{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T09:53:52Z","timestamp":1762077232997,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T00:00:00Z","timestamp":1668643200000},"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>In this paper, an unrelated parallel machine scheduling problem with job (product) and machine acceptance and renewable resource constraints was considered. The main idea of this research was to establish a production facility without (or with minimum) investment in machinery, equipment, and location. This problem can be applied to many real problems. The objective was to maximize the net profit; that is, the total revenue minus the total cost, including fixed costs of jobs, job transportation costs, renting costs of machines, renting cost of resources, and transportation costs of resources. A mixed-integer linear programming (MILP) model and several heuristics (greedy, GRASP, and simulated annealing) are presented to solve the problem.<\/jats:p>","DOI":"10.3390\/a15110433","type":"journal-article","created":{"date-parts":[[2022,11,18]],"date-time":"2022-11-18T04:08:40Z","timestamp":1668744520000},"page":"433","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Unrelated Parallel Machine Scheduling with Job and Machine Acceptance and Renewable Resource Allocation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0715-2168","authenticated-orcid":false,"given":"Alexandru-Liviu","family":"Olteanu","sequence":"first","affiliation":[{"name":"Lab-STICC, UMR 6285, CNRS, Universit\u00e9 Bretagne Sud, F-56100 Lorient, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3855-9072","authenticated-orcid":false,"given":"Marc","family":"Sevaux","sequence":"additional","affiliation":[{"name":"Lab-STICC, UMR 6285, CNRS, Universit\u00e9 Bretagne Sud, F-56100 Lorient, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1019-7081","authenticated-orcid":false,"given":"Mohsen","family":"Ziaee","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Bojnord, Bojnord, Iran"},{"name":"Lab-STICC, UMR 6285, CNRS, Universit\u00e9 Bretagne Sud, F-56100 Lorient, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,17]]},"reference":[{"key":"ref_1","first-page":"100022","article-title":"Models and an exact method for the unrelated parallel machine scheduling problem with setups and resources","volume":"5","year":"2020","journal-title":"Expert Syst. Appl. X"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2732","DOI":"10.1016\/j.tcs.2009.04.006","article-title":"A ptas for parallel batch scheduling with rejection and dynamic job arrivals","volume":"410","author":"Cao","year":"2009","journal-title":"Theor. Comput. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.ipl.2017.12.004","article-title":"Minimizing total load on a proportionate flowshop with position-dependent processing times and job-rejection","volume":"132","author":"Fiszman","year":"2018","journal-title":"Inf. Process. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1016\/j.ipl.2012.06.009","article-title":"Scheduling on parallel identical machines with job-rejection and position-dependent processing times","volume":"112","author":"Gerstl","year":"2012","journal-title":"Inf. Process. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.tcs.2015.12.020","article-title":"Scheduling with job rejection and nonsimultaneous machine available time on unrelated parallel machines","volume":"616","author":"Jiang","year":"2016","journal-title":"Theor. Comput. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3642","DOI":"10.1016\/j.tcs.2010.06.008","article-title":"Parallel-machine scheduling with deteriorating jobs and rejection","volume":"411","author":"Li","year":"2010","journal-title":"Theor. Comput. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1016\/j.ejor.2019.10.014","article-title":"Branch-relax-and-check: A tractable decomposition method for order acceptance and identical parallel machine scheduling","volume":"286","author":"Naderi","year":"2019","journal-title":"Eur. J. Oper. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s10951-014-0386-9","article-title":"Multipurpose machine scheduling with rejection and identical job processing times","volume":"18","author":"Shabtay","year":"2015","journal-title":"J. Sched."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1016\/j.cor.2011.10.012","article-title":"Scheduling unrelated parallel machines with optional machines and jobs selection","volume":"39","author":"Ruiz","year":"2012","journal-title":"Comput. Oper. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1016\/j.ejor.2006.11.050","article-title":"Minimizing the number of machines for minimum length schedules","volume":"199","author":"Finke","year":"2009","journal-title":"Eur. J. Oper. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.ijpe.2013.06.018","article-title":"A two-stage flow shop batch-scheduling problem with the option of using not-all-machines","volume":"146","author":"Gerstl","year":"2013","journal-title":"Int. J. Prod. Econ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s10951-013-0343-z","article-title":"The optimal number of used machines in a two-stage flexible flowshop scheduling problem","volume":"17","author":"Gerstl","year":"2014","journal-title":"J. Sched."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"119300","DOI":"10.1016\/j.jclepro.2019.119300","article-title":"Green manufacturing: Order acceptance and scheduling subject to the budgets of energy consumption and machine launch","volume":"248","author":"Kong","year":"2020","journal-title":"J. Clean. Prod."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1016\/j.ejor.2008.10.008","article-title":"Minimizing the number of machines for scheduling jobs with equal processing times","volume":"199","author":"Kravchenko","year":"2009","journal-title":"Eur. J. Oper. