Abstract
This paper considers one parallel machine scheduling problem in which the processing time of a job is a simple linear increasing function of its starting time. The objective is to minimize the makespan, and our focus is on the case with an arbitrary number of parallel machines. We prove that LIST rule is \((1+b_{max})^{\frac{m-1}{m}}\)-approximation where m is the number of machines and b max is the maximum deteriorating rate of job. We then propose one heuristic LDR (Largest deteriorating Rate first). The heuristic is proved \((1+b_{min})^{\frac{m-1}{m}}\)-approximation where b min is the minimum deteriorating rate. We further show that this ratio is tight when m = 2,3 and 4.
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References
Pinedo, M.: Scheduling: Theory, Algorithms, and Systems, 2nd edn. Prentice-Hall, Englewood Cliffs (2000)
Cheng, T., Ding, Q., Lin, B.: A concise survey of scheduling with time-dependent processing times. European Journal of Operational Research 152, 1–13 (2004)
Gupta, J., Gupta, S.: Single facility scheduling with nonlinear processing times. Computers and Industrial Engineering 14, 387–393 (1988)
Browne, S., Yechiali, U.: Scheduling deteriorating jobs on a single processor. Operations Research 38, 495–498 (1990)
Mosheiov, G.: V-shaped policies for scheduling deteriorating jobs. Operations Research 39, 979–991 (1991)
Mosheiov, G.: Scheduling jobs under simple linear deterioration. Computers and Operations Research 21, 653–659 (1994)
Cheng, T., Ding, Q.: Single machine scheduling with step-deteriorating processing times. European Journal of Operational Research 134, 623–630 (2001)
Mosheiov, G.: Multi-machine scheduling with linear deterioration. INFOR 36(4), 205–214 (1998)
Chen, Z.L.: Parallel machine scheduling with time dependent processing times. Discrete Applied Mathematics 70, 81–93 (1996)
Chen, Z.L.: Erratum to Parallel machine scheduling with time dependent processing times. Discrete Applied Mathematics 70, 81–93 (1996); Discrete Applied Mathematics 75, 103 (1997)
Ji, M., Cheng, T.C.E.: Parallel-machine scheduling with simple linear deterioration to minimize total completion time. European Journal of Operational Research 188, 342–347 (2008)
Ji, M., Cheng, T.C.E.: Parallel-machine scheduling of simple linear deteriorating jobs. Theoretical Computer Science 410, 38–40 (2009)
Kang, L., Ng, C.T.: A note on a fully polynomial-time approximation scheme for parallel-machine scheduling with deteriorating jobs. International Journal of Production Economics 109, 180–184 (2007)
Alidaee, B., Womer, N.: Scheduling with time dependent processing times: Review and extentions. Journal of the Operational Research Society 50, 711–720 (1999)
Cheng, T., Kang, L., Ng, C.: Due-date assignment and single machine scheduling with deteriorating jobs. Journal of Operational Research Society 55, 198–203 (2004)
Lodree, E., Gerger, C.: A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration. European Journal of Operational Research 201, 644–648 (2010)
Cheng, Y., Sun, S.: Scheduling linear deterorating jobs with rejection on a single machine. European Journal of Operational Research 194, 18–27 (2009)
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© 2011 Springer-Verlag Berlin Heidelberg
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Liu, M., Zheng, F., Xu, Y., Wang, L. (2011). Heuristics for Parallel Machine Scheduling with Deterioration Effect. In: Wang, W., Zhu, X., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2011. Lecture Notes in Computer Science, vol 6831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22616-8_4
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DOI: https://doi.org/10.1007/978-3-642-22616-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22615-1
Online ISBN: 978-3-642-22616-8
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