Abstract
In this paper we study the scheduling problem of minimizing makespan on identical parallel machines with time-dependent processing times. We first consider the problem with time-dependent processing times on two identical machines to minimize makespan, which is NP-hard. We give a fully polynomial-time approximation scheme for the problem. Furthermore, we generalize the result to the case with m machines.
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References
Behzad, M., Chartrand, G., Wall, C.: On minimal regular digraphs with given girth. Fund. Math. 69, 227–231 (1970)
Bachman, A., Janiak, A.: Minimizing maximum lateness under linear deterioration. European Journal of Operational Research 126, 557–566 (2000)
Bachman, A., Janiak, A., Kovalyov, M.Y.: Minimizing the total weighted completion time of deteriorating jobs. Information Processing Letters 81, 81–84 (2002)
Browne, S., Yechiali, U.: Scheduling deteriorating jobs on a single processor. Operations Research 38, 495–498 (1990)
Cheng, T.C.E., Kang, L., Ng, C.T.: Due-date assignment and single machine scheduling with deteriorating jobs. Journal of Operational Research Society 55, 198–203 (2004)
Cheng, T.C.E., Ding, Q., Kovalyov, M.Y., Bachman, A., Janiak, A.: Scheduling jobs with piecewise linear decreasing processing times. Naval Research Logistics 50, 531–554 (2003)
Cheng, T.C.E., Ding, Q., Lin, B.M.T.: A concise survey of scheduling with time-dependent processing times. European Journal of Operational Research 152, 1–13 (2004)
Cheng, T.C.E., Ding, Q.: Single machine scheduling with deadlines and increasing rates of processing times. Acta Informatica 36, 673–692 (2000)
Chen, Z.L.: Parallel machine scheduling with time-dependent processing times. Discrete Applied Mathematics 70, 81–93 (1996)
Chen, Z.L.: A note on single-processor scheduling with time dependent execution time. Operational Research Letter 17, 127–129 (1995)
Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Discrete Math. 5, 287–326 (1979)
Gupta, J.N.D., Gupta, S.K.: Single facility scheduling with nonlinear processing times. Computers and Industrial Engineering 14, 387–394 (1988)
Gupta, S.K., Kunnathur, A.S., Dandapani, K.: Optimal repayment polices for multiple loans. OMEGA 15, 323–330 (1987)
Ho, K.I.J., Leung, J.Y.T., Wei, W.D.: Complexity of scheduling tasks with time dependent execution time. Information Processing Letter 48, 315–320 (1993)
Kovalyov, M.Y., Kubiak, W.: A fully polynomial approximation scheme for minimizing makespan of deteriorating jobs. Journal of Heuristics 3, 287–297 (1998)
Mosheiov, G.: Multi-machines scheduling with linear deterioration. INFOR 36, 205–214 (1998)
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© 2005 Springer-Verlag Berlin Heidelberg
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Kang, L.Y., Cheng, T.C.E., Ng, C.T., Zhao, M. (2005). Scheduling to Minimize Makespan with Time-Dependent Processing Times. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_92
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DOI: https://doi.org/10.1007/11602613_92
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30935-2
Online ISBN: 978-3-540-32426-3
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