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.cor.2015.05.010","article-title":"Hybrid flow shop scheduling with not-all-machines options via local search with controlled deterioration","volume":"65","author":"Lei","year":"2016","journal-title":"Comput. Oper. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1007\/s10878-019-00429-7","article-title":"Parallel-machine scheduling with job-dependent cumulative deterioration effect and rejection","volume":"38","author":"Li","year":"2019","journal-title":"J. Comb. Optim."},{"key":"ref_17","first-page":"1099","article-title":"Flowshop scheduling with learning effect and job rejection","volume":"23","author":"Mor","year":"2019","journal-title":"J. Sched."},{"key":"ref_18","unstructured":"Yildirim, M.B., Barut, M., and Cakar, T. (2004, January 16\u201319). A neuro-genetic algorithm for parallel machine scheduling to determine the number of machines and priority scheduling rules. Proceedings of the International Conference on Productivity and Quality Research, 10th Commemorative International, Miami, FL, USA."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.orl.2009.01.008","article-title":"Scheduling with a minimum number of machines","volume":"37","author":"Yu","year":"2009","journal-title":"Oper. Res. Lett."},{"key":"ref_20","first-page":"1853","article-title":"Flexible flow shop scheduling problem to minimize makespan with renewable resources","volume":"28","author":"Abbaszadeh","year":"2019","journal-title":"Sci. Iran."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"171533","DOI":"10.1109\/ACCESS.2019.2955975","article-title":"Optimize unrelated parallel machines scheduling problems with multiple limited additional resources, sequence-dependent setup times and release date constraints","volume":"7","author":"Alharkan","year":"2019","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.cor.2014.06.002","article-title":"Optimal interval scheduling with a resource constraint","volume":"51","author":"Angelelli","year":"2014","journal-title":"Comput. Oper. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3650","DOI":"10.1016\/j.tcs.2011.03.025","article-title":"On the complexity of interval scheduling with a resource constraint","volume":"412","author":"Angelelli","year":"2011","journal-title":"Theor. Comput. Sci."},{"key":"ref_24","unstructured":"Leung, J.Y.-T. (2004). Scheduling with discrete resource constraints. Handbook of Scheduling-Algorithms, Models, and Performance Analysis, Chapman and Hall\/CRC."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1016\/j.ejor.2018.05.056","article-title":"Algorithms for the unrelated parallel machine scheduling problem with a resource constraint","volume":"271","author":"Fleszar","year":"2018","journal-title":"Eur. J. Oper. Res."},{"key":"ref_26","unstructured":"Leung, J.Y.-T. (2004). Scheduling with resource constraints-continuous resources. Handbook of Scheduling-Algorithms, Models, and Performance Analysis, Chapman and Hall\/CRC."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/S0166-218X(97)00138-8","article-title":"Uniform machine scheduling of unit-time jobs subject to resource constraints","volume":"84","author":"Kovalyov","year":"1998","journal-title":"Discret. Appl. Math."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s10601-011-9115-6","article-title":"Optimal methods for resource allocation and scheduling: A cross-disciplinary survey","volume":"17","author":"Lombardi","year":"2012","journal-title":"Constraints"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1002\/1099-1425(200101\/02)4:1<3::AID-JOS57>3.0.CO;2-D","article-title":"Machine scheduling with transportation considerations","volume":"4","author":"Lee","year":"2001","journal-title":"J. Sched."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1016\/j.ijpe.2008.07.007","article-title":"Analysis and algorithms for coordinated scheduling of parallel machine manufacturing and 3pl transportation","volume":"115","author":"Li","year":"2008","journal-title":"Int. J. Prod. Econ."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s10732-019-09420-1","article-title":"A coordinated production and transportation scheduling problem with minimum sum of order delivery times","volume":"26","author":"Liu","year":"2020","journal-title":"J. Heuristics"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1287\/opre.1080.0688","article-title":"Integrated production and outbound distribution scheduling: Review and extensions","volume":"58","author":"Chen","year":"2010","journal-title":"Oper. Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.cor.2014.01.011","article-title":"The production routing problem: A review of formulations and solution algorithms","volume":"55","author":"Adulyasak","year":"2015","journal-title":"Comput. Oper. Res."},{"key":"ref_34","unstructured":"Garey, M.R., and Johnson, D.S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman & Co."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by simulated annealing","volume":"220","author":"Kirkpatrick","year":"1983","journal-title":"Science"},{"key":"ref_36","unstructured":"Boyan, J.A. (1998). Learning Evaluation Functions for Global Optimization. [Ph.D. Thesis, Carnegie Mellon University]."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1137\/141000671","article-title":"Julia: A fresh approach to numerical computing","volume":"59","author":"Bezanson","year":"2017","journal-title":"SIAM Rev."},{"key":"ref_38","unstructured":"Gurobi Optimization, LLC (2022, September 08). Gurobi Optimizer Reference Manual. Available online: https:\/\/www.gurobi.com."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/11\/433\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:20:15Z","timestamp":1760145615000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/11\/433"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,17]]},"references-count":38,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["a15110433"],"URL":"https:\/\/doi.org\/10.3390\/a15110433","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2022,11,17]]}}}