{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T22:17:20Z","timestamp":1772057840814,"version":"3.50.1"},"reference-count":33,"publisher":"Emerald","issue":"1","license":[{"start":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T00:00:00Z","timestamp":1592524800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["GS"],"published-print":{"date-parts":[[2020,6,19]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title><jats:p>This paper presents a mixed-integer programming model for a single machine earliness\/tardiness scheduling problem where the objective is to minimize total earliness\/tardiness duration when the uncertainty of parameters such as processing times and due date is coded with grey numbers.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title><jats:p>Grey theory and grey numbers are used for illustrating the uncertainty of parameters in processing times and common due date, where the objective is to minimize the total earliness\/tardiness duration. The paper proposes a 0\u20131 mathematical model for the problem and an effective heuristic method for the problem by using expected processing times for ordering jobs.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title><jats:p>The uncertainty of the processing times and common due date are encoded with grey numbers and a position-dependent mixed-integer mathematical programming model is proposed for the problem in order to minimize total grey earliness\/tardiness duration of jobs having grey processing times and a common due date. By using expected processing times for ranking grey processing times, <jats:italic>V<\/jats:italic>-shaped property of the problem and an efficient heuristic method for the problem are proposed. Solutions obtained from the heuristic method show that the heuristic is effective. The experimental study also reveals that while differences between upper and lower bounds of grey processing times decrease, the proposed heuristic's performance decreases.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title><jats:p>The grey theory and grey numbers have been rarely used as machine scheduling problems. Therefore, this study provides an important contribution to the literature.<\/jats:p><\/jats:sec>","DOI":"10.1108\/gs-01-2020-0010","type":"journal-article","created":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T10:18:41Z","timestamp":1592561921000},"page":"95-109","source":"Crossref","is-referenced-by-count":10,"title":["Single machine earliness\/tardiness scheduling problem with grey processing times and the grey common due date"],"prefix":"10.1108","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7088-2104","authenticated-orcid":false,"given":"O\u011fuzhan Ahmet","family":"Ar\u0131k","sequence":"first","affiliation":[]}],"member":"140","reference":[{"issue":"4","key":"key2021021515241764900_ref001","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1080\/21681015.2018.1437792","article-title":"A hybrid integer grey programming for an integrated problem of project selection and scheduling with interval data","volume":"35","year":"2018","journal-title":"Journal of Industrial and Production Engineering"},{"issue":"4","key":"key2021021515241764900_ref002","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1108\/GS-05-2019-0011","article-title":"Simple assembly line balancing problem of Type 1 with grey demand and grey task durations","volume":"9","year":"2019","journal-title":"Grey Systems: Theory and Application"},{"issue":"6","key":"key2021021515241764900_ref003","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/0305-0548(89)90043-9","article-title":"V-shape property of optimal sequence of jobs about a common due date on a single machine","volume":"16","year":"1989","journal-title":"Computers and Operations Research"},{"key":"key2021021515241764900_ref004","first-page":"7272","article-title":"Earliness\/tardiness scheduling problem under uncertainty based on grey chance constrained programming","year":"2006"},{"issue":"6","key":"key2021021515241764900_ref005","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1002\/(SICI)1520-6750(199709)44:6<531::AID-NAV2>3.0.CO;2-4","article-title":"Scheduling stochastic jobs with asymmetric earliness and tardiness penalties","volume":"44","year":"1997","journal-title":"Naval Research Logistics"},{"key":"key2021021515241764900_ref006","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.techfore.2018.04.031","article-title":"Sustainable resource allocation for power generation: the role of big data in enabling interindustry architectural innovation","volume":"144","year":"2019","journal-title":"Technological Forecasting and Social Change"},{"issue":"10","key":"key2021021515241764900_ref007","doi-asserted-by":"crossref","first-page":"2329","DOI":"10.1016\/0043-1354(96)00124-8","article-title":"A grey fuzzy multiobjective programming approach for the optimal planning of a reservoir watershed. Part A: theoretical development","volume":"30","year":"1996","journal-title":"Water Research"},{"issue":"5","key":"key2021021515241764900_ref008","doi-asserted-by":"crossref","first-page":"864","DOI":"10.1007\/s11425-007-0193-2","article-title":"Scheduling jobs on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties","volume":"51","year":"2008","journal-title":"Science in China, Series A: Mathematics"},{"issue":"2","key":"key2021021515241764900_ref009","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1016\/j.cie.2007.12.020","article-title":"The use of the Taguchi method with grey relational analysis to optimize the thin-film sputtering process with multiple quality characteristic in color filter manufacturing","volume":"56","year":"2009","journal-title":"Computers and Industrial Engineering"},{"issue":"2","key":"key2021021515241764900_ref010","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1080\/03052159608941111","article-title":"IPWM: an interval parameter water quality management model","volume":"26","year":"1996","journal-title":"Engineering Optimization"},{"issue":"4","key":"key2021021515241764900_ref011","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1080\/02630259208970657","article-title":"A grey linear programming approach for municipal solid waste management planning under uncertainty","volume":"9","year":"1992","journal-title":"Civil Engineering Systems"},{"issue":"1","key":"key2021021515241764900_ref012","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1080\/02630259408970136","article-title":"Grey fuzzy dynamic programming: application to municipal solid waste management planning problems","volume":"11","year":"1994","journal-title":"Civil Engineering Systems"},{"issue":"3","key":"key2021021515241764900_ref013","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1016\/0377-2217(94)00093-R","article-title":"Grey