{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T15:09:51Z","timestamp":1790694591528,"version":"4.1.0"},"reference-count":56,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T00:00:00Z","timestamp":1591660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper considers the general lot sizing and scheduling problem with rich constraints exemplified by means of rework and lifetime constraints for defective items (GLSP-RP), which finds numerous applications in industrial settings, for example, the food processing industry and the pharmaceutical industry. To address this problem, we propose the Late Acceptance Hill-climbing Matheuristic (LAHCM) as a novel solution framework that exploits and integrates the late acceptance hill climbing algorithm and exact approaches for speeding up the solution process in comparison to solving the problem by means of a general solver. The computational results show the benefits of incorporating exact approaches within the LAHCM template leading to high-quality solutions within short computational times.<\/jats:p>","DOI":"10.3390\/a13060138","type":"journal-article","created":{"date-parts":[[2020,6,10]],"date-time":"2020-06-10T05:11:46Z","timestamp":1591765906000},"page":"138","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Late Acceptance Hill-Climbing Matheuristic for the General Lot Sizing and Scheduling Problem with Rich Constraints"],"prefix":"10.3390","volume":"13","author":[{"given":"Andreas","family":"Goerler","sequence":"first","affiliation":[{"name":"Institute of Information Systems, University of Hamburg, 20146 Hamburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eduardo","family":"Lalla-Ruiz","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Business Information Systems, University of Twente, 7522 NH Enschede, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1296-4221","authenticated-orcid":false,"given":"Stefan","family":"Vo\u00df","sequence":"additional","affiliation":[{"name":"Institute of Information Systems, University of Hamburg, 20146 Hamburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,9]]},"reference":[{"key":"ref_1","unstructured":"Goerler, A., Pahl, J., and Vo\u00df, S. (2017). Simultaneous Lot Sizing and Scheduling for Contamination Sensitive Items with Rework Options, Institute of Information Systems, University of Hamburg. Working Paper."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Maniezzo, V., St\u00fctzle, T., and Vo\u00df, S. (2009). Matheuristics: Hybridizing Metaheuristics and Mathematical Programming. Annals of Information Systems 10, Springer.","DOI":"10.1007\/978-1-4419-1306-7"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1016\/j.ejor.2018.01.032","article-title":"A matheuristic decomposition approach for the scheduling of a single-source and multiple destinations pipeline system","volume":"268","author":"Meira","year":"2018","journal-title":"Eur. J. Oper. Res."},{"key":"ref_4","first-page":"671","article-title":"A popmusic approach for the multi-depot cumulative capacitated vehicle routing problem","volume":"14","year":"2019","journal-title":"Optim. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Caserta, M., and Vo\u00df, S. (2020). Accelerating mathematical programming techniques with the corridor method. Int. J. Prod. Res.","DOI":"10.1080\/00207543.2020.1740343"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s10472-014-9444-4","article-title":"POPMUSIC as a matheuristic for the berth allocation problem","volume":"76","year":"2016","journal-title":"Ann. Math. Artif. Intell."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s13675-014-0030-7","article-title":"A survey on matheuristics for routing problems","volume":"2","author":"Archetti","year":"2014","journal-title":"EURO J. Comput. Optim."},{"key":"ref_8","unstructured":"Burke, E.K., and Bykov, Y. (2008, January 18). A late acceptance strategy in hill-climbing for exam timetabling problems. Proceedings of the PATAT 2008 Conference, Montreal, QC, Canada."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Terzi, M., Arbaoui, T., Yalaoui, F., and Benatchba, K. (2020, January 23\u201326). Solving the Unrelated Parallel Machine Scheduling Problem with Setups Using Late Acceptance Hill Climbing. Proceedings of the Asian Conference on Intelligent Information and Database Systems, Phuket, Thailand.","DOI":"10.1007\/978-3-030-41964-6_22"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1080\/07408170600559706","article-title":"Scheduling and lot sizing with sequence-dependent setup: A literature review","volume":"38","author":"Zhu","year":"2006","journal-title":"IIE Trans."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00291-015-0429-4","article-title":"Simultaneous lotsizing and scheduling problems: A classification and review of models","volume":"39","author":"Copil","year":"2017","journal-title":"OR Spectr."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01539800","article-title":"The general lotsizing and scheduling problem","volume":"19","author":"Fleischmann","year":"1997","journal-title":"OR Spectr."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/S0377-2217(99)00159-9","article-title":"Simultaneous lotsizing and scheduling by combining local search with dual reoptimization","volume":"120","author":"Meyr","year":"2000","journal-title":"Eur J. Oper. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s00291-004-0181-7","article-title":"A note on The general lot sizing and scheduling problem","volume":"27","year":"2005","journal-title":"OR Spectr."