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Scheduling unit length jobs on parallel machines with lookahead information

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Abstract

This paper studies two closely related online-list scheduling problems of a set of n jobs with unit processing times on a set of m multipurpose machines. It is assumed that there are k different job types, where each job type can be processed on a unique subset of machines. In the classical definition of online-list scheduling, the scheduler has all the information about the next job to be scheduled in the list while there is uncertainty about all the other jobs in the list not yet scheduled. We extend this classical definition to include lookahead abilities, i.e., at each decision point, in addition to the information about the next job in the list, the scheduler has all the information about the next h jobs beyond the current one in the list. We show that for the problem of minimizing the makespan there exists an optimal (1-competitive) algorithm for the online problem when there are two job types. That is, the online algorithm gives the same minimal makespan as the optimal offline algorithm for any instance of the problem. Furthermore, we show that for more than two job types no such online algorithm exists. We also develop several dynamic programming algorithms to solve a stochastic version of the problem, where the probability distribution of the job types is known and the objective is to minimize the expected makespan.

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References

  • Albers, S. (1997). On the influence of lookahead in competitive paging algorithms. Algorithmica, 18, 283–305.

    Article  Google Scholar 

  • Albers, S. (2003). Online algorithms: a survey. Mathematical Programming, 97, 3–26.

    Google Scholar 

  • Azar, Y., Naor, J., & Rom, R. (1995). The competitiveness of on-line assignments. Journal of Algorithms, 18(2), 221–237.

    Article  Google Scholar 

  • Bar-Noy, A., Freund, A., & Naor, J. (2001). On-line load balancing in a hierarchical server topology. SIAM Journal on Computing, 31(2), 527–549.

    Article  Google Scholar 

  • Bartal, Y., Fiat, A., Karloff, H. J., & Vohra, R. (1995). New algorithms for an ancient scheduling problem. Journal of Computer and System Sciences, 51, 359–366.

    Article  Google Scholar 

  • Beaty, S. J. (1992). Lookahead scheduling. In Proceedings of the 25th annual international symposium on microarchilecture (Micro-25) (pp. 256–259).

  • Chen, B., Van Vliet, A., & Woeginger, G. J. (1994). New upper and lower bounds for online scheduling. Operations Research Letters, 16, 221–230.

    Article  Google Scholar 

  • Brucker, P. (2001). Scheduling algorithms. New York: Springer.

    Google Scholar 

  • Coleman, B., & Mao, W. (2002). Lookahead scheduling in a real-time context. In Proceedings of the 6th international joint conference on information science (pp. 205–209).

  • Coleman, B., & Mao, W. (2003). Lookahead scheduling of unrelated machines. In Proceedings of the 7th international joint conference on computer science and informatics (pp. 397–400).

  • Coleman, B. (2006). Quality vs performance lookahead scheduling. In Proceedings of the 9th international joint conference on information science (pp. 324–327).

  • Galambos, G., & Woeginger, G. (1993). An online scheduling heuristic with better worst case ratio than Graham’s list scheduling. SIAM Journal on Computing, 22, 349–355.

    Article  Google Scholar 

  • Glass, A., & Kellerer, H. (2007). Parallel machine scheduling with job assignment restrictions. Naval Research Logistics, 54, 250–257.

    Article  Google Scholar 

  • Glass, C. A., & Mills, H. R. (2006). Scheduling unit length jobs with parallel nested machine processing set restriction. Computers and Operations Research, 33, 620–638.

    Article  Google Scholar 

  • Graham, R. L. (1966). Bounds for certain multiprocessor anomalies. Bell System Technical Journal, 45, 1563–1581.

    Google Scholar 

  • Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics, 3, 287–326.

    Article  Google Scholar 

  • Grove, E. F. (1995). Online bin packing with lookahead. In Proceedings of the sixth annual ACM-SIAM symposium on discrete algorithms (pp. 430–436).

  • Harvey, N. J. A., Ladner, R. E., Lovasz, L., & Tamir, T. (2006). Semi-matchings for bipartite graphs and load balancing. Journal of Algorithms, 59(1), 53–78.

    Article  Google Scholar 

  • Huo, Y., & Leung, J. Y.-T. (2010). Parallel machine scheduling with nested processing set restrictions. European Journal of Operational Research, 204, 229–236.

    Article  Google Scholar 

  • Hwang, H. C., Chang, S. Y., & Lee, K. (2004). Parallel machine scheduling under a grade of service provision. Computers and Operations Research, 31, 2055–2061.

    Article  Google Scholar 

  • Hwang, H. C., Chang, S. Y., & Hong, Y. (2004). A posterior competitiveness for list scheduling algorithm on machines with eligibility constraints. Asia-Pacific Journal of Operational Research, 21(1), 117–125.

