Abstract
This paper considers a single-machine scheduling with linear deterioration rate of processing speed and multiple rate-modifying activities simultaneously. A rate-modifying activity can change the processing rate of machine under consideration, which means after each rate-modifying activity the speed of the machine is fully recovered. The integration of these two concept is motivated by human operators and semi-automatic systems that experience performance degradation over time and require rate-modifying activities for recovery. The objective is to minimize the makespan. We need to decide the sequence of jobs and when to schedule the rate-modifying activities. An optimal schedule is proposed, which can solve the problem in O(nlogn) time where n is the number of jobs.
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References
Eilon, S.: On a mechanistic approach to fatigue and rest periods. Int. J. Prod. Res. 3, 327–332 (1964)
Gentzler, G.L., Khalil, T.M., Sivazlian, B.B.: Quantitative models for optimal rest period scheduling. Omega-Int. J. Manag. Sci. 5, 215–220 (1977)
Bechtold, S.E., Janaro, R.E., Sumners, D.L.: Maximization of labor productivity through multi-rest break scheduling. Manag. Sci. 30, 1442–1458 (1984)
Lee, C.Y., Leon, V.J.: Machine scheduling with a rate-modifying activity. Eur. J. Oper. Res. 128, 119–128 (2001)
Lee, C.Y., Lin, C.S.: Single-machine scheduling with maintenance and repair rate-modifying activities. Eur. J. Oper. Res. 135, 493–513 (2001)
Lodree, E.J., Geiger, C.D.: A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration. Eur. J. Oper. Res. 201, 644–648 (2010)
Lodree, E.J., Geiger, C.D., Jiang, X.: Taxonomy for integration scheduling theory and human factors: Review and research opportunities. Int. J. Ind. Ergonom. 39, 39–51 (2009)
Browne, S., Yechiali, U.: Scheduling deteriorating job on a single processor. Oper. Res. 38, 495–498 (1990)
Mosheiov, G.: ∧-shaped policies of schedule deteriorating jobs. J. Oper. Res. Soc. 47, 1184–1191 (1996)
Alidaee, B., Womer, N.K.: Scheduling with time dependent processing times: Review and extensions. J. Oper. Res. Soc. 50, 711–720 (1999)
Cheng, T.C.E., Ding, Q., Lin, B.M.T.: A concise survey of scheduling with time-dependent processing times. Eur. J. Oper. Res. 152, 1–13 (2004)
Zhao, C.L., Tang, H.Y.: A note to due-window assignment and single machine scheduling with deteriorating jobs and a rate-modifying activity. Comput. Oper. Res. 39, 1300–1303 (2012)
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Yu, S. (2013). An Optimal Single-Machine Scheduling with Linear Deterioration Rate and Rate-Modifying Activities. In: Widmayer, P., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2013. Lecture Notes in Computer Science, vol 8287. Springer, Cham. https://doi.org/10.1007/978-3-319-03780-6_29
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DOI: https://doi.org/10.1007/978-3-319-03780-6_29
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03779-0
Online ISBN: 978-3-319-03780-6
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