang Y, Zhang Y, Tang J (2019) A distributionally robust optimization approach for surgery block allocation. Eur J Oper Res 273(2):740\u2013753","journal-title":"Eur J Oper Res"},{"key":"554_CR27","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.cor.2018.12.014","volume":"104","author":"TI Wickert","year":"2019","unstructured":"Wickert TI, Smet P, Berghe GV (2019) The nurse rerostering problem: strategies for reconstructing disrupted schedules. Comput Oper Res 104:319\u2013337","journal-title":"Comput Oper Res"},{"key":"554_CR28","doi-asserted-by":"publisher","first-page":"1358","DOI":"10.1287\/opre.2014.1314","volume":"62","author":"W Wiesemann","year":"2014","unstructured":"Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper Res 62:1358\u201376","journal-title":"Oper Res"},{"issue":"2","key":"554_CR29","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1111\/j.1540-5915.2010.00269.x","volume":"41","author":"PD Wright","year":"2010","unstructured":"Wright PD, Bretthauer KM (2010) Strategies for addressing the nursing shortage: coordinated decision making and workforce flexibility. Decis Sci 41(2):373\u2013401","journal-title":"Decis Sci"},{"key":"554_CR30","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/j.jmsy.2020.12.013","volume":"58","author":"C-C Wu","year":"2021","unstructured":"Wu C-C, Bai D, Zhang X, Cheng S-R, Lin J-C, Wu Z-L, Lin W-C (2021) A robust customer order scheduling problem along with scenario-dependent component processing times and due dates. J Manuf Syst 58:291\u2013305","journal-title":"J Manuf Syst"},{"key":"554_CR31","doi-asserted-by":"publisher","first-page":"100765","DOI":"10.1016\/j.swevo.2020.100765","volume":"60","author":"C-C Wu","year":"2021","unstructured":"Wu C-C, Bai D, Chen J-H, Lin W-C, Xing L, Lin J-C, Cheng S-R (2021) Several variants of simulated annealing hyper-heuristic for a single-machine scheduling with two scenario-based dependent processing times. Swarm Evol Comput 60:100765","journal-title":"Swarm Evol Comput"},{"issue":"17","key":"554_CR32","doi-asserted-by":"publisher","first-page":"5372","DOI":"10.1080\/00207543.2020.1778208","volume":"59","author":"C-C Wu","year":"2021","unstructured":"Wu C-C, Gupta JND, Cheng S-R, Lin BMT, Yip S-H, Lin W-C (2021) Robust scheduling of a two-stage assembly shop with scenario-dependent processing times. Int J Prod Res 59(17):5372\u20135387","journal-title":"Int J Prod Res"},{"issue":"6","key":"554_CR33","doi-asserted-by":"publisher","first-page":"1042","DOI":"10.1016\/j.omega.2012.08.004","volume":"41","author":"PD Wright","year":"2013","unstructured":"Wright PD, Mahar S (2013) Centralized nurse scheduling to simultaneously improve schedule cost and nurse satisfaction. Omega 41(6):1042\u20131052","journal-title":"Omega"},{"issue":"2","key":"554_CR34","doi-asserted-by":"publisher","first-page":"1433","DOI":"10.1016\/j.apm.2020.08.035","volume":"89","author":"M Yang","year":"2021","unstructured":"Yang M, Liu Y, Yang G (2021) Multi-period dynamic distributionally robust pre-positioning of emergency supplies under demand uncertainty. Appl Math Model 89(2):1433\u20131458","journal-title":"Appl Math Model"},{"issue":"3","key":"554_CR35","doi-asserted-by":"publisher","first-page":"1855","DOI":"10.1137\/15M1038529","volume":"26","author":"J Zhang","year":"2016","unstructured":"Zhang J, Xu H, Zhang L (2016) Quantitative stability analysis for distributionally robust optimization with moment constraints. SIAM J Optim 26(3):1855\u20131882","journal-title":"SIAM J Optim"},{"key":"554_CR36","doi-asserted-by":"publisher","first-page":"2749","DOI":"10.1007\/s00500-019-04362-z","volume":"24","author":"P Zhang","year":"2020","unstructured":"Zhang P, Liu Y, Yang G, Zhang G (2020) A distributionally robust optimization model for designing humanitarian relief network with resource reallocation. Soft Comput 24:2749\u20132767","journal-title":"Soft Comput"},{"issue":"1","key":"554_CR37","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1057\/palgrave.jors.2602522","volume":"60","author":"X Zhu","year":"2009","unstructured":"Zhu X, Sherali HD (2009) Two-stage workforce planning under demand fluctuations and uncertainty. J Oper Res Soc 60(1):94\u2013103","journal-title":"J Oper Res Soc"},{"issue":"1\u20132","key":"554_CR38","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s10107-011-0494-7","volume":"137","author":"S Zymler","year":"2013","unstructured":"Zymler S, Kuhn D, Rustem B (2013) Distributionally robust joint chance constraints with second-order moment information. Math Program 137(1\u20132):167\u2013198","journal-title":"Math Program"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-021-00554-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-021-00554-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-021-00554-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T13:18:42Z","timestamp":1666876722000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-021-00554-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,22]]},"references-count":38,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["554"],"URL":"https:\/\/doi.org\/10.1007\/s40747-021-00554-z","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,22]]},"assertion":[{"value":"19 July 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 September 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2021","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 corresponding author states that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}