{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T15:52:18Z","timestamp":1772812338139,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T00:00:00Z","timestamp":1611792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>The management of industrial systems is done through different levels, ranging from strategic (designing the system), to tactical (planning the activities and assigning the resources) and operational (scheduling the activities). In this paper, we focus on the latter level by considering a real-world scheduling problem from a plastic injection company, where the production process combines parallel machines and a set of resources. We present a scheduling algorithm that combines a metaheuristic and a list algorithm. Two metaheuristics are tested and compared when used in the proposed scheduling approach: the stochastic descent and the simulated annealing. The method\u2019s performances are analyzed through an experimental study and the obtained results show that its outcomes outperform those of the scheduling policy conducted in a case-study company. Moreover, besides being able to solve large real-world problems in a reasonable amount of time, the proposed approach has a structure that makes it flexible and easily adaptable to several different planning and scheduling problems. Indeed, since it is composed by a reusable generic part, the metaheuristic, it is only required to develop a list algorithm adapted to the objective function and constraints of the new problem to be solved.<\/jats:p>","DOI":"10.3390\/app11031202","type":"journal-article","created":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T05:23:05Z","timestamp":1611811385000},"page":"1202","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Lot-Sizing and Scheduling for the Plastic Injection Molding Industry\u2014A Hybrid Optimization Approach"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6926-6101","authenticated-orcid":false,"given":"Nathalie","family":"Klement","sequence":"first","affiliation":[{"name":"Arts et M\u00e9tiers Institute of Technology, LISPEN, HESAM Universit\u00e9, 59000 Lille, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7178-0129","authenticated-orcid":false,"given":"Mohamed Amine","family":"Abdeljaouad","sequence":"additional","affiliation":[{"name":"CEA Tech Hauts-de-France, 59000 Lille, France"}]},{"given":"Leonardo","family":"Porto","sequence":"additional","affiliation":[{"name":"CEMMPRE, Department of Mechanical Engineering, University of Coimbra, 3030-790 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7693-9570","authenticated-orcid":false,"given":"Crist\u00f3v\u00e3o","family":"Silva","sequence":"additional","affiliation":[{"name":"CEMMPRE, Department of Mechanical Engineering, University of Coimbra, 3030-790 Coimbra, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sokolov, B., Ivanov, D., and Dolgui, A. (2020). A generic decision support tool to planning and assignment problems: Industrial applications and industry 4.0. Scheduling in Industry 4.0 and Cloud Manufacturing, Springer International Publishing.","DOI":"10.1007\/978-3-030-43177-8"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2987","DOI":"10.1016\/j.cor.2004.04.012","article-title":"Scheduling injection molding operations with multiple resource constraints and sequence dependent setup times and costs","volume":"32","author":"Dastidar","year":"2005","journal-title":"Comput. Oper. Res."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Van Wassenhove, L.N., and De Bodt, M.A. (1983). Capacitated lot sizing for injection moulding: A case study. J. Oper. Res. Soc., 34.","DOI":"10.2307\/2581124"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Nagarur, N., Vrat, P., and Duongsuwan, W. (1997). Production planning and scheduling for injection molding of pipe fittings a case study. Int. J. Prod. Econ., 53.","DOI":"10.1016\/S0925-5273(97)00109-6"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1287\/opre.38.6.937","article-title":"Ford whitman harris and the economic order quantitymodel","volume":"38","author":"Erlenkotter","year":"1990","journal-title":"Oper. Res."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Copil, K., W\u00f6rbelauer, M., Meyr, H., and Tempelmeier, H. (2016). Simultaneous lotsizing and scheduling problems: A classification and review of models. OR Spectr., 1\u201364.","DOI":"10.1007\/s00291-015-0429-4"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/j.ejor.2004.12.019","article-title":"The combined cutting stock and lot-sizing problem in industrial processes","volume":"174","author":"Gramani","year":"2006","journal-title":"Eur. J. Oper. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1142\/S0217595909002286","article-title":"Combining process selection and lot sizing models for production scheduling of eletrofused grains","volume":"26","author":"Luche","year":"2009","journal-title":"Asia-Pac. J. Oper. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1016\/j.cor.2010.10.013","article-title":"Combined planning and scheduling in a divergent production system with co-production:A case study in the lumber industry","volume":"38","author":"Gaudreault","year":"2011","journal-title":"Comput. Oper. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1016\/j.cie.2016.05.024","article-title":"Production planning in the molded pulp packaging industry","volume":"98","author":"Martinez","year":"2016","journal-title":"Comput. Ind. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Potts, C.N., and Van Wassenhove, L. (1992). Integrating scheduling with batching and lot-sizing: A review of algorithms and complexity. J. Oper. Res. Soc., 395\u2013406.","DOI":"10.1057\/palgrave.jors.0430502"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0377-2217(97)00030-1","article-title":"Lot sizing and scheduling: Survey and extensions","volume":"99","author":"Drexl","year":"1997","journal-title":"Eur. J. Oper. Res."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Jordan, C. (1996). Discrete lot-sizing and scheduling by batch sequencing. Batching and Scheduling, Springer.","DOI":"10.1007\/978-3-642-48403-2"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/S0377-2217(99)00153-8","article-title":"Scheduling with batching: A review","volume":"120","author":"Potts","year":"2000","journal-title":"Eur. J. Oper. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0360-8352(97)00091-0","article-title":"Parallel machine scheduling with release time and machine eligibility restrictions","volume":"33","author":"Centeno","year":"1997","journal-title":"Comput. Ind. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1080\/00207540310001631584","article-title":"Minimizing makespan on parallel machines with release time and machine eligibility restrictions","volume":"42","author":"Centeno","year":"2004","journal-title":"Int. J. Prod. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1016\/j.ejor.2004.06.038","article-title":"A genetic algorithm for hybrid flowshops with sequence dependent setup times and machine eligibility","volume":"169","author":"Ruiz","year":"2006","journal-title":"Eur. J. Oper. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S0736-5845(02)00077-7","article-title":"Unrelated parallel machine scheduling with setup times and a total weighted tardiness objective","volume":"19","author":"Kim","year":"2003","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s00170-016-8477-8","article-title":"A parallel machine batch scheduling problem in a brewing company","volume":"87","author":"Jobish","year":"2016","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2118","DOI":"10.1080\/00207543.2011.575090","article-title":"A batching, and scheduling algorithm for the diffusion area in semiconductor manufacturing","volume":"50","author":"Yugma","year":"2012","journal-title":"Int. J. Prod. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0167-5060(08)70743-X","article-title":"Complexity of machine scheduling problems","volume":"1","author":"Lenstra","year":"1977","journal-title":"Ann. Discret. Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1016\/j.amc.2006.01.068","article-title":"Minimizing the sum of earliness\/tardiness in identical parallel machines schedule with incompatible job families: An improved MIP approach","volume":"181","author":"Omar","year":"2006","journal-title":"Appl. Math. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Toutouh, J., Nesmachnow, S., and Alba, E. (2012). Fast energy-aware olsr routing invanets by means of a parallel evolutionary algorithm. Clust. Comput., 16.","DOI":"10.1007\/s10586-012-0208-9"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Afsar, H.M., Lcomme, P., Ren, L., Prodhon, C., and Vigo, D. (2016, January 28). Resolution of a job-shop problem with transportation constraints: A master\/slave approach. Proceedings of the 8th IFAC Conference on Manufacturing Modelling, Management and Control MIM, Troyes, France.","DOI":"10.1016\/j.ifacol.2016.07.889"},{"key":"ref_25","first-page":"572","article-title":"An analogy between bin packing problem and permutation problem: A new encoding scheme","volume":"Volume 438","author":"Gourgand","year":"2014","journal-title":"Advances in Production Management Systems. Innovative and Knowledge-Based Production Management in a Global-Local World"},{"key":"ref_26","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_27","doi-asserted-by":"crossref","unstructured":"Klement, N., Gourgand, M., and Grangeon, N. (2017, January 21\u201323). Medical imaging: Exams planning and resource assignment: Hybridization of a metaheuristic and a list algorithm. Proceedings of the 10th International Conference on Health Informatics, Porto, Portugal.","DOI":"10.5220\/0006113002600267"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1063\/1.1699114","article-title":"Equation of state calculations by fast computing machines","volume":"21","author":"Metropolis","year":"1953","journal-title":"J. Chem. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Aarts, E., and van Laarhoven, P. (1987). Simulated Annealing: Theory and Applications, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-015-7744-1"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Silva, C., and Ferreira, L.M. (2004). Microplano\u2014A scheduling support system for the plastic injection industry. E-Manufacturing: Business Paradigms and Supporting Technologies, Springer.","DOI":"10.1007\/978-1-4419-8945-1_9"}],"container-title":["Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-3417\/11\/3\/1202\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:16:32Z","timestamp":1760159792000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-3417\/11\/3\/1202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,28]]},"references-count":30,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["app11031202"],"URL":"https:\/\/doi.org\/10.3390\/app11031202","relation":{},"ISSN":["2076-3417"],"issn-type":[{"value":"2076-3417","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,28]]}}}