Soft due window assignment and scheduling of unit-time jobs on parallel machines
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We study problems of scheduling n unit-time jobs on m identical parallel machines, in which a common due window has to be assigned to all jobs. If a job is completed within the due window, then no scheduling cost incurs. Otherwise, a job-dependent earliness or tardiness cost incurs. The job completion times, the due window location and the size are integer valued decision variables. The objective is to find a job schedule as well as the location and the size of the due window such that a weighted sum or maximum of costs associated with job earliness, job tardiness and due window location and size is minimized. We establish properties of optimal solutions of these min-sum and min-max problems and reduce them to min-sum (traditional) or min-max (bottleneck) assignment problems solvable in O(n 5/m 2) and O(n 4.5log0.5 n/m 2) time, respectively. More efficient solution procedures are given for the case in which the due window size cost does not exceed the due window start time cost, the single machine case, the case of proportional earliness and tardiness costs and the case of equal earliness and tardiness costs.
KeywordsScheduling Parallel machines Earliness-tardiness Due window Unit-time jobs
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- Anger F, Lee CY, Martin-Vega L (1986) Single machine scheduling with tight windows. Department of Industrial and System Engineering, University of Florida, Gainsville, Res. Rep 86–16Google Scholar
- Bodin L, Golden B, Assad A, Ball M (1983) Routing and scheduling of vehicles and crews: the state of the art. Comput Oper Res 10: 62–212Google Scholar
- Burkard R, Cela E (1999) Linear assignment problems and extensions. In: Handbook of combinatorial optimization, Supplement vol A, Kluwer, Dordrecht, pp 75–149Google Scholar
- Janiak A, Winczaszek M (2003) An optimal algorithm for a single processor scheduling problem with a common due window. In: Proceedings of 9th IEEE international conference on methods and models in automation and robotics, Miedzyzdroje, Poland, 25–28 August 2003, pp 1213–1216Google Scholar
- Karakostas G, Kolliopoulos S, Wang J (2009) An fptas for the minimum total weightedtardiness problem with a fixed number of distinct due dates. In: Lecture notes in computer science, vol 5609. Springer, Berlin, pp 238–248. doi: 10.1007/978-3-642-02882-3_24
- Lee CY (1991) Earliness-tardiness scheduling problems with constant size of due window. Department of Industrial and System Engineering, University of Florida, Gainsville, Res. Rep. 91–17Google Scholar
- Mosheiov G (2001) A due-window determination in minmax scheduling problems. INFOR 39: 107–123Google Scholar
- Torn A, Zilinskas A (1989) Global optimization. In: (eds) Lecture notes in computer science, vol 350. Springer, HeidelbergGoogle Scholar
- Yen B, Wan G (1999) Single machine bicriteria scheduling: a survey. Int J Ind Eng Theory 10: 222–231Google Scholar