{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T04:35:03Z","timestamp":1768278903413,"version":"3.49.0"},"reference-count":61,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,2,3]],"date-time":"2021-02-03T00:00:00Z","timestamp":1612310400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,2,3]],"date-time":"2021-02-03T00:00:00Z","timestamp":1612310400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100007343","name":"Universit\u00e0 degli Studi di Brescia","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100007343","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Manag Sci"],"published-print":{"date-parts":[[2021,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this work, we study a stochastic single machine scheduling problem in which the features of learning effect on processing times, sequence-dependent setup times, and machine configuration selection are considered simultaneously. More precisely, the machine works under a set of configurations and requires stochastic sequence-dependent setup times to switch from one configuration to another. Also, the stochastic processing time of a job is a function of its position and the machine configuration. The objective is to find the sequence of jobs and choose a configuration to process each job to minimize the makespan. We first show that the proposed problem can be formulated through two-stage and multi-stage Stochastic Programming models, which are challenging from the computational point of view. Then, by looking at the problem as a multi-stage dynamic random decision process, a new deterministic approximation-based formulation is developed. The method first derives a mixed-integer non-linear model based on the concept of accessibility to all possible and available alternatives at each stage of the decision-making process. Then, to efficiently solve the problem, a new accessibility measure is defined to convert the model into the search of a shortest path throughout the stages. Extensive computational experiments are carried out on various sets of instances. We discuss and compare the results found by the resolution of plain stochastic models with those obtained by the deterministic approximation approach. Our approximation shows excellent performances both in terms of solution accuracy and computational time.<\/jats:p>","DOI":"10.1007\/s10287-020-00386-1","type":"journal-article","created":{"date-parts":[[2021,2,3]],"date-time":"2021-02-03T21:02:34Z","timestamp":1612386154000},"page":"267-297","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Stochastic single machine scheduling problem as a multi-stage dynamic random decision process"],"prefix":"10.1007","volume":"18","author":[{"given":"Mina","family":"Roohnavazfar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3502-5289","authenticated-orcid":false,"given":"Daniele","family":"Manerba","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lohic","family":"Fotio Tiotsop","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seyed Hamid Reza","family":"Pasandideh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roberto","family":"Tadei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,2,3]]},"reference":[{"key":"386_CR1","doi-asserted-by":"crossref","first-page":"219","DOI":"10.3934\/jimo.2014.10.219","volume":"10","author":"MO Adamu","year":"2014","unstructured":"Adamu MO, Adewumi AO (2014) A survey of single machine scheduling to minimize weighted number of tardy jobs. J Ind Manag Optim 10:219\u2013241","journal-title":"J Ind Manag Optim"},{"key":"386_CR2","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1109\/TC.1984.1676440","volume":"33","author":"AK Agrawala","year":"1984","unstructured":"Agrawala AK, Coffman JR, Garey MR, Tripathi SK (1984) A static optimization algorithm expected flow time on uniform processors. IEEE Trans Comput 33:351\u2013357","journal-title":"IEEE Trans Comput"},{"key":"386_CR3","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/j.ejor.2015.04.004","volume":"246","author":"A Allahverdi","year":"2015","unstructured":"Allahverdi