DOI QR코드

DOI QR Code

No Tardiness Rescheduling with Order Disruptions

  • Received : 2012.11.13
  • Accepted : 2013.02.18
  • Published : 2013.03.31

Abstract

This paper considers a single machine rescheduling problem whose original (efficiency related) objective is minimizing makespan. We assume that disruptions such as order cancelations and newly arrived orders occur after the initial scheduling, and we reschedule this disrupted schedule with the objective of minimizing a disruption related objective while preserving the original objective. The disruption related objective measures the impact of the disruptions as difference of completion times in the remaining (uncanceled) jobs before and after the disruptions. The artificial due dates for the remaining jobs are set to completion times in the original schedule while newly arrived jobs do not have due dates. Then, the objective of the rescheduling is minimizing the maximum earliness without tardiness. In order to preserve the optimality of the original objective, we assume that no-idle time and no tardiness are allowed while rescheduling. We first define this new problem and prove that the general version of the problem is unary NP-complete. Then, we develop three simple but intuitive heuristics. For each of the three heuristics, we find a tight bound on the measure called modified z-approximation ratio. The best theoretical bound is found to be 0.5 - ${\varepsilon}$ for some ${\varepsilon}$ > 0, and it implies that the solution value of the best heuristic is at most around a half of the worst possible solution value. Finally, we empirically evaluate the heuristics and demonstrate that the two best heuristics perform much better than the other one.

Keywords

Rescheduling;Order Disruption;Heuristic Analysis;Minimizing Maximum Earliness

References

  1. Azizoglu, M., Koksalan, M., and Koksalan, S. K. (2003), Scheduling to minimize maximum earliness and number of tardy jobs where machine idle time is allowed, Journal of the Operational Research Society, 54(6), 661-664. https://doi.org/10.1057/palgrave.jors.2601478
  2. Clausen, J., Larsen, J., Larsen, A., and Hansen, J. (2001), Disruption management-operations research between planning and execution, OR/MS Today, 28(5), 40-43.
  3. Graham, R. L., Lawler, E. L., Lenstra, J. K., and Rinnooy Kan, A. H. G. (1979), Optimization and approximation in deterministic sequencing and scheduling: a survey, Annals of Discrete Mathematics, 5, 287-326. https://doi.org/10.1016/S0167-5060(08)70356-X
  4. Garey, M. R. and Johnson, D. S. (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, CA.
  5. Guner, E., Erol, S., and Tani, K. (1998), One machine scheduling to minimize the maximum earliness with minimum number of tardy jobs, International Journal of Production Economics, 55(2), 213-219. https://doi.org/10.1016/S0925-5273(98)00062-0
  6. Hall, N. G. and Potts, C. N. (2004), Rescheduling for new orders, Operations Research, 52(3), 440-453. https://doi.org/10.1287/opre.1030.0101
  7. Hassin, R. and Khuller, S. (2001), z-Approximations, Journal of Algorithms, 41(2), 429-442. https://doi.org/10.1006/jagm.2001.1187
  8. Johnson, D. S., Demers, A., Ullman, J. D., Garey, M. R., and Graham, R. L. (1974), Worst-case performance bounds for simple one-dimensional packing algorithms, SIAM Journal on Computing, 3(4), 299-325. https://doi.org/10.1137/0203025
  9. Karp, R. M. (1972), Reducibility among combinatorial problems. In: Miller, R. and Thatcher, J. W. (eds.), Complexity of Computer Computations, Plenum Press, New York, NY.
  10. Kopanos, G. M., Capon-Garcia, E., Espuna, A., and Puigjaner, L. (2008), Costs for rescheduling actions: a critical issue for reducing the gap between scheduling theory and practice, Industrial and Engineering Chemistry Industry, 47(22), 8785-8795. https://doi.org/10.1021/ie8005676
  11. Mandel, M. and Mosheiov, G. (2001), Minimizing maximum earliness on parallel identical machines, Computers and Operations Research, 28(4), 317-327. https://doi.org/10.1016/S0305-0548(99)00103-3
  12. Molaee, E., Moslehi, G., and Reisi, M. (2010), Minimizing maximum earliness and number of tardy jobs in the single machine scheduling problem, Computers and Mathematics with Applications, 60(11), 2909-2919. https://doi.org/10.1016/j.camwa.2010.09.046
  13. Ozlen, M. and Azizoglu, M. (2011), Rescheduling unrelated parallel machines with total flow time and total disruption cost criteria, Journal of the Operational Research Society, 62, 152-164. https://doi.org/10.1057/jors.2009.157
  14. Qi, X., Bard, J. F., and Yu, G. (2006), Disruption management for machine scheduling: the case of SPT schedules, International Journal of Production Economics, 103(1), 166-184. https://doi.org/10.1016/j.ijpe.2005.05.021
  15. Unal, A. T., Uzsoy, R., and Kiran, A. S. (1997), Rescheduling on a single machine with part-type dependent setup times and deadlines, Annals of Operations Research, 70, 93-113. https://doi.org/10.1023/A:1018955111939
  16. Wu, S. D., Storer, R. H., and Chang, P. C. (1993), Onemachine rescheduling heuristics with efficiency and stability as criteria, Computers and Operations Research, 20(1), 1-14. https://doi.org/10.1016/0305-0548(93)90091-V
  17. Yang, J. and Posner, M. E. (2012), Rescheduling with order disruptions (Working Paper), The Ohio State University, Columbus, OH.

Cited by

  1. A Special Case of Three Machine Flow Shop Scheduling vol.15, pp.1, 2016, https://doi.org/10.7232/iems.2016.15.1.032

Acknowledgement

Supported by : University of Seoul