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Haase, K. (1994). Lotsizing and Scheduling for Production Planning, Springer. Lecture Notes in Economics and Mathematical Systems.","DOI":"10.1007\/978-3-642-45735-7"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF01539882","article-title":"Capacitated Lot-Sizing with Sequence Dependent Setup Costs","volume":"18","author":"Haase","year":"1996","journal-title":"OR Spectr."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/S0377-2217(01)00373-3","article-title":"Simultaneous lotsizing and scheduling on parallel machines","volume":"139","author":"Meyr","year":"2002","journal-title":"Eur. J. Oper. Res."},{"key":"ref_18","first-page":"585","article-title":"Simultane Losgr\u00f6\u00dfen- und Reihenfolgeplanung bei mehrstufiger kontinuierlicher Fertigung","volume":"74","author":"Meyr","year":"2004","journal-title":"Z. Betriebswirtschaft"},{"key":"ref_19","first-page":"33","article-title":"Multi-stage simultaneous lot-sizing and scheduling for flow line production","volume":"35","author":"Seeanner","year":"2013","journal-title":"Spectrum"},{"key":"ref_20","unstructured":"Toledo, C., Kimms, A., Fran\u00e7a, P., and Morabito, R. (2006). A Mathematical Model for the Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem, University of Campinas. Working Paper."},{"key":"ref_21","unstructured":"Toledo, C., Fran\u00e7a, P., and Rosa, K. (2008, January 16\u201320). Meta-heuristic approaches for a soft drink industry problem. Proceedings of the ACM Symposium on Applied Computing, Ceara, Brazil."},{"key":"ref_22","unstructured":"Toledo, C., de Jesus Filho, J., and Fran\u00e7a, P. (2008, January 18). Meta-heuristic approaches for a soft drink industry problem. Proceedings of the 2008 IEEE International Conference on Emerging Technologies and Factory Automation, Hamburg, Germany."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3097","DOI":"10.1080\/00207540701675833","article-title":"Multi-population genetic algorithm to solve the synchronized and integrated two-level lot sizing and scheduling problem","volume":"47","author":"Toledo","year":"2009","journal-title":"Int. J. Prod. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1016\/j.ejor.2008.03.035","article-title":"Solution approaches for the soft drink integrated production lot sizing and scheduling problem","volume":"196","author":"Ferreira","year":"2009","journal-title":"Eur. J. Oper. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1016\/j.cor.2009.06.007","article-title":"Relax and fix heuristics to solve one-stage one-machine lot-scheduling models for small-scale soft drink plants","volume":"37","author":"Ferreira","year":"2010","journal-title":"Comput. Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.ijpe.2011.11.028","article-title":"Single-stage formulations for synchronised two-stage lot sizing and scheduling in soft drink production","volume":"136","author":"Ferreira","year":"2012","journal-title":"Int. J. Prod. Econ."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.cor.2014.02.012","article-title":"A genetic algorithm\/mathematical programming approach to solve a two-level soft drink production problem","volume":"48","author":"Toledo","year":"2014","journal-title":"Comput. Oper. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.cie.2014.02.008","article-title":"An optimization approach for the lot sizing and scheduling problem in the brewery industry","volume":"72","author":"Baldo","year":"2014","journal-title":"Comput. Ind. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Ribeiro, C., and Hansen, P. (2002). POPMUSIC Partial Optimization Metaheuristic Under Special Intensification Conditions. Essays and Surveys in Metaheuristics, Kluwer.","DOI":"10.1007\/978-1-4615-1507-4"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1016\/j.ijpe.2005.04.011","article-title":"Simultaneous lot sizing and scheduling for multi-product multi-level production","volume":"104","author":"Fandel","year":"2006","journal-title":"Int. J. Prod. Econ."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/s10845-008-0207-0","article-title":"Rolling-horizon and fix-and-relax heuristics for the multi-product multi-level capacitated lotsizing problem with sequence-dependent setups","volume":"21","author":"Mohammadi","year":"2010","journal-title":"J. Intell. Manuf."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1007\/s00170-010-2594-6","article-title":"Integrating lotsizing, loading, and scheduling decisions in flexible flow shops","volume":"50","author":"Mohammadi","year":"2010","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s00170-009-2366-3","article-title":"A new algorithmic approach for capacitated lot-sizing problem in flow shops with sequence-dependent setups","volume":"49","author":"Mohammadi","year":"2010","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1016\/j.cie.2009.02.011","article-title":"Lot sizing and sequencing optimisation at an animal-feed plant","volume":"57","author":"Toso","year":"2009","journal-title":"Comput. Ind. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Lang, J. (2010). Production and Inventory Management with Substitutions, Springer. Lecture Notes in Economics and Mathematical Systems.","DOI":"10.1007\/978-3-642-04247-8"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"7315","DOI":"10.1080\/00207543.2010.535570","article-title":"Synchronisation of scarce resources for a parallel machine lotsizing problem","volume":"49","author":"Almeder","year":"2011","journal-title":"Int. J. Prod. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2463","DOI":"10.1080\/00207543.2010.532910","article-title":"A hybrid general lot-sizing and scheduling formulation for a production process with a two-stage product structure","volume":"49","author":"Transchel","year":"2011","journal-title":"Int. J. Prod. