{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T21:16:35Z","timestamp":1769548595443,"version":"3.49.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T00:00:00Z","timestamp":1747094400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T00:00:00Z","timestamp":1747094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Oper Res Int J"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s12351-025-00921-5","type":"journal-article","created":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T07:38:54Z","timestamp":1747121934000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A note: approximation algorithms for batch scheduling on shops with job rejection"],"prefix":"10.1007","volume":"25","author":[{"given":"Gur","family":"Mosheiov","sequence":"first","affiliation":[]},{"given":"Assaf","family":"Sarig","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,13]]},"reference":[{"key":"921_CR1","volume-title":"Scheduling equal processing time jobs: a survey","author":"P Baptiste","year":"2003","unstructured":"Baptiste P, Brucker P (2003) Scheduling equal processing time jobs: a survey. Universit\u00e4t Osnabr\u00fcck, Fachbereich Mathematik\/Informatik"},{"key":"921_CR2","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1051\/ro\/1996300100651","volume":"30","author":"H Br\u00e4sel","year":"1996","unstructured":"Br\u00e4sel H, Kluge D, Werner F (1996) Polynomial time algorithms for special open shop problems with precedence constraints and unit processing times. RAIRO-Oper Res 30:65\u201379","journal-title":"RAIRO-Oper Res"},{"key":"921_CR3","doi-asserted-by":"publisher","first-page":"2732","DOI":"10.1016\/j.tcs.2009.04.006","volume":"410","author":"Z Cao","year":"2009","unstructured":"Cao Z, Yang X (2009) A PTAS for parallel batch scheduling with rejection and dynamic job arrivals. Theoret Comput Sci 410:2732\u20132745","journal-title":"Theoret Comput Sci"},{"key":"921_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2021.06.012","volume":"298","author":"JW Fowler","year":"2022","unstructured":"Fowler JW, M\u00f6nch L (2022) A survey of scheduling with parallel batch (p-batch) processing. Eur J Oper Res 298:1\u201324","journal-title":"Eur J Oper Res"},{"key":"921_CR5","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.dam.2015.10.021","volume":"204","author":"C He","year":"2016","unstructured":"He C, Leung JYT, Lee K, Pinedo ML (2016) Scheduling a single machine with parallel batching to minimize makespan and total rejection cost. Discret Appl Math 204:150\u2013163","journal-title":"Discret Appl Math"},{"key":"921_CR6","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1051\/ro\/2017040","volume":"52","author":"W Huang","year":"2018","unstructured":"Huang W, Wu CC, Liu S (2018) Single-machine batch scheduling problem with job rejection and resource dependent processing times. RAIRO-Oper Res 52:315\u2013334","journal-title":"RAIRO-Oper Res"},{"key":"921_CR7","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/S0166-218X(99)00202-4","volume":"100","author":"SA Kravchenko","year":"2000","unstructured":"Kravchenko SA (2000) On the complexity of minimizing the number of late jobs in unit time open shop. Discret Appl Math 100:127\u2013132","journal-title":"Discret Appl Math"},{"key":"921_CR8","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1007\/s10951-011-0231-3","volume":"14","author":"SA Kravchenko","year":"2011","unstructured":"Kravchenko SA, Werner F (2011) Parallel machine problems with equal processing times: a survey. J Sched 14:435\u2013444","journal-title":"J Sched"},{"key":"921_CR9","doi-asserted-by":"crossref","unstructured":"Li X, Feng H (2010) Minimize the sum of total completion time and total rejection penalties on a single parallel batching machine. In: 2010 WASE international conference on information engineering. 2: 200\u2013202","DOI":"10.1109\/ICIE.2010.143"},{"key":"921_CR10","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/s40305-014-0062-y","volume":"2","author":"SS Li","year":"2014","unstructured":"Li SS, Chen RX (2014) Scheduling a bounded parallel-batching machine with incompatible job families and rejection. J Oper Res Soc China 2:499\u2013510","journal-title":"J Oper Res Soc China"},{"key":"921_CR11","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.tcs.2008.02.015","volume":"396","author":"L Lu","year":"2008","unstructured":"Lu L, Zhang L, Yuan J (2008) The unbounded parallel batch machine scheduling with release dates and rejection to minimize makespan. Theoret Comput Sci 396:283\u2013289","journal-title":"Theoret Comput Sci"},{"key":"921_CR12","doi-asserted-by":"publisher","first-page":"2748","DOI":"10.1016\/j.cor.2008.12.003","volume":"36","author":"L Lu","year":"2009","unstructured":"Lu L, Cheng TE, Yuan J, Zhang L (2009) Bounded single-machine parallel-batch scheduling with release dates and rejection. Comput Oper Res 36:2748\u20132751","journal-title":"Comput Oper