Abstract
In the one-machine scheduling problems analysed in this paper, the processing time of a job depends on the time at which the job is started. More precisely, the horizon is divided into time windows and with each one a coefficient is associated that is used to determine the actual processing time of a job starting in it. Two models are introduced, and one of them has direct connections with models considered in previous papers on scheduling problems with time-dependent processing times. Various computational complexity results are presented for the makespan criterion, which show that the problem is NP-hard, even with two time windows. Solving procedures are also proposed for some special cases.
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References
Gawiejnowicz S (1996). A brief survey of continuous models of scheduling. Found Comput Decis Sci 21: 81–100.
Alidaee B and Womer NK (1999). Scheduling with time dependent processing times: review and extensions. J Opl Res Soc 50: 711–720.
Cheng TCE, Ding Q and Lin BMT (2004). A concise survey of scheduling with time-dependent processing times. Eur J Opl Res 152: 1–13.
Tanaev VS, Gordon VS and Shafransky YM (1980). Scheduling Theory Single Stage Systems. Nauka: Moscow (English translation 1994, Kluwer Academic Publisher: Dordrecht).
Gupta JND and Gupta SK (1988). Single facility scheduling with nonlinear processing times. Comput Ind Eng 14: 387–393.
Browne S and Yechiali U (1990). Scheduling deteriorating jobs on a single processor. Opns Res 38: 495–498.
Gawiejnowicz S and Pankowska L (1995). Scheduling jobs with varying processing times. Inform Process Lett 54: 175–178.
Sundararaghavan PS and Kunnathur AS (1994). Single machine scheduling with start time dependent processing times: some solvable cases. Eur J Opl Res 78: 394–403.
Mosheiov G (1995). Scheduling jobs with step-deterioration; minimizing makespan on a single and multi-machine. Comput Ind Eng 28: 869–879.
Kononov AV (1997). On scheduling of a single machine jobs with processing times nonlinear in time. In: Korshunov AD (ed). Operations Research and Discrete Analysis. Kluwer Academic Publisher, New-York, pp 109–122.
Cai J-Y, Cai P and Zhu Y (1998). On a scheduling problem of time deteriorating jobs. J Complexity 14: 190–209.
Kubiak W and Van de Velde S (1998). Scheduling deteriorating jobs to minimize makespan. Naval Res Logist 45: 511–523.
Garey MR and Johnson DS (1979). Computers and Intractability; a Guide to the Theory of NP-Completeness. Freeman: San Francisco.
Martello S and Toth P (1990). Knapsack Problems: Algorithms and Computer Implementations. Wiley: Chichester.
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3This research was conducted while this author was at the Ecole des Mines de Nantes.
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Lahlou, C., Dauzère-Pérès, S. Single-machine scheduling with time window-dependent processing times. J Oper Res Soc 57, 133–139 (2006). https://doi.org/10.1057/palgrave.jors.2601931
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DOI: https://doi.org/10.1057/palgrave.jors.2601931