integer programming: an application to waste management planning under uncertainty","volume":"83","year":"1995","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"key2021021515241764900_ref014","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0038-0121(95)98604-T","article-title":"Grey fuzzy integer programming: an application to regional waste management planning under uncertainty","volume":"29","year":"1995","journal-title":"Socio-Economic Planning Sciences"},{"issue":"2","key":"key2021021515241764900_ref015","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/0377-2217(90)90375-L","article-title":"Multiobjective programming in optimization of the interval objective function","volume":"48","year":"1990","journal-title":"European Journal of Operational Research"},{"issue":"5","key":"key2021021515241764900_ref016","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/S0167-6911(82)80025-X","article-title":"Control problems of grey systems","volume":"1","year":"1982","journal-title":"Systems and Control Letters"},{"issue":"7","key":"key2021021515241764900_ref017","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1016\/j.advwatres.2006.04.003","article-title":"Grey fuzzy optimization model for water quality management of a river system","volume":"29","year":"2006","journal-title":"Advances in Water Resources"},{"issue":"2","key":"key2021021515241764900_ref018","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1108\/K-04-2014-0073","article-title":"N-person grey game","volume":"44","year":"2015","journal-title":"Kybernetes"},{"issue":"6","key":"key2021021515241764900_ref019","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/0305-0548(92)90007-R","article-title":"V-shape property for optimal schedules with monotone penalty functions","volume":"19","year":"1992","journal-title":"Computers and Operations Research"},{"issue":"1","key":"key2021021515241764900_ref020","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.cie.2006.10.010","article-title":"Job scheduling to minimize the weighted waiting time variance of jobs","volume":"52","year":"2007","journal-title":"Computers and Industrial Engineering"},{"key":"key2021021515241764900_ref021","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-642-16158-2_1","article-title":"Introduction to grey systems theory","volume":"68","year":"2010","journal-title":"Understanding Complex Systems"},{"issue":"1-2","key":"key2021021515241764900_ref022","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s10479-017-2566-4","article-title":"Integrated grey relational analysis and multi objective grey linear programming for sustainable electricity generation planning","volume":"269","year":"2018","journal-title":"Annals of Operations Research"},{"issue":"4","key":"key2021021515241764900_ref023","first-page":"566","article-title":"A single machine capacitated production planning problem under uncertainty: a grey linear programming approach","volume":"29","year":"2016","journal-title":"International Journal of Engineering, Transactions A: Basics"},{"issue":"3","key":"key2021021515241764900_ref024","doi-asserted-by":"crossref","first-page":"284","DOI":"10.7305\/automatika.53-3.80","article-title":"Application of grey system theory to software projects ranking","volume":"53","year":"2012","journal-title":"Automatika"},{"issue":"17","key":"key2021021515241764900_ref025","first-page":"2320","article-title":"Rescheduling algorithm based on uncertain processing time of operations for a flexible job-shop","volume":"25","year":"2014","journal-title":"Zhongguo Jixie Gongcheng\/China Mechanical Engineering"},{"issue":"4","key":"key2021021515241764900_ref026","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1080\/07362990008809689","article-title":"Single-machine scheduling with random machine breakdowns and randomly compressible processing times","volume":"18","year":"2000","journal-title":"Stochastic Analysis and Applications"},{"issue":"3","key":"key2021021515241764900_ref027","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/0377-2217(86)90306-1","article-title":"A V-shape property of optimal schedule of jobs about a common due date","volume":"23","year":"1986","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"key2021021515241764900_ref028","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/0377-2217(92)90120-X","article-title":"Single machine scheduling with coefficient of variation minimization","volume":"62","year":"1992","journal-title":"European Journal of Operational Research"},{"issue":"4","key":"key2021021515241764900_ref029","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1002\/ird.2362","article-title":"Optimization OF the cropping pattern OF main cereals and improving water productivity: application OF the water footprint concept","volume":"68","year":"2019","journal-title":"Irrigation and Drainage"},{"issue":"2","key":"key2021021515241764900_ref030","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/0377-2217(91)90249-U","article-title":"Sequencing jobs on a single machine with a common due date and stochastic processing times","volume":"51","year":"1991","journal-title":"European Journal of Operational Research"},{"key":"key2021021515241764900_ref031","unstructured":"Sotskov, Y.N. and Werner, F. (Eds.) (2014), Sequencing and Scheduling with Inaccurate Data, Nova Science Publishers, New York."},{"issue":"1-2","key":"key2021021515241764900_ref032","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/BF02832346","article-title":"Stochastic single machine scheduling subject to machines breakdowns with quadratic early-tardy penalties for the preemptive-repeat model","volume":"25","year":"2007","journal-title":"Journal of Applied Mathematics and Computing"},{"issue":"3","key":"key2021021515241764900_ref033","first-page":"383","article-title":"Application of gray prediction and linear programming model in economic management","volume":"32","year":"2017","journal-title":"Revista de La Facultad de Ingenieria"}],"container-title":["Grey Systems: Theory and Application"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-01-2020-0010\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-01-2020-0010\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T00:45:28Z","timestamp":1753404328000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/gs\/article\/11\/1\/95-109\/198291"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,19]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,6,19]]}},"alternative-id":["10.1108\/GS-01-2020-0010"],"URL":"https:\/\/doi.org\/10.1108\/gs-01-2020-0010","relation":{},"ISSN":["2043-9377"],"issn-type":[{"value":"2043-9377","type":"print"}],"subject":[],"published":{"date-parts":[[2020,6,19]]}}}