{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T18:41:24Z","timestamp":1757616084833,"version":"3.44.0"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T00:00:00Z","timestamp":1469664000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T00:00:00Z","timestamp":1469664000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11471023"],"award-info":[{"award-number":["11471023"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2025,7]]},"DOI":"10.1007\/s10479-016-2254-9","type":"journal-article","created":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T07:27:04Z","timestamp":1469690824000},"page":"1283-1306","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Stochastic customer order scheduling to minimize long-run expected order cycle time"],"prefix":"10.1007","volume":"350","author":[{"given":"Xiaoyun","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaping","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manxi","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zihuan","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanni","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,7,28]]},"reference":[{"issue":"6","key":"2254_CR1","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1002\/nav.20092","volume":"52","author":"R Ahmadi","year":"2005","unstructured":"Ahmadi, R., Bagchi, U., & Roemer, T. A. (2005). Coordinated scheduling of customer orders for quick response. Naval Research Logistics (NRL), 52(6), 493\u2013512.","journal-title":"Naval Research Logistics (NRL)"},{"key":"2254_CR2","unstructured":"Baccelli, F., & Makowski, A. (1985). Simple computable bounds for the fork-join queue. In 19th annual conference information sciences and systems (pp. 436\u2013441). The Johns Hopkins University."},{"issue":"1","key":"2254_CR3","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1109\/5.21076","volume":"77","author":"F Baccelli","year":"1989","unstructured":"Baccelli, F., & Makowski, A. M. (1989). Queueing models for systems with synchronization constraints. Proceedings of the IEEE, 77(1), 138\u2013161.","journal-title":"Proceedings of the IEEE"},{"issue":"3","key":"2254_CR4","doi-asserted-by":"publisher","first-page":"629","DOI":"10.2307\/1427640","volume":"21","author":"F Baccelli","year":"1989","unstructured":"Baccelli, F., Makowski, A. M., & Shwartz, A. (1989). The fork-join queue and related systems with synchronization constraints: Stochastic ordering and computable bounds. Advances in Applied Probability, 21(3), 629\u2013660.","journal-title":"Advances in Applied Probability"},{"issue":"10","key":"2254_CR5","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.1109\/71.730531","volume":"9","author":"S Balsamo","year":"1998","unstructured":"Balsamo, S., Donatiello, L., & Van Dijk, N. M. (1998). Bound performance models of heterogeneous parallel processing systems. IEEE Transactions on Parallel and Distributed Systems, 9(10), 1041\u20131056.","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"issue":"5","key":"2254_CR6","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1002\/(SICI)1520-6750(199608)43:5<629::AID-NAV3>3.0.CO;2-7","volume":"43","author":"JD Blocher","year":"1996","unstructured":"Blocher, J. D., & Chhajed, D. (1996a). The customer order lead-time problem on parallel machines. Naval Research Logistics (NRL), 43(5), 629\u2013654.","journal-title":"Naval Research Logistics (NRL)"},{"issue":"5","key":"2254_CR7","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1002\/(SICI)1520-6750(199608)43:5<629::AID-NAV3>3.0.CO;2-7","volume":"43","author":"JD Blocher","year":"1996","unstructured":"Blocher, J. D., & Chhajed, D. (1996b). The customer order lead-time problem on parallel machines. Naval Research Logistics, 43(5), 629\u2013654.","journal-title":"Naval Research Logistics"},{"issue":"5","key":"2254_CR8","doi-asserted-by":"publisher","first-page":"874","DOI":"10.1109\/TPDS.2010.168","volume":"22","author":"RJ Chen","year":"2011","unstructured":"Chen, R. J. (2011). An upper bound solution for homogeneous fork\u2013join queuing systems. IEEE Transactions on Parallel and Distributed Systems, 22(5), 