Res"},{"key":"921_CR13","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1016\/j.cor.2011.05.014","volume":"39","author":"B Mor","year":"2012","unstructured":"Mor B, Mosheiov G (2012) Batch scheduling on uniform machines to minimize total flow-time. Comput Oper Res 39:571\u2013575","journal-title":"Comput Oper Res"},{"key":"921_CR14","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1016\/j.ejor.2006.01.052","volume":"187","author":"G Mosheiov","year":"2008","unstructured":"Mosheiov G, Oron D (2008a) A single machine batch scheduling problem with bounded batch size. Eur J Oper Res 187:1069\u20131079","journal-title":"Eur J Oper Res"},{"key":"921_CR15","doi-asserted-by":"publisher","first-page":"1282","DOI":"10.1016\/j.ejor.2006.03.068","volume":"187","author":"G Mosheiov","year":"2008","unstructured":"Mosheiov G, Oron D (2008b) Open-shop batch scheduling with identical jobs. Eur J Oper Res 187:1282\u20131292","journal-title":"Eur J Oper Res"},{"key":"921_CR16","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1002\/nav.21740","volume":"64","author":"G Mosheiov","year":"2017","unstructured":"Mosheiov G, Strusevich VA (2017) Determining optimal sizes of bounded batches with rejection via quadratic min-cost flow. Nav Res Logist 64:217\u2013224","journal-title":"Nav Res Logist"},{"key":"921_CR17","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1002\/nav.20028","volume":"51","author":"G Mosheiov","year":"2004","unstructured":"Mosheiov G, Oron D, Ritov Y (2004) Flow-shop batch scheduling to minimize total flow-time. Nav Res Logist 51:783\u2013799","journal-title":"Nav Res Logist"},{"key":"921_CR18","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1016\/j.orl.2004.09.007","volume":"33","author":"G Mosheiov","year":"2005","unstructured":"Mosheiov G, Oron D, Ritov Y (2005) Minimizing flow-time on a single machine with integer batch sizes. Oper Res Lett 33:497\u2013501","journal-title":"Oper Res Lett"},{"key":"921_CR19","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/0167-6377(85)90011-2","volume":"4","author":"C Santos","year":"1985","unstructured":"Santos C, Magazine M (1985) Batching in single operation manufacturing systems. Oper Res Lett 4:99\u2013103","journal-title":"Oper Res Lett"},{"key":"921_CR20","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.ejor.2013.08.013","volume":"233","author":"D Shabtay","year":"2014","unstructured":"Shabtay D (2014) The single machine serial batch scheduling problem with rejection to minimize total completion time and total rejection cost. Eur J Oper Res 233:64\u201374","journal-title":"Eur J Oper Res"},{"key":"921_CR21","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10951-012-0303-z","volume":"16","author":"D Shabtay","year":"2013","unstructured":"Shabtay D, Gaspar N, Kaspi M (2013) A survey on offline scheduling with rejection. J Sched 16:3\u201328","journal-title":"J Sched"},{"key":"921_CR22","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1016\/0167-6377(92)90027-Z","volume":"11","author":"DF Shallcross","year":"1992","unstructured":"Shallcross DF (1992) A polynomial algorithm for a one machine batching problem. Oper Res Lett 11:213\u2013218","journal-title":"Oper Res Lett"},{"issue":"16\u201318","key":"921_CR23","doi-asserted-by":"publisher","first-page":"1877","DOI":"10.1016\/j.tcs.2010.02.006","volume":"411","author":"L Zhang","year":"2010","unstructured":"Zhang L, Lu L, Yuan J (2010) Single-machine scheduling under the job rejection constraint. Theoret Comput Sci 411(16\u201318):1877\u20131882","journal-title":"Theoret Comput Sci"},{"key":"921_CR24","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/s12351-015-0193-x","volume":"16","author":"J Zou","year":"2016","unstructured":"Zou J, Miao C (2016) The single machine serial batch scheduling problems with rejection. Oper Res Int J 16:211\u2013221","journal-title":"Oper Res Int J"}],"container-title":["Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-025-00921-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12351-025-00921-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-025-00921-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T19:04:42Z","timestamp":1750187082000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12351-025-00921-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,13]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["921"],"URL":"https:\/\/doi.org\/10.1007\/s12351-025-00921-5","relation":{},"ISSN":["1109-2858","1866-1505"],"issn-type":[{"value":"1109-2858","type":"print"},{"value":"1866-1505","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,13]]},"assertion":[{"value":"18 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 February 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 May 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose. The authors have no conflicts of interest to declare that are relevant to the content of this article. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"47"}}