    Article  Google Scholar 

  • Jiang, Y. W., He, Y., & Tang, C. M. (2006). Optimal online algorithms for scheduling on two identical machines under a grade of service. Journal of Zhejiang University Science A, 7(3), 309–314.

    Article  Google Scholar 

  • Kafura, D. G., & Shen, V. Y. (1977). Task scheduling on a multiprocessor system with independent memories. SIAM Journal on Computing, 6, 167–187.

    Article  Google Scholar 

  • Karger, D. R., Phillips, S. J., & Torng, E. (1996). A better algorithm for an ancient scheduling problem. Journal of Algorithms, 20, 400–430.

    Article  Google Scholar 

  • Lee, K., Leung, J. Y.-T., & Pinedo, M. L. (2010, accepted for publication). Scheduling jobs with equal processing times subject to machine eligibility constraints, Journal of Scheduling.

  • Lenstra, J. K., Shmoys, D. B., & Tardos, E. (1990). Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46, 259–271.

    Article  Google Scholar 

  • Leung, J. Y. T., & Li, C. L. (2008). Scheduling with processing time restriction: a survey. International Journal of Production Economics, 116(2), 251–262.

    Google Scholar 

  • Lin, Y., & Li, W. (2004). Parallel machine scheduling of machine-dependent jobs with unit-length. European Journal of Operational Research, 156, 261–266.

    Article  Google Scholar 

  • Meng, J. Y., Soh, Y. C., & Wang, Y. Y. (1995). Lookahead control policies and decision rules for dynamic scheduling of an FMS. In Proceedings of the IEEE international conference on systems and man and cybernetics (Vol. 5, pp. 4125–4130).

  • Ou, J., Leung, J. Y. T., & Li, C. L. (2008). Scheduling parallel machines with inclusive processing set restrictions. Naval Research Logistics, 55(4), 328–338.

    Article  Google Scholar 

  • Park, J., Chang, S. Y., & Lee, K. (2006). Online and semi-online scheduling of two machines under a grade of service provision. Operations Research Letters, 34(6), 692–696.

    Article  Google Scholar 

  • Pinedo, M. (1995). Scheduling: theory, algorithms and systems. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Pinedo, M. (2004). Offline deterministic scheduling, stochastic scheduling, and online deterministic scheduling: a comparative overview. In J. Y. T. Leung (Ed.), Handbook of scheduling. Boca Raton: CRC Press.

    Google Scholar 

  • Pruhs, K., Sgall, J., & Torng, E. (2004). Online scheduling. In J. Y. T. Leung (Ed.), Handbook of scheduling. Boca Raton: CRC Press.

    Google Scholar 

  • Rudin III, J., & Chandrasekaran, R. (2003). Improved bounds for the online scheduling problem. SIAM Journal on Computing, 32, 717–735.

    Article  Google Scholar 

  • Shchepin, E. V., & Vakhania, N. (2005). An optimal rounding gives a better approximation for scheduling unrelated machines. Operations Research Letters, 33(2), 127–133.

    Article  Google Scholar 

  • Sgall, J. (1998). On-line scheduling—a survey. In A. Fiat & G. Woeginger (Eds.), Lecture notes in computer science. On-line algorithms. Berlin: Springer.

    Google Scholar 

  • Sleator, D. D., & Tarjan, R. E. (1985). Amortized efficiency of list update and paging rules. Communications of the ACM, 28, 202–208.

    Article  Google Scholar 

  • Van der Zee, D. J., Van Harten, A., & Schuur, P. C. (2001). On-line scheduling of multi-server batch operations. IIE Transactions, 33, 569–586.

    Google Scholar 

  • Van der Zee, D. J. (2003). Look-ahead strategies for controlling batch operations in industry—an overview. In Proceedings of the 2003 winter simulation conference (pp. 1480–1487).

  • Vairaktarakis, G. L., & Cai, X. (2003). The value of processing flexibility in multipurpose machines. IIE Transactions, 35(8), 763–774.

    Article  Google Scholar 

  • Zhou, P., Jiang, Y. W., & He, Y. (2007). Parallel machine scheduling problem with two GoS levels. Applied Mathematics: A Journal of Chinese Universities (Series A), 22(3), 275–284 (in Chinese).

    Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Dvir Shabtay

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  1. Marvin Mandelbaum
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  2. Dvir Shabtay
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Correspondence to Dvir Shabtay.

Additional information

Dvir Shabtay would like to dedicate this paper to the memory of his dear friend, colleague and co-author Marvin Mandelbaum who passed away on September 8, 2009.

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Mandelbaum, M., Shabtay, D. Scheduling unit length jobs on parallel machines with lookahead information. J Sched 14, 335–350 (2011). https://doi.org/10.1007/s10951-010-0192-y

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