A (2015) The third comprehensive survey on scheduling problems with setup times\/costs. Eur J Oper Res 246:345\u2013378","journal-title":"Eur J Oper Res"},{"key":"386_CR4","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/S0305-0483(98)00042-5","volume":"27","author":"A Allahverdi","year":"1999","unstructured":"Allahverdi A, Gupta JND, Aldowaisan T (1999) A review of scheduling research involving setup considerations. Omega 27:219\u2013239","journal-title":"Omega"},{"key":"386_CR5","doi-asserted-by":"publisher","first-page":"2041","DOI":"10.1016\/j.apm.2010.11.017","volume":"35","author":"F Angel-Bello","year":"2011","unstructured":"Angel-Bello F, Alvarez A, Pacheco J, Martinez I (2011) A single machine scheduling problem with availability constraints and sequence-dependent setup costs. Appl Math Model 35:2041\u20132050","journal-title":"Appl Math Model"},{"key":"386_CR6","doi-asserted-by":"publisher","first-page":"1642","DOI":"10.1080\/00207543.2017.1355576","volume":"56","author":"A Azzouz","year":"2018","unstructured":"Azzouz A, Ennigrou M, Ben Said L (2018) Scheduling problems under learning effects: classification and cartography. Int J Prod Res 56:1642\u20131661","journal-title":"Int J Prod Res"},{"key":"386_CR7","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1007\/s00170-010-2526-5","volume":"50","author":"U Bahalke","year":"2010","unstructured":"Bahalke U, Ulmeh AM, Shahanaghi K (2010) Meta-heuristics to solve single machine scheduling problem with sequence-dependent setup time and deteriorating jobs. Int J Adv Manuf Technol 50:749\u2013759","journal-title":"Int J Adv Manuf Technol"},{"key":"386_CR8","doi-asserted-by":"publisher","DOI":"10.1002\/9780470451793","volume-title":"Principles of Sequencing and Scheduling","author":"KR Baker","year":"2009","unstructured":"Baker KR, Trietsch D (2009) Principles of Sequencing and Scheduling. Wiley, Hoboken"},{"key":"386_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-0237-4","volume-title":"Introduction to stochastic programming","author":"JR Birge","year":"2011","unstructured":"Birge JR, Louveaux F (2011) Introduction to stochastic programming, 2nd edn. Springer, New York","edition":"2"},{"key":"386_CR10","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/S0377-2217(98)00246-X","volume":"115","author":"D Biskup","year":"1999","unstructured":"Biskup D (1999) Single-machine scheduling with learning considerations. Eur J Oper Res 115:173\u2013178","journal-title":"Eur J Oper Res"},{"key":"386_CR11","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s10951-007-0026-8","volume":"10","author":"X Cai","year":"2007","unstructured":"Cai X, Wang L, Zhou X (2007) Single-machine scheduling to stochastically minimize maximum lateness. J Sched 10:293\u2013301","journal-title":"J Sched"},{"key":"386_CR12","doi-asserted-by":"publisher","first-page":"2476","DOI":"10.1016\/j.ins.2008.02.002","volume":"178","author":"TCE Cheng","year":"2008","unstructured":"Cheng TCE, Wu CC, Lee WC (2008) Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects. Inf Sci 178:2476\u20132487","journal-title":"Inf Sci"},{"key":"386_CR13","doi-asserted-by":"crossref","first-page":"8804","DOI":"10.1016\/j.amc.2011.04.005","volume":"217","author":"TCE Cheng","year":"2011","unstructured":"Cheng TCE, Wu WH, Cheng SR, Wu CC (2011) Two-agent scheduling with position-based deteriorating jobs and learning effects. Appl Math Comput 217:8804\u20138824","journal-title":"Appl Math Comput"},{"key":"386_CR14","doi-asserted-by":"publisher","first-page":"490","DOI":"10.1016\/j.ins.2012.09.001","volume":"221","author":"TCE Cheng","year":"2013","unstructured":"Cheng TCE, Kuo WH, Yang DL (2013) Scheduling with a position-weighted learning effect based on sum-of-logarithm-processing-times and job position. Inf Sci 221:490\u2013500","journal-title":"Inf Sci"},{"key":"386_CR15","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1287\/mnsc.41.2.363","volume":"41","author":"RL Daniels","year":"1995","unstructured":"Daniels RL, Kouvelis P (1995) Robust scheduling to hedge agains processing