{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:30:06Z","timestamp":1787027406551,"version":"build-2736575974"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T00:00:00Z","timestamp":1577059200000},"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>We study a resource leveling problem with variable job duration. The considered problem includes both scheduling and resource management decisions. The planning horizon is fixed and separated into a set of time periods of equal length. There are several types of resources and their amount varies from one period to another. There is a set of jobs. For each job, a fixed volume of work has to be completed without any preemption while using different resources. If necessary, extra resources can be used at additional costs during each time period. The optimization goal is to minimize the total overload costs required for the execution of all jobs by the given deadline. The decision variables specify the starting time of each job, the duration of the job and the resource amount assigned to the job during each period (it may vary over periods). We propose a new generalized mathematical formulation for this optimization problem. The formulation is compared with existing approaches from the literature. Theoretical study and computational experiments show that our approach provides more flexible resource allocation resulting in better final solutions.<\/jats:p>","DOI":"10.3390\/a13010006","type":"journal-article","created":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T03:15:01Z","timestamp":1577070901000},"page":"6","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Generalized MILP Formulation for the Period-Aggregated Resource Leveling Problem with Variable Job Duration"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6350-6565","authenticated-orcid":false,"given":"Ilia","family":"Tarasov","sequence":"first","affiliation":[{"name":"ISAE-SUPAERO, University of Toulouse, 10 avenue Edouard Belin-BP 54032, 31055 Toulouse CEDEX 4, France"},{"name":"V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya street, Moscow 117997, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5918-0753","authenticated-orcid":false,"given":"Alain","family":"Ha\u00eft","sequence":"additional","affiliation":[{"name":"ISAE-SUPAERO, University of Toulouse, 10 avenue Edouard Belin-BP 54032, 31055 Toulouse CEDEX 4, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5367-7846","authenticated-orcid":false,"given":"Olga","family":"Batta\u00efa","sequence":"additional","affiliation":[{"name":"Kedge Business School (Talence), 680 cours de la Liberation, 33405 Talence CEDEX, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0166-218X(83)90012-4","article-title":"Scheduling subject to resource constraints: Classification and complexity","volume":"5","author":"Blazewicz","year":"1983","journal-title":"Discret. 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