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.1057\/jors.2011.159","article-title":"Three time-based scale formulations for the two-stage lot sizing and scheduling in process industries","volume":"63","author":"Camargo","year":"2012","journal-title":"J. Oper. Res. Soc."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.ejor.2013.10.017","article-title":"HOPS Hamming-Oriented Partition Search for production planning in the spinning industry","volume":"234","author":"Camargo","year":"2014","journal-title":"Eur. J. Oper. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cie.2012.01.008","article-title":"Integrated pulp and paper mill planning and scheduling","volume":"63","author":"Santos","year":"2012","journal-title":"Comput. Ind. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1804","DOI":"10.1016\/j.cor.2013.01.015","article-title":"A hybrid VNS approach for the short-term production planning and scheduling: A case study in the pulp and paper industry","volume":"40","author":"Figueira","year":"2013","journal-title":"Comput. Oper. Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.cor.2014.12.008","article-title":"Unequal individual genetic algorithm with intelligent diversification for the lot-scheduling problem in integrated mills using multiple-paper machines","volume":"59","author":"Furlan","year":"2015","journal-title":"Comput. Oper. Res."},{"key":"ref_43","unstructured":"Wolter, A., and Helber, S. (2013). Simultaneous Production and Maintenance Planning for a Single Capacitated Resource Facing Both a Dynamic Demand and Intensive Wear and Tear, Leibniz Universit\u00e4t Hannover, Wirtschaftswissenschaftliche Fakult\u00e4t. Hannover Economic Papers (HEP)."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"167","DOI":"10.5267\/j.uscm.2014.4.003","article-title":"A rolling horizon-based heuristic to solve a multi-level general lot sizing and scheduling problem with multiple machines (MLGLSP_MM) in job shop manufacturing system","volume":"2","author":"Mohammadi","year":"2014","journal-title":"Uncertain Supply Chain Manag."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00170-014-6598-5","article-title":"Simultaneous lot-sizing and scheduling in flexible job shop problems","volume":"78","author":"Rohaninejad","year":"2015","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Pahl, J., Vo\u00df, S., and Woodruff, D.L. (2011, January 4\u20137). Discrete Lot-Sizing and Scheduling with Sequence-Dependent Setup Times and Costs Including Deterioration and Perishability Constraints. Proceedings of the Hawaiian International Conference on Systems Sciences (HICSS), Kauai, HI, USA.","DOI":"10.1109\/HICSS.2011.169"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.cor.2017.09.005","article-title":"A computational study of the general lot-sizing and scheduling model under demand uncertainty via robust and stochastic approaches","volume":"90","author":"Alem","year":"2018","journal-title":"Comput. Oper. Res."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1051\/ro\/2019021","article-title":"General lot-sizing and scheduling for perishable food products","volume":"54","author":"Alipour","year":"2020","journal-title":"RAIRO-Oper. Res."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2284","DOI":"10.1080\/00207543.2015.1070970","article-title":"Dynamic lot-sizing with rework of defective items and minimum lot-size constraints","volume":"54","author":"Goerler","year":"2016","journal-title":"Int. J. Prod. Res."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s10951-013-0352-y","article-title":"An adaptive artificial bee colony and late-acceptance hill-climbing algorithm for examination timetabling","volume":"17","author":"Alzaqebah","year":"2014","journal-title":"J. Sched."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Goerler, A., Schulte, F., and Vo\u00df, S. (2013). An Application of Late Acceptance Hill-Climbing to the Traveling Purchaser Problem, Springer. Lecture Notes in Computer Science.","DOI":"10.1007\/978-3-642-41019-2_13"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10845-013-0770-x","article-title":"A late acceptance hill-climbing algorithm for balancing two-sided assembly lines with multiple constraints","volume":"26","author":"Yuan","year":"2015","journal-title":"J. Intell. Manuf."},{"key":"ref_53","unstructured":"Tierney, K. (2013, January 1). Late acceptance hill climbing for the liner shipping fleet repositioning problem. Proceedings of the 14th EU\/ME Workshop, Hamburg, Germany."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.ejor.2016.07.012","article-title":"The late acceptance Hill-Climbing heuristic","volume":"258","author":"Burke","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.ejor.2020.03.027","article-title":"A cutoff time strategy based on the coupon collector\u2019s problem","volume":"286","author":"Lobo","year":"2020","journal-title":"Eur. J. Oper. Res."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"109342","DOI":"10.1016\/j.engstruct.2019.109342","article-title":"Finding the train composition causing the greatest fatigue damage in railway bridges by Late Acceptance Hill Climbing","volume":"196","year":"2019","journal-title":"Eng. Struct."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/6\/138\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:37:11Z","timestamp":1760175431000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/6\/138"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,9]]},"references-count":56,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["a13060138"],"URL":"https:\/\/doi.org\/10.3390\/a13060138","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,9]]}}}