{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T10:10:13Z","timestamp":1776939013723,"version":"3.51.4"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,8,18]],"date-time":"2018-08-18T00:00:00Z","timestamp":1534550400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001825","name":"Styrelsen for Forskning og Innovation","doi-asserted-by":"publisher","award":["1355-00166B"],"award-info":[{"award-number":["1355-00166B"]}],"id":[{"id":"10.13039\/501100001825","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"name":"HEC Montr\u00e9al Foundation"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sched"],"published-print":{"date-parts":[[2019,4]]},"DOI":"10.1007\/s10951-018-0582-0","type":"journal-article","created":{"date-parts":[[2018,8,18]],"date-time":"2018-08-18T04:43:00Z","timestamp":1534567380000},"page":"155-172","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Daily course pattern formulation and valid inequalities for the curriculum-based course timetabling problem"],"prefix":"10.1007","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4665-6761","authenticated-orcid":false,"given":"Niels-Christian Fink","family":"Bagger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guy","family":"Desaulniers","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jacques","family":"Desrosiers","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,8,18]]},"reference":[{"key":"582_CR1","doi-asserted-by":"crossref","unstructured":"Achterberg, T. (2009). Scip: Solving constraint integer programs. Mathematical Programming Computation 1(1):1\u201341. \n                    http:\/\/mpc.zib.de\/index.php\/MPC\/article\/view\/4","DOI":"10.1007\/s12532-008-0001-1"},{"key":"582_CR2","first-page":"1","volume":"218","author":"R As\u00edn Ach\u00e1","year":"2012","unstructured":"As\u00edn Ach\u00e1, R., & Nieuwenhuis, R. (2012). Curriculum-based course timetabling with sat and maxsat. Annals of Operations Research, 218, 1\u201321.","journal-title":"Annals of Operations Research"},{"key":"582_CR3","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1007\/s10951-005-4780-1","volume":"8","author":"P Avella","year":"2005","unstructured":"Avella, P., & Vasil\u2019Ev, I. (2005). A computational study of a cutting plane algorithm for university course timetabling. Journal of Scheduling, 8, 497\u2013514.","journal-title":"Journal of Scheduling"},{"key":"582_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11750-015-0372-1","volume":"23","author":"A Bettinelli","year":"2015","unstructured":"Bettinelli, A., Cacchiani, V., Roberti, R., & Toth, P. (2015). An overview of curriculum-based course timetabling. TOP, 23, 1\u201337.","journal-title":"TOP"},{"issue":"1","key":"582_CR5","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s10479-010-0707-0","volume":"194","author":"A Bonutti","year":"2012","unstructured":"Bonutti, A., De Cesco, F., Di Gaspero, L., & Schaerf, A. (2012). Benchmarking curriculum-based course timetabling: Formulations, data formats, instances, validation, visualization, and results. Annals of Operations Research, 194(1), 59\u201370.","journal-title":"Annals of Operations Research"},{"key":"582_CR6","unstructured":"Bonutti, A., Gaspero, L.D., & Schaerf, A. (2016). Curriculum-based course timetabling. \n                    http:\/\/tabu.diegm.uniud.it\/ctt\/index.php\n                    \n                  . Retrieved December 30 2016."},{"issue":"9","key":"582_CR7","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1145\/362342.362367","volume":"16","author":"C Bron","year":"1973","unstructured":"Bron, C., & Kerbosch, J. (1973). Algorithm 457: Finding all cliques of an undirected graph. Communications of the ACM, 16(9), 575\u2013577. \n                    https:\/\/doi.org\/10.1145\/362342.362367\n                    \n                  .","journal-title":"Communications of the ACM"},{"key":"582_CR8","doi-asserted-by":"publisher","unstructured":"Burke, E. K., Mare\u010dek, J., Parkes, A.J., & Rudov\u00e1, H. (2008). Penalising patterns in timetables: Novel integer programming formulations. In: Kalcsics J, Nickel S (eds) Operations Research Proceedings 2007, Operations Research Proceedings,( Vol. 2007, pp. 409\u2013414). Springer: Berlin Heidelberg. \n                    https:\/\/doi.org\/10.1007\/978-3-540-77903-2_63","DOI":"10.1007\/978-3-540-77903-2_63"},{"issue":"3","key":"582_CR9","doi-asserted-by":"publisher","first-page":"582","DOI":"10.1016\/j.cor.2009.02.023","volume":"37","author":"EK Burke","year":"2010","unstructured":"Burke, E. K., Mare\u010dek, J., Parkes, A. J., & Rudov\u00e1, H. (2010a). Decomposition, reformulation, and diving in university course timetabling. Computers & Operations Research, 37(3), 582\u2013597.","journal-title":"Computers & Operations Research"},{"issue":"1","key":"582_CR10","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/s10479-010-0716-z","volume":"179","author":"EK Burke","year":"2010","unstructured":"Burke, E. K., Mare\u010dek, J., Parkes, A. J., & Rudov\u00e1, H. (2010b). A supernodal formulation of vertex colouring with application in course timetabling. Annals of Operations Research, 179(1), 105\u2013130.","journal-title":"Annals of Operations