{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:33:57Z","timestamp":1740123237295,"version":"3.37.3"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T00:00:00Z","timestamp":1702944000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T00:00:00Z","timestamp":1702944000000},"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":["Ann Oper Res"],"published-print":{"date-parts":[[2024,7]]},"DOI":"10.1007\/s10479-023-05759-8","type":"journal-article","created":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T19:02:27Z","timestamp":1703012547000},"page":"347-377","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Measuring the slack between lower bounds for scheduling on parallel machines"],"prefix":"10.1007","volume":"338","author":[{"given":"Jacques","family":"Carlier","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2482-5042","authenticated-orcid":false,"given":"Claire","family":"Hanen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,12,19]]},"reference":[{"key":"5759_CR1","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1023\/A:1018995000688","volume":"92","author":"P Baptiste","year":"1999","unstructured":"Baptiste, P., Le Pape, C., & Nuijten, W. (1999). Satisfiability tests and time-bound adjustments for cumulative scheduling problems. Annals of Operations Research, 92, 305\u2013333.","journal-title":"Annals of Operations Research"},{"key":"5759_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-1479-4","volume-title":"Constraint-based scheduling: Applying constraint programming to scheduling problems","author":"P Baptiste","year":"2001","unstructured":"Baptiste, P., Le Pape, C., & Nuijten, W. (2001). Constraint-based scheduling: Applying constraint programming to scheduling problems (Vol. 39). Springer."},{"key":"5759_CR3","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1016\/0377-2217(87)90243-8","volume":"29","author":"J Carlier","year":"1987","unstructured":"Carlier, J. (1987). Scheduling jobs with release dates and tails on identical machines to minimize the makespan. European Journal of Operational Research, 29, 298\u2013306.","journal-title":"European Journal of Operational Research"},{"key":"5759_CR4","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1023\/A:1018968332237","volume":"83","author":"J Carlier","year":"1998","unstructured":"Carlier, J., & Pinson, E. (1998). Jackson\u2019s pseudo preemptive schedule for the $$pm\\vert r_i, q_i \\vert c_{\\max }$$ scheduling problem. Annals of Operations Research, 83, 41\u201358.","journal-title":"Annals of Operations Research"},{"issue":"1","key":"5759_CR5","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.dam.2003.09.009","volume":"145","author":"J Carlier","year":"2004","unstructured":"Carlier, J., & Pinson, E. (2004). Jackson\u2019s pseudo-preemptive schedule and cumulative scheduling problems. Discrete Applied Mathematics, 145(1), 80\u201394.","journal-title":"Discrete Applied Mathematics"},{"key":"5759_CR6","unstructured":"Carlier, J., Pinson, E., Sahli, A., & Jouglet, A. (2021) Comparison of three classical lower bounds for the Cumulative Scheduling Problem. (submitted)."},{"key":"5759_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-023-05596-9","author":"J Carlier","year":"2023","unstructured":"Carlier, J., Sahli, A., & Jouglet, A. (2023). Algorithms to compute the energetic lower bounds of the cumulative scheduling problem. Annals of Operations Research. https:\/\/doi.org\/10.1007\/s10479-023-05596-9","journal-title":"Annals of Operations Research"},{"issue":"11","key":"5759_CR8","doi-asserted-by":"publisher","first-page":"3419","DOI":"10.1080\/00207543.2021.1923853","volume":"60","author":"J Carlier","year":"2022","unstructured":"Carlier, J., Sahli, A., Jouglet, A., & Pinson, E. (2022). A faster checker of the energetic reasoning for the cumulative scheduling problem. International Journal of Production Research, 60(11), 3419\u20133434.","journal-title":"International Journal of Production Research"},{"key":"5759_CR9","unstructured":"Erschler, J., & Lopez, C.T. P. (1989). Scheduling under time and resource constraints. In Proceedings of workshop on manufacturing scheduling, 11th IJCAI, Detroit, USA."},{"key":"5759_CR10","unstructured":"Erschler, J., & Lopez, P. (1990). Energy-based approach for task scheduling under time and resources constraints. In 2nd international workshop on project management and scheduling, Compi\u00e8gne (France) (pp. 115\u2013121)."},{"issue":"2","key":"5759_CR11","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.2140\/pjm.1957.7.1073","volume":"7","author":"D Gale","year":"1957","unstructured":"Gale, D. (1957). A theorem on flows in networks. Pacific Journal of Mathematics, 7(2), 1073\u20131082. Publisher: Pacific Journal of Mathematics, A Non-profit Corporation.","journal-title":"Pacific Journal of Mathematics"},{"key":"5759_CR12","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/S0167-5060(08)70356-X","volume":"5","author":"R Graham","year":"1977","unstructured":"Graham, R., Lawler, E. L., Lenstra, J. K., & Kan, A. H. G. R. (1977). Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics, 5, 287\u2013326.","journal-title":"Annals of Discrete Mathematics"},{"key":"5759_CR13","doi-asserted-by":"crossref","unstructured":"Hanen, C., Munier\u00a0Kordon, A., & Pedersen, T. (2021) Two deadline reduction algorithms for scheduling dependent tasks on parallel processors (extended version). hal-0320029.","DOI":"10.1007\/978-3-030-78230-6_14"},{"issue":"5","key":"5759_CR14","doi-asserted-by":"publisher","first-page":"1187","DOI":"10.1016\/j.cor.2011.05.022","volume":"39","author":"M Haouari","year":"2012","unstructured":"Haouari, M., Kooli, A., & N\u00e9ron, E. (2012). Enhanced energetic reasoning-based lower bounds for the resource constrained project scheduling problem. Computers and Operations Research, 39(5), 1187\u20131194.","journal-title":"Computers and Operations Research"},{"issue":"3","key":"5759_CR15","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/s10951-013-0354-9","volume":"17","author":"M Haouari","year":"2014","unstructured":"Haouari, M., Kooli, A., N\u00e9ron, E., & Carlier, J. (2014). A preemptive bound for the Resource Constrained Project Scheduling Problem. Journal of Scheduling, 17(3), 237\u2013248.","journal-title":"Journal of Scheduling"},{"issue":"1","key":"5759_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2021.05.004","volume":"297","author":"S Hartmann","year":"2022","unstructured":"Hartmann, S., & Briskorn, D. (2022). An updated survey of variants and extensions of the resource-constrained project scheduling problem. European Journal of Operational Research, 297(1), 1\u201314. https:\/\/doi.org\/10.1016\/j.ejor.2021.05.004","journal-title":"European Journal of Operational Research"},{"issue":"4","key":"5759_CR17","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/s10951-008-0070-z","volume":"11","author":"L Hidri","year":"2008","unstructured":"Hidri, L., Gharbi, A., & Haouari, M. (2008). Energetic reasoning revisited: Application to parallel machine scheduling. Journal of Scheduling, 11(4), 239\u2013252. Publisher: Springer.","journal-title":"Journal of Scheduling"},{"key":"5759_CR18","doi-asserted-by":"crossref","unstructured":"Laborie, P., & Nuijten, W. (2008). Constraint programming formulations and propagation algorithms. In Resource-constrained project scheduling (pp. 63\u201372). Wiley.","DOI":"10.1002\/9780470611227.ch4"},{"key":"5759_CR19","doi-asserted-by":"crossref","unstructured":"Lahrichi, A. (1982). Ordonnancements. La notion de \"parties obligatoires\" et son application aux probl\u00e8mes cumulatifs. RAIRO - Operations Research - Recherche Op\u00e9rationnelle, 16(3), 241\u2013262","DOI":"10.1051\/ro\/1982160302411"},{"issue":"3","key":"5759_CR20","doi-asserted-by":"publisher","first-page":"812","DOI":"10.1145\/322326.322337","volume":"29","author":"C Martel","year":"1982","unstructured":"Martel, C. (1982). Preemptive scheduling with release times, deadlines, and due times. Journal of the Association of Computing Machinery, 29(3), 812\u2013829. Place: New York, NY, USA Publisher: ACM.","journal-title":"Journal of the Association of Computing Machinery"},{"key":"5759_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1287\/mnsc.6.1.1","volume":"6","author":"R McNaughton","year":"1959","unstructured":"McNaughton, R. (1959). Scheduling with deadlines and loss functions. Management Science, 6, 1\u201312.","journal-title":"Management Science"},{"key":"5759_CR22","doi-asserted-by":"crossref","unstructured":"N\u00e9ron, E. (2008). Resource and precedence constraint relaxation. In Resource-constrained project scheduling (pp. 37\u201348). Wiley.","DOI":"10.1002\/9780470611227.ch2"},{"key":"5759_CR23","doi-asserted-by":"crossref","unstructured":"Ouellet, Y., & Quimper, C.-G. (2018). A $$\\cal{O} {(n\\log ^{2} n)}$$ checker and $$\\cal{O} {(n^{2}\\log n)}$$ filtering algorithm for the energetic reasoning. In W. J. van Hoeve (Ed.), CPAIOR 2018, June 26\u201329. Lecture notes in computer science (Vol. 10848, pp. 477\u2013494). Springer.","DOI":"10.1007\/978-3-319-93031-2_34"},{"issue":"2\u20133","key":"5759_CR24","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/0166-218X(94)00105-M","volume":"57","author":"E Sanlaville","year":"1995","unstructured":"Sanlaville, E. (1995). Nearly on line scheduling of preemptive independent tasks. Discrete Applied Mathematics, 57(2\u20133), 229\u2013241.","journal-title":"Discrete Applied Mathematics"},{"issue":"4","key":"5759_CR25","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1016\/j.orl.2003.08.008","volume":"32","author":"F Tercinet","year":"2004","unstructured":"Tercinet, F., Lent\u00e9, C., & N\u00e9ron, E. (2004). Mixed satisfiability tests for multiprocessor scheduling with release dates and deadlines. Operations Research Letters, 32(4), 326\u2013330.","journal-title":"Operations Research Letters"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-023-05759-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-023-05759-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-023-05759-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T16:25:30Z","timestamp":1721060730000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-023-05759-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,19]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,7]]}},"alternative-id":["5759"],"URL":"https:\/\/doi.org\/10.1007\/s10479-023-05759-8","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"type":"print","value":"0254-5330"},{"type":"electronic","value":"1572-9338"}],"subject":[],"published":{"date-parts":[[2023,12,19]]},"assertion":[{"value":"3 December 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 December 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"Author Claire Hanen declares that she has no conflict of interest. Author Jacques Carlier declares that he has no conflict of interest.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}