874\u2013878.","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"issue":"5","key":"2254_CR9","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1137\/0145052","volume":"45","author":"L Flatto","year":"1985","unstructured":"Flatto, L. (1985). Two parallel queues created by arrivals with two demands II. SIAM Journal on Applied Mathematics, 45(5), 861\u2013878.","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"5","key":"2254_CR10","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.1137\/0144074","volume":"44","author":"L Flatto","year":"1984","unstructured":"Flatto, L., & Hahn, S. (1984). Two parallel queues created by arrivals with two demands I. SIAM Journal on Applied Mathematics, 44(5), 1041\u20131053.","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"2254_CR11","doi-asserted-by":"crossref","unstructured":"Garg, N., Kumar, A., & Pandit, V. (2007) Order scheduling models: hardness and algorithms. In Foundations of software technology and theoretical computer science (pp. 96\u2013107). Springer.","DOI":"10.1007\/978-3-540-77050-3_8"},{"issue":"5\u20138","key":"2254_CR12","doi-asserted-by":"publisher","first-page":"1177","DOI":"10.1007\/s00170-012-4064-9","volume":"64","author":"M Godinho Filho","year":"2013","unstructured":"Godinho Filho, M., & Saes, E. V. (2013). From time-based competition to quick response manufacturing: The evolution of research aimed at lead time reduction. The International Journal of Advanced Manufacturing Technology, 64(5\u20138), 1177\u20131191.","journal-title":"The International Journal of Advanced Manufacturing Technology"},{"issue":"4","key":"2254_CR13","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1145\/2157.322409","volume":"30","author":"B Hajek","year":"1983","unstructured":"Hajek, B. (1983). The proof of a folk theorem on queuing delay with applications to routing in networks. Journal of the ACM (JACM), 30(4), 834\u2013851.","journal-title":"Journal of the ACM (JACM)"},{"issue":"1\u20134","key":"2254_CR14","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1023\/A:1014903232563","volume":"107","author":"NG Hall","year":"2001","unstructured":"Hall, N. G., Sriskandarajah, C., & Ganesharajah, T. (2001). Operational decisions in agv-served flowshop loops: Scheduling. Annals of Operations Research, 107(1\u20134), 161\u2013188.","journal-title":"Annals of Operations Research"},{"key":"2254_CR15","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1007\/978-3-540-45232-4_10","volume-title":"Computer performance evaluation, modelling techniques and tools","author":"P Harrison","year":"2003","unstructured":"Harrison, P., & Zertal, S. (2003). Queueing models with maxima of service times. Computer performance evaluation, modelling techniques and tools (pp. 152\u2013168). Berlin: Springer."},{"key":"2254_CR16","volume-title":"Factory physics","author":"WJ Hopp","year":"2008","unstructured":"Hopp, W. J., & Spearman, M. L. (2008). Factory physics. New York: McGraw-Hill Irwin."},{"key":"2254_CR17","unstructured":"Humblet, P. A. (1982). Determinism minimizes waiting time in queues. MIT LIDS, technical report, p. 1207."},{"key":"2254_CR18","first-page":"177","volume":"3","author":"FM Julien","year":"1990","unstructured":"Julien, F. M., & Magazine, M. J. (1990). Scheduling customer orders\u2014An alternative production scheduling approach. Journal of Manufacturing and Operations Management, 3, 177\u2013199.","journal-title":"Journal of Manufacturing and Operations Management"},{"issue":"2","key":"2254_CR19","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1109\/12.16501","volume":"38","author":"C Kim","year":"1989","unstructured":"Kim, C., & Agrawala, A. K. (1989). Analysis of the fork\u2013join queue. IEEE Transactions on Computers, 38(2), 250\u2013255.","journal-title":"IEEE Transactions on Computers"},{"key":"2254_CR20","unstructured":"Lebrecht, A. S., & Knottenbelt, W. J. (2007) Response time approximations in fork\u2013join queues. In 23rd UK performance engineering workshop (UKPEW)."