time uncertainity in single-stage production. Manage Sci 41:363\u2013376","journal-title":"Manage Sci"},{"key":"386_CR16","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1016\/0305-0483(74)90094-2","volume":"2","author":"R Dudek","year":"1974","unstructured":"Dudek R, Smith M, Panwalkar S (1974) Use of a case study in sequencing\/scheduling research. Omega 2:253\u2013261","journal-title":"Omega"},{"key":"386_CR17","doi-asserted-by":"publisher","first-page":"3273","DOI":"10.1080\/00207543.2019.1581383","volume":"57","author":"F Ertem","year":"2019","unstructured":"Ertem F, Ozcelik Tugba Sarac F (2019) Single machine scheduling problem with stochastic sequence-dependent setup times. Int J Prod Res 57:3273\u20133289","journal-title":"Int J Prod Res"},{"key":"386_CR18","first-page":"48","volume":"15","author":"LF Escudero","year":"2007","unstructured":"Escudero LF, Garin A, Merino M, Perez G (2007) The value of the stochastic solution in multistage problems. Soc Estad Invest Oper 15:48\u201364","journal-title":"Soc Estad Invest Oper"},{"key":"386_CR19","doi-asserted-by":"publisher","unstructured":"Fadda E, Fotio Tiotsop L, Manerba D, Tadei R (2020) The stochastic multi-path traveling salesman problem with dependent random travel costs. Transp Sci 54(5):1372\u20131387. https:\/\/doi.org\/10.1287\/trsc.2020.0996","DOI":"10.1287\/trsc.2020.0996"},{"key":"386_CR20","doi-asserted-by":"publisher","unstructured":"Galambos J (1994) Extreme value theory for applications. In: Galambos J, Lechner J, Simiu E (eds) Extreme value theory and applications. Springer, Boston. https:\/\/doi.org\/10.1007\/978-1-4613-3638-9_1","DOI":"10.1007\/978-1-4613-3638-9_1"},{"key":"386_CR21","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1016\/0020-0190(96)00021-X","volume":"57","author":"SA Gawiejnowicz","year":"1996","unstructured":"Gawiejnowicz SA (1996) A note on scheduling on a single processor with speed dependent on a number of executed jobs. Inf Process Lett 57:297\u2013300","journal-title":"Inf Process Lett"},{"key":"386_CR22","first-page":"73","volume":"25","author":"W Hansen","year":"1959","unstructured":"Hansen W (1959) How accessibility shapes land use. J Am Plan Assoc 25:73\u201376","journal-title":"J Am Plan Assoc"},{"key":"386_CR23","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1007\/s10845-015-1033-9","volume":"28","author":"K Hu","year":"2015","unstructured":"Hu K, Zhang X, Gen M, Jo J (2015) A new model for single machine scheduling with uncertain processing time. J Intell Manuf 28:717\u2013725","journal-title":"J Intell Manuf"},{"key":"386_CR24","doi-asserted-by":"publisher","unstructured":"Huo JZ, Ning L, Sun L (2018) Group scheduling with general autonomous and induced learning effect. Math Prob Eng 2018:2172378. https:\/\/doi.org\/10.1155\/2018\/2172378","DOI":"10.1155\/2018\/2172378"},{"key":"386_CR25","first-page":"165","volume":"13","author":"V Kaplanoglu","year":"2014","unstructured":"Kaplanoglu V (2014) Multi-agent based approach for single machine scheduling with sequence-dependent setup times and machine maintenance. Appl Math Model 13:165\u2013179","journal-title":"Appl Math Model"},{"key":"386_CR26","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.ipl.2006.11.002","volume":"102","author":"W-H Kuo","year":"2007","unstructured":"Kuo W-H, Yang D-L (2007) Single machine scheduling with past-sequence-dependent setup times and learning effects. Inf Process Lett 102:22\u201326","journal-title":"Inf Process Lett"},{"key":"386_CR27","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/s00236-003-0132-9","volume":"40","author":"WC Lee","year":"2004","unstructured":"Lee WC, Wu CC, Sung HJ (2004) A bi-criterion single-machine scheduling problem with learning considerations. Acta Inf 40:303\u2013315","journal-title":"Acta Inf"},{"key":"386_CR28","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/s10287-005-0037-x","volume":"2","author":"K Leksakul","year":"2005","unstructured":"Leksakul K, Techanitisawad A (2005) An application of the neural network energy function to machine sequencing. CMS 