Scheduling with State-Dependent Machine Speed
Conference paper
First Online:
- 390 Downloads
Abstract
We study a preemptive single machine scheduling problem where the machine speed is externally given and depends on the number unfinished jobs. The objective is to minimize the sum of weighted completion times. We develop a greedy algorithm that solves the problem to optimality when we work with either unit weights or unit processing times. If both weights and processing times are arbitrary, we show the problem is NP-hard by making a reduction from 3-partition.
Keywords
Speed Machining Unit Processing Requirement Total Weighted Completion Time Gawiejnowicz Job Completion
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Notes
Acknowledgements
We thank Urtzi Ayesta for helpful discussion after posing this open question during the Daghstuhl Seminar 13111 “Scheduling” in 2013. Furthermore, we thank the organizers of this seminar and Schloss Daghstuhl for providing the right atmosphere to facilitate research.
References
- 1.Albers, S.: Review articles: energy-efficient algorithms. Commun. ACM 53(5), 86–96 (2010)MathSciNetCrossRefGoogle Scholar
- 2.Alidaee, B., Ahmadian, A.: Scheduling on a single processor with variable speed. Inf. Process. Lett. 60, 189–193 (1996)MathSciNetCrossRefGoogle Scholar
- 3.Ayesta, U.: Scheduling (dagstuhl seminar 13111): scheduling with time-varying capacities. Dagstuhl Rep. 3(3), 29 (2013)Google Scholar
- 4.Bekker, R., Boxma, O.J.: An M/G/1 queue with adaptable service speed. Stochastic Models 23(3), 373–396 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
- 5.Bertrand, J.W.M., Ooijen, H.P.G.: Workload based order release and productivity : a missing link. Prod. Plan. Control : The Manage. Oper. 13(7), 665–678 (2002)CrossRefGoogle Scholar
- 6.Ewalid, A., Mintra, D.: Analysis and design of rate-based congestion control of high-speed networks, i: stochastic fluid models, access regulation. Queueing Syst. 9, 29–64 (1991)CrossRefGoogle Scholar
- 7.Ewalid, A., Mintra, D.: Statistical multiplexing with loss priorities in rate-based congestion control of high-speed networks. IEEE Trans. Commun. 42, 2989–3002 (1994)CrossRefGoogle Scholar
- 8.Demers, A.J., Yao, F.F., Shenker, S.: A scheduling model for reduced CPU energy. In: FOCS, pp. 374–382 (1995)Google Scholar
- 9.Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Co., New York (1979)zbMATHGoogle Scholar
- 10.Gawiejnowicz, S.: A note on scheduling on a single processor with speed dependent on a number of executed jobs. Inf. Process. Lett. 57, 297–300 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
- 11.Mandjes, M., Mintra, D.: A simple model of network access: feedback adaptation of rates and admission control. In: Proceedings of Infocom, pp. 3–12 (2002)Google Scholar
- 12.Megow, N., Verschae, J.: Dual techniques for scheduling on a machine with varying speed. In: Fomin, F.V., Freivalds, R.U., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part I. LNCS, vol. 7965, pp. 745–756. Springer, Heidelberg (2013)CrossRefGoogle Scholar
- 13.Boxma, O.J., Bekker, R., Borst, S.C., Kelly, O.: Queues with workload-dependent arrival and service rates. Queueing Syst. 46(3–4), 537–556 (2004)MathSciNetzbMATHGoogle Scholar
- 14.Ramanan, K.A., Weiss, A.: Sharing bandwidth in ATM. In: Proceedings of the Allerton Conference, pp. 732–740 (1997)Google Scholar
- 15.Smith, W.E.: Various optimizers for single-stage production. Naval Res. Logist. Q. 3, 59–66 (1956)CrossRefGoogle Scholar
Copyright information
© Springer International Publishing Switzerland 2015