},{"issue":"1","key":"2254_CR21","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.ijpe.2013.01.025","volume":"144","author":"IS Lee","year":"2013","unstructured":"Lee, I. S. (2013). Minimizing total tardiness for the order scheduling problem. International Journal of Production Economics, 144(1), 128\u2013134.","journal-title":"International Journal of Production Economics"},{"issue":"5","key":"2254_CR22","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/s10951-005-2860-x","volume":"8","author":"JYT Leung","year":"2005","unstructured":"Leung, J. Y. T., Li, H., & Pinedo, M. (2005a). Order scheduling in an environment with dedicated resources in parallel. Journal of Scheduling, 8(5), 355\u2013386.","journal-title":"Journal of Scheduling"},{"key":"2254_CR23","doi-asserted-by":"crossref","unstructured":"Leung, J. Y. T., Li, H., & Pinedo, M. (2005b) Order scheduling models: an overview. In Multidisciplinary scheduling: Theory and applications (pp. 37\u201353). Springer.","DOI":"10.1007\/0-387-27744-7_3"},{"issue":"2","key":"2254_CR24","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1016\/j.ejor.2004.03.030","volume":"168","author":"JYT Leung","year":"2006","unstructured":"Leung, J. Y. T., Li, H., & Pinedo, M. (2006). Scheduling orders for multiple product types with due date related objectives. European Journal of Operational Research, 168(2), 370\u2013389.","journal-title":"European Journal of Operational Research"},{"issue":"8","key":"2254_CR25","doi-asserted-by":"publisher","first-page":"945","DOI":"10.1016\/j.dam.2006.09.012","volume":"155","author":"JYT Leung","year":"2007","unstructured":"Leung, J. Y. T., Li, H., & Pinedo, M. (2007). Scheduling orders for multiple product types to minimize total weighted completion time. Discrete Applied Mathematics, 155(8), 945\u2013970.","journal-title":"Discrete Applied Mathematics"},{"issue":"3","key":"2254_CR26","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1109\/71.674321","volume":"9","author":"JCS Lui","year":"1998","unstructured":"Lui, J. C. S., Muntz, R. R., & Towsley, D. (1998). Computing performance bounds of fork\u2013join parallel programs under a multiprocessing environment. IEEE Transactions on Parallel and Distributed Systems, 9(3), 295\u2013311.","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"key":"2254_CR27","unstructured":"Makowski, A. M., & Philips, T. K. (1989). Simple proofs of some folk theorems for parallel queues. IBM reasearch report 14556."},{"key":"2254_CR28","volume-title":"Toyota production system: An integrated approach to just-in-time","author":"Y Monden","year":"2012","unstructured":"Monden, Y. (2012). Toyota production system: An integrated approach to just-in-time. Boca Raton: CRC Press."},{"issue":"6","key":"2254_CR29","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1109\/12.2213","volume":"37","author":"R Nelson","year":"1988","unstructured":"Nelson, R., & Tantawi, A. N. (1988). Approximate analysis of fork\u2013join synchronization in parallel queues. IEEE Transactions on Computers, 37(6), 739\u2013743.","journal-title":"IEEE Transactions on Computers"},{"issue":"4","key":"2254_CR30","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1023\/A:1024284828374","volume":"6","author":"CT Ng","year":"2003","unstructured":"Ng, C. T., Cheng, T. C. E., & Yuan, J. J. (2003). Concurrent open shop scheduling to minimize the weighted number of tardy jobs. Journal of Scheduling, 6(4), 405\u2013412.","journal-title":"Journal of Scheduling"},{"issue":"6","key":"2254_CR31","doi-asserted-by":"publisher","first-page":"560","DOI":"10.1016\/j.orl.2004.12.005","volume":"33","author":"D Pinotsi","year":"2005","unstructured":"Pinotsi, D., & Zazanis, M. A. (2005). Synchronized queues with deterministic arrivals. Operations Research Letters, 33(6), 560\u2013566.","journal-title":"Operations Research Letters"},{"issue":"4","key":"2254_CR32","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/s10951-006-7042-y","volume":"9","author":"TA Roemer","year":"2006","unstructured":"Roemer, T. A. (2006). A note on the complexity of the concurrent open shop problem. Journal of Scheduling, 9(4), 389\u2013396.","journal-title":"Journal of Scheduling"},{"issue":"4","key":"2254_CR33","first-page":"41","volume":"66","author":"G Stalk","year":"1988","unstructured":"Stalk, G. (1988). Time\u2014The next source of competitive advantage. Harvard Business Review, 66(4), 41\u201351.","journal-title":"Harvard Business Review"},{"key":"2254_CR34","doi-asserted-by":"publisher","DOI":"10.1080\/08956308.1990.11670646","volume-title":"Competing against time: How time-based competition is reshaping global markets","author":"G Stalk","year":"1990","unstructured":"Stalk, G., & Hout, T. M. (1990). Competing against time: How time-based competition is reshaping global markets. New York: Free Press."