2:309\u2013338","journal-title":"CMS"},{"key":"386_CR29","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1109\/TEM.2016.2618764","volume":"64","author":"H Li","year":"2016","unstructured":"Li H (2016) Stochastic single-machine scheduling with learning effect. IEEE Trans Eng Manage 64:94\u2013102","journal-title":"IEEE Trans Eng Manage"},{"key":"386_CR30","doi-asserted-by":"publisher","first-page":"1682","DOI":"10.1016\/j.cor.2011.10.003","volume":"39","author":"CC Lu","year":"2012","unstructured":"Lu CC, Lin SW, Ying KC (2012) Robust scheduling on a single machine to minimize total flow time. Comput Oper Res 39:1682\u20131691","journal-title":"Comput Oper Res"},{"key":"386_CR31","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.cie.2014.04.013","volume":"74","author":"CC Lu","year":"2010","unstructured":"Lu CC, Ying KC, Lin SW (2010) Robust single machine scheduling for minimizing total flow time in the presence of uncertain processing times. Comput Ind Eng 74:102\u2013110","journal-title":"Comput Ind Eng"},{"key":"386_CR32","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10287-016-0272-3","volume":"14","author":"F Maggioni","year":"2017","unstructured":"Maggioni F, Potra FA, Bertocchi M (2017) A scenario-based framework for supply planning under uncertainty: stochastic programming versus robust optimization approaches. Comput Manag Sci 14:5\u201344","journal-title":"Comput Manag Sci"},{"key":"386_CR33","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.ijpe.2018.01.035","volume":"198","author":"D Manerba","year":"2018","unstructured":"Manerba D, Mansini R, Perboli G (2018) The capacitated supplier selection with total quantity discount policy and activation costs under uncertainity. Int J Prod Econ 198:119\u2013132","journal-title":"Int J Prod Econ"},{"key":"386_CR34","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1016\/S0377-2217(00)00175-2","volume":"132","author":"G Mosheiov","year":"2001","unstructured":"Mosheiov G (2001) Scheduling problems with a learning effect. Eur J Oper Res 132:687\u2013693","journal-title":"Eur J Oper Res"},{"key":"386_CR35","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/j.asoc.2018.06.051","volume":"71","author":"S Mustu","year":"2018","unstructured":"Mustu S, Eren T (2018) The single machine scheduling problem with sequence-dependent setup times and a learning effect on processing times. Appl Soft Comput 71:291\u2013306","journal-title":"Appl Soft Comput"},{"key":"386_CR36","doi-asserted-by":"publisher","first-page":"1291","DOI":"10.1016\/j.dam.2011.10.037","volume":"160","author":"G Perboli","year":"2012","unstructured":"Perboli G, Tadei R, Baldi M (2012) The stochastic generalized bin packing problem. Discrete Appl Math 160:1291\u20131297","journal-title":"Discrete Appl Math"},{"key":"386_CR37","doi-asserted-by":"publisher","first-page":"1000","DOI":"10.1016\/j.ejor.2013.11.040","volume":"236","author":"G Perboli","year":"2014","unstructured":"Perboli G, Tadei R, Gobbato L (2014) The multi-handler Knapsack problem under uncertainty. Eur J Oper Res 236:1000\u20131007","journal-title":"Eur J Oper Res"},{"key":"386_CR38","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/j.cor.2015.08.010","volume":"66","author":"J Pereira","year":"2016","unstructured":"Pereira J (2016) The robust (minmax regret) single machine scheduling with interval processing times and total weighted completion time objective. Comput Oper Res 66:141\u2013152","journal-title":"Comput Oper Res"},{"key":"386_CR39","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-2361-4","volume-title":"Scheduling: theory, algorithms, and systems","author":"ML Pinedo","year":"2012","unstructured":"Pinedo ML (2012) Scheduling: theory, algorithms, and systems. Springer, New York"},{"key":"386_CR40","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s10951-009-0160-6","volume":"13","author":"DP Ronconi","year":"2010","unstructured":"Ronconi DP, Powell WB (2010) Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming. J Sched 13:597\u2013607","journal-title":"J