Research"},{"issue":"1","key":"582_CR11","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s10479-010-0828-5","volume":"194","author":"EK Burke","year":"2012","unstructured":"Burke, E. K., Mare\u010dek, J., Parkes, A. J., & Rudov\u00e1, H. (2012). A branch-and-cut procedure for the udine course timetabling problem. Annals of Operations Research, 194(1), 71\u201387.","journal-title":"Annals of Operations Research"},{"issue":"10","key":"582_CR12","doi-asserted-by":"publisher","first-page":"2466","DOI":"10.1016\/j.cor.2013.02.010","volume":"40","author":"V Cacchiani","year":"2013","unstructured":"Cacchiani, V., Caprara, A., Roberti, R., & Toth, P. (2013). A new lower bound for curriculum-based course timetabling. Computers & Operations Research, 40(10), 2466\u20132477.","journal-title":"Computers & Operations Research"},{"key":"582_CR13","unstructured":"Di\u00a0Gaspero L, McCollum B, Schaerf A (2007) The second international timetabling competition (itc-2007): Curriculum-based course timetabling (track 3). Tech. rep., School of Electronics, Electrical Engineering and Computer Science, Queenes University SARC Building, Belfast, United Kingdom."},{"issue":"2","key":"582_CR14","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1145\/321694.321699","volume":"19","author":"J Edmonds","year":"1972","unstructured":"Edmonds, J., & Karp, R. M. (1972). Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM, 19(2), 248\u2013264. \n                    https:\/\/doi.org\/10.1145\/321694.321699\n                    \n                  .","journal-title":"Journal of the ACM"},{"key":"582_CR15","unstructured":"Gurobi Optimization, Inc.(2016). Gurobi optimizer reference manual. \n                    http:\/\/www.gurobi.com"},{"issue":"3","key":"582_CR16","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1016\/j.ejor.2011.02.019","volume":"212","author":"JK Hao","year":"2011","unstructured":"Hao, J. K., & Benlic, U. (2011). Lower bounds for the ITC-2007 curriculum-based course timetabling problem. European Journal of Operational Research, 212(3), 464\u2013472.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"582_CR17","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1145\/359340.359346","volume":"21","author":"LT Kou","year":"1978","unstructured":"Kou, L. T., Stockmeyer, L. J., & Wong, C. K. (1978). Covering edges by cliques with regard to keyword conflicts and intersection graphs. Communications of the ACM, 21(2), 135\u2013139.","journal-title":"Communications of the ACM"},{"key":"582_CR18","first-page":"235","volume-title":"Experimental algorithms, lecture notes in computer science","author":"G Lach","year":"2008","unstructured":"Lach, G., & L\u00fcbbecke, M. (2008). Optimal university course timetables and the partial transversal polytope. In C. McGeoch (Ed.), Experimental algorithms, lecture notes in computer science (Vol. 5038, pp. 235\u2013248). Berlin\/Heidelberg: Springer."},{"key":"582_CR19","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s10479-010-0700-7","volume":"194","author":"G Lach","year":"2012","unstructured":"Lach, G., & L\u00fcbbecke, M. (2012). Curriculum based course timetabling: New solutions to udine benchmark instances. Annals of Operations Research, 194, 255\u2013272.","journal-title":"Annals of Operations Research"},{"issue":"1","key":"582_CR20","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1287\/ijoc.1090.0320","volume":"22","author":"B McCollum","year":"2010","unstructured":"McCollum, B., Schaerf, A., Paechter, B., McMullan, P., Lewis, R., Parkes, A. J., et al. (2010). Setting the research agenda in automated timetabling: The second international timetabling competition. Informs Journal on Computing, 22(1), 120\u2013130.","journal-title":"Informs Journal on Computing"},{"key":"582_CR21","doi-asserted-by":"publisher","DOI":"10.1002\/9781118627372","volume-title":"Integer and combinatorial optimization","author":"GL Nemhauser","year":"1988","unstructured":"Nemhauser, G. L., & Wolsey, L. A. (1988). Integer and combinatorial optimization. New York, NY: Wiley-Interscience."},{"issue":"1","key":"582_CR22","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1287\/opre.35.1.45","volume":"35","author":"TJ Roy Van","year":"1987","unstructured":"Van Roy, T. J., & Wolsey, L. A. (1987). Solving mixed integer programming problems using automatic reformulation. Operations Research, 35(1), 45\u201357.","journal-title":"Operations Research"}],"container-title":["Journal of Scheduling"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10951-018-0582-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10951-018-0582-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10951-018-0582-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T05:46:08Z","timestamp":1569303968000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10951-018-0582-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,18]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["582"],"URL":"https:\/\/doi.org\/10.1007\/s10951-018-0582-0","relation":{},"ISSN":["1094-6136","1099-1425"],"issn-type":[{"value":"1094-6136","type":"print"},{"value":"1099-1425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,18]]},"assertion":[{"value":"18 August 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}