},{"key":"2254_CR35","unstructured":"Varki, E., Merchant, A., & Chen, H. (2008). The M\/M\/1 fork-join queue with variable sub-tasks. Citeseer. http:\/\/www.cs.unh.edu\/varki\/publication\/open.pdf."},{"issue":"1","key":"2254_CR36","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/0166-5316(94)90016-7","volume":"20","author":"S Varma","year":"1994","unstructured":"Varma, S., & Makowski, A. M. (1994). Interpolation approximations for symmetric fork\u2013join queues. Performance Evaluation, 20(1), 245\u2013265.","journal-title":"Performance Evaluation"},{"issue":"1","key":"2254_CR37","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/s10479-006-0020-0","volume":"144","author":"M Vidovic","year":"2006","unstructured":"Vidovic, M., & Kim, K. H. (2006). Estimating the cycle time of three-stage material handling systems. Annals of Operations Research, 144(1), 181\u2013200.","journal-title":"Annals of Operations Research"},{"issue":"5","key":"2254_CR38","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1016\/j.omega.2005.09.007","volume":"35","author":"G Wang","year":"2007","unstructured":"Wang, G., & Cheng, T. C. E. (2007). Customer order scheduling to minimize total weighted completion time. Omega, 35(5), 623\u2013626.","journal-title":"Omega"},{"key":"2254_CR39","first-page":"268","volume":"22","author":"PD Welch","year":"1983","unstructured":"Welch, P. D. (1983). The statistical analysis of simulation results. The Computer Performance Modeling Handbook, 22, 268\u2013328.","journal-title":"The Computer Performance Modeling Handbook"},{"key":"2254_CR40","doi-asserted-by":"crossref","unstructured":"Whitt, W. (1980). The effect of variability in the GI\/G\/s queue. Journal of Applied Probability, 17, 1062\u20131071.","DOI":"10.2307\/3213215"},{"issue":"1","key":"2254_CR41","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1109\/TASE.2013.2291899","volume":"12","author":"X Xu","year":"2013","unstructured":"Xu, X., Ma, Y., Zhou, Z., & Zhao, Y. (2013). Customer order scheduling on unrelated parallel machines to minimize total completion time. IEEE Transactions on Automation Science and Engineering, 12(1), 244\u2013257.","journal-title":"IEEE Transactions on Automation Science and Engineering"},{"issue":"7","key":"2254_CR42","doi-asserted-by":"publisher","first-page":"1921","DOI":"10.1016\/j.cor.2003.12.008","volume":"32","author":"J Yang","year":"2005","unstructured":"Yang, J. (2005). The complexity of customer order scheduling problems on parallel machines. Computers & Operations Research, 32(7), 1921\u20131939.","journal-title":"Computers & Operations Research"},{"issue":"1","key":"2254_CR43","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/s10951-005-5315-5","volume":"8","author":"J Yang","year":"2005","unstructured":"Yang, J., & Posner, M. E. (2005). Scheduling parallel machines for the customer order problem. Journal of Scheduling, 8(1), 49\u201374.","journal-title":"Journal of Scheduling"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-016-2254-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-016-2254-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-016-2254-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-016-2254-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T17:24:24Z","timestamp":1757093064000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-016-2254-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,28]]},"references-count":43,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["2254"],"URL":"https:\/\/doi.org\/10.1007\/s10479-016-2254-9","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"type":"print","value":"0254-5330"},{"type":"electronic","value":"1572-9338"}],"subject":[],"published":{"date-parts":[[2016,7,28]]},"assertion":[{"value":"28 July 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}