Sched"},{"key":"386_CR41","first-page":"100124","volume":"6","author":"M Roohnavazfar","year":"2019","unstructured":"Roohnavazfar M, Manerba D, De Martin JC, Tadei R (2019) Optimal paths in multi-stage stochastic decision networks. Oper Res Perspect 6:100124","journal-title":"Oper Res Perspect"},{"key":"386_CR42","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.cie.2005.01.002","volume":"48","author":"DK Seo","year":"2005","unstructured":"Seo DK, Klein CM, Jang W (2005) Single machine stochastic scheduling to minimize the expected number of tardy jobs using mathematical programming models. Comput Ind Eng 48:153\u2013161","journal-title":"Comput Ind Eng"},{"key":"386_CR43","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1504\/EJIE.2014.064754","volume":"8","author":"HM Soroush","year":"2014","unstructured":"Soroush HM (2014) Stochastic bicriteria single machine scheduling with sequence-dependent job attributes and job-dependent learning effects. Eur J Ind Eng 8:421\u2013456","journal-title":"Eur J Ind Eng"},{"key":"386_CR44","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1016\/j.ejor.2006.05.036","volume":"181","author":"HM Soroush","year":"2007","unstructured":"Soroush HM (2007) Minimizing the weighted number of early and tardy jobs in a stochastic single machine scheduling problem. Eur J Oper Res 181:266\u2013287","journal-title":"Eur J Oper Res"},{"key":"386_CR45","doi-asserted-by":"publisher","first-page":"2635","DOI":"10.1016\/j.cor.2006.12.021","volume":"35","author":"G Stecco","year":"2008","unstructured":"Stecco G, Cordeau J, Moretti E (2008) A branch and cut algorithm for the production scheduling problem with sequence-dependent and time-dependent setup time. Comput Oper Res 35:2635\u20132655","journal-title":"Comput Oper Res"},{"key":"386_CR46","doi-asserted-by":"publisher","first-page":"843","DOI":"10.1016\/j.cie.2009.02.014","volume":"57","author":"L Sun","year":"2009","unstructured":"Sun L (2009) Single-machine scheduling problems with deteriorating jobs and learning effects. Comput Ind Eng 57:843\u2013846","journal-title":"Comput Ind Eng"},{"issue":"5","key":"386_CR47","doi-asserted-by":"publisher","first-page":"1207","DOI":"10.1007\/s11590-019-01412-1","volume":"14","author":"R Tadei","year":"2020","unstructured":"Tadei R, Perboli G, Manerba D (2020) The multi-stage dynamic random decision process with unknown distribution of the random utilities. Optim Lett 14(5):1207\u20131218","journal-title":"Optim Lett"},{"key":"386_CR48","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s13676-014-0056-2","volume":"6","author":"R Tadei","year":"2017","unstructured":"Tadei R, Perboli G, Perfetti F (2017) The multi-path Traveling Salesman Problem with stochastic travel costs. Euro J Transp Log 6:3\u201323","journal-title":"Euro J Transp Log"},{"key":"386_CR49","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.orl.2009.01.005","volume":"37","author":"R Tadei","year":"2009","unstructured":"Tadei R, Ricciardi N, Perboli G (2009) The stochastic p-median problem with unknown cost probability distribution. Oper Res Lett 37:135\u2013141","journal-title":"Oper Res Lett"},{"key":"386_CR50","doi-asserted-by":"publisher","first-page":"2394","DOI":"10.1016\/j.cor.2008.09.012","volume":"36","author":"MD Toksari","year":"2009","unstructured":"Toksari MD, Guner E (2009) Parallel machine earliness\/tardiness scheduling problem under the effects of position based learning and linear\/nonlinear deterioration. Comput Oper Res 36:2394\u20132417","journal-title":"Comput Oper Res"},{"key":"386_CR51","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s10951-007-0022-z","volume":"11","author":"M Trietsch","year":"2008","unstructured":"Trietsch M, Baker KR (2008) Minimizing the number of tardy jobs with stochastically-ordered processing times. J Sched 11:59\u201369","journal-title":"J Sched"},{"key":"386_CR52","doi-asserted-by":"publisher","first-page":"2068","DOI":"10.1016\/j.apm.2010.11.041","volume":"35","author":"SJ Yang","year":"2011","unstructured":"Yang SJ, Yang DL (2011) Single-machine scheduling simultaneous