Journal of Global Optimization

, Volume 9, Issue 3–4, pp 395–416

Machine scheduling with an availability constraint

  • Chung-Yee Lee
Article

Abstract

Most literature in scheduling assumes that machines are available simultaneously at all times. However, this availability may not be true in real industry settings. In this paper, we assume that the machine may not always be available. This happens often in the industry due to a machine breakdown (stochastic) or preventive maintenance (deterministic) during the scheduling period. We study the scheduling problem under this general situation and for the deterministic case.

We discuss various performance measures and various machine environments. In each case, we either provide a polynomial optimal algorithm to solve the problem, or prove that the problem is NP-hard. In the latter case, we develop pseudo-polynomial dynamic programming models to solve the problem optimally and/or provide heuristics with an error bound analysis.

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References

  1. Adiri, I., Bruno, J., Frostig, E., and A.H.G. Rinnooy Kan, “Single Machine Flow-Time Scheduling with a Single Breakdown,” Acta Informatica, 26, (1989), pp. 679–696.Google Scholar
  2. Baker, K., Elements of Sequencing and Scheduling, (1993), unpublished manuscript.Google Scholar
  3. Blazewicz, J., K. Ecker, G. Schmidt, and J. Weglarz, Scheduling in Computer and Manufacturing Systems, Springer-Verlag, 1993, New York.Google Scholar
  4. Garey, M. R., and D. S. Johnson, Computer and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, 1979, New York.Google Scholar
  5. Graves, S. C., “A Review on Production Scheduling,” Operations Research, 29, (1981), pp. 646–676.Google Scholar
  6. Herrmann, J., C.-Y. Lee, and J. Snowdon, “A Classification of Static Scheduling Problems,” in Complexity in Numerical Optimization, P. M. Pardalos (ed.), (1993), pp. 203–253, World Scientific.Google Scholar
  7. Kaspi, M. and B. Montreuil, “On the Scheduling of Identical Parallel Processes with Arbitrary Initial Processor Available Times,” Research Report 88-12, School of Industrial Engineering, Purdue University, 1988.Google Scholar
  8. Kraemer, F., ad C.-Y. Lee,` “Common Due-Window Scheduling,” Production and Operations Management, 2, (1993), pp. 262–275.Google Scholar
  9. Lawler, E.L., J.K. Lenstra, A.H.G. Rinnooy Kan, and D. Shmoys, “Sequencing and Scheduling: Algorithms and Complexity,” in Handbook in Operations Research and Management Science, Vol. 4: Logistics of Production and Inventory, S.S. Graves, A.H.G. Rinnooy Kan, and P. Zipkin (eds.), pp. 445–522, North-Holland, New York, 1993.Google Scholar
  10. Lee, C.-Y., “Parallel Machines Scheduling with Non-Simultaneous Machine Available Time,” Discrete Applied Mathematics, 30,(1991), pp. 53–61.Google Scholar
  11. Lee, C.-Y., “Minimizing the Makespan in the Two-Machine Flowshop Scheduling Problem with an Availability Constraint,” (1995), submitted for publication.Google Scholar
  12. Lee, C.-Y., and S. D. Liman, “Single Machine Flow-Time Scheduling With Scheduled Maintenance,” Acta Informatica, 29, (1992), pp. 375–382.Google Scholar
  13. Lee, C.-Y., and S. D. Liman, “Capacitated two-parallel machines scheduling to minimize sum of job completion times,” Discrete Applied Mathematics, 41, (1993), pp. 211–222.Google Scholar
  14. Lei, L., and T.-J. Wong, “The Minimum Common-Cycle Algorithm for Cyclic Scheduling of Two Material Handling Hoists with Time Window Constraints,” Management Science, 37, (1991), pp. 1629–1639.Google Scholar
  15. Liman, S., Scheduling with Capacities and Due-Dates, Ph.D. Dissertation, Industrial and Systems Engineering Department, University of Florida, 1991.Google Scholar
  16. Morton, T. E., and D. W. Prentico, Heuristic Scheduling Systems, John Wiley & Sons, Inc. New York, 1993.Google Scholar
  17. Mosheiov, G., “Minimizing the Sum of Job Completion Times on Capacitated Parallel Machines,” Mathl. Comput. Modelling, 20, 1994, pp. 91–99.Google Scholar
  18. Pinedo, M., Scheduling: Theory, Algorithms, and Systems, Prentice Hall, 1995, Englewood Cliffs, New Jersey, 1995.Google Scholar
  19. Sahni, S., “Approximation Algorithms for the 0/1 Kanpsack Problem,” Journal of the Association for Computing Machinery, 20, 1975, pp. 115–124.Google Scholar
  20. Schmidt, G., “Scheduling Independent Tasks with Deadlines on Semi-identical Processors,” Journal of Operational Research Society, 39, 1984, 271–277.Google Scholar
  21. Tanaev, V. S., Y. N. Sotskov, and V. A. Strusevich, Scheduling Theory. Multi-Stage Systems, Kluwer Academic Publishers, 1994, The Netherlands.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Chung-Yee Lee
    • 1
  1. 1.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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