with position-based and sum-of-processing-times-based learning considerations under group technology assumption. Appl Math Model 35:2068\u20132074","journal-title":"Appl Math Model"},{"key":"386_CR53","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1023\/A:1013333232691","volume":"6","author":"J Yang","year":"2002","unstructured":"Yang J, Yu G (2002) The robust single machine scheduling problem. J Comb Optim 6:17\u201333","journal-title":"J Comb Optim"},{"key":"386_CR54","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1111\/j.1540-5915.1979.tb00026.x","volume":"10","author":"LE Yelle","year":"1979","unstructured":"Yelle LE (1979) The learning curve: historical review and comprehensive survey. Decis Sci 10:302\u2013328","journal-title":"Decis Sci"},{"key":"386_CR55","first-page":"222","volume":"10","author":"BPC Yen","year":"2003","unstructured":"Yen BPC, Wan G (2003) Single machine bicriteria scheduling: a survey. Int J Ind Eng Theory Appl Pract 10:222\u2013231","journal-title":"Int J Ind Eng Theory Appl Pract"},{"key":"386_CR56","doi-asserted-by":"publisher","first-page":"3623","DOI":"10.1016\/j.apm.2010.03.011","volume":"34","author":"Y Yin","year":"2010","unstructured":"Yin Y, Xu D, Wang J (2010) Single-machine scheduling with a general sum-of-actual-processing-times-based and job-position-based learning effect. Appl Math Model 34:3623\u20133630","journal-title":"Appl Math Model"},{"key":"386_CR57","first-page":"6236","volume":"383","author":"KC Ying","year":"2012","unstructured":"Ying KC, Bin Mokhtar M (2012) Heuristic model for dynamic single machine group scheduling in laser cutting job shop to minimize the makespan. Manuf Sci Technol 383:6236\u20136241","journal-title":"Manuf Sci Technol"},{"key":"386_CR58","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s10951-007-0034-8","volume":"11","author":"M van den Akker","year":"2008","unstructured":"van den Akker M, Hoogeveen H (2008) Minimizing the number of late jobs in a stochastic setting using a chance constraint. J Sched 11:59\u201369","journal-title":"J Sched"},{"key":"386_CR59","doi-asserted-by":"publisher","first-page":"918","DOI":"10.1016\/j.cie.2013.09.001","volume":"66","author":"X Zhang","year":"2013","unstructured":"Zhang X, Sun L, Wang J (2013) Single machine scheduling with autonomous learning and induced learning. Comput Ind Eng 66:918\u2013924","journal-title":"Comput Ind Eng"},{"key":"386_CR60","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s10951-012-0306-9","volume":"16","author":"Y Zhang","year":"2013","unstructured":"Zhang Y, Wu X, Zhou X (2013) Stochastic scheduling problems with general position-based learning effects and stochastic breakdowns. J Sched 16:331\u2013336","journal-title":"J Sched"},{"key":"386_CR61","first-page":"741","volume":"11","author":"CL Zhao","year":"2004","unstructured":"Zhao CL, Zhang WL, Tang HY (2004) Machine scheduling problems with a learning effect. Dyn Contin, Discrete Impuls Syst, Ser A: Math Anal 11:741\u2013750","journal-title":"Dyn Contin, Discrete Impuls Syst, Ser A: Math Anal"}],"container-title":["Computational Management Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-020-00386-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10287-020-00386-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-020-00386-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T21:05:44Z","timestamp":1698613544000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10287-020-00386-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,3]]},"references-count":61,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,7]]}},"alternative-id":["386"],"URL":"https:\/\/doi.org\/10.1007\/s10287-020-00386-1","relation":{},"ISSN":["1619-697X","1619-6988"],"issn-type":[{"value":"1619-697X","type":"print"},{"value":"1619-6988","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,3]]},"assertion":[{"value":"29 December 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 December 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 February 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}