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The One-Machine Problem with Delayed Precedence Constraints and its Use in Job Shop Scheduling

Author

Listed:
  • Egon Balas

    (Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890)

  • Jan Karel Lenstra

    (Department of Mathematics and Computing Science, Eindhoven University of Technology, PO Box 513, Eindhoven 5600 MB, The Netherlands)

  • Alkis Vazacopoulos

    (College of Business Administration, Fairleigh Dickinson University, 1000 River Road, Teaneck, New Jersey 07666)

Abstract

We study the one machine scheduling problem with release and delivery times and the minimum makespan objective, in the presence of constraints that for certain pairs of jobs require a delay between the completion of the first job and the start of the second (delayed precedence constraints). This problem arises naturally in the context of the Shifting Bottleneck Procedure for the general job shop scheduling problem, as a relaxation of the latter, tighter than the standard one-machine relaxation. The paper first highlights the difference between the two relaxations through some relevant complexity results. Then it introduces a modified Longest Tail Heuristic whose analysis identifies those situations that permit efficient branching. As a result, an optimization algorithm is developed whose performance is comparable to that of the best algorithms for the standard one-machine problem. Embedding this algorithm into a modified version of the Shifting Bottleneck Procedure that uses the tighter one-machine relaxation discussed here results in a considerable overall improvement in performance on all classes of job shop scheduling problems.

Suggested Citation

  • Egon Balas & Jan Karel Lenstra & Alkis Vazacopoulos, 1995. "The One-Machine Problem with Delayed Precedence Constraints and its Use in Job Shop Scheduling," Management Science, INFORMS, vol. 41(1), pages 94-109, January.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:1:p:94-109
    DOI: 10.1287/mnsc.41.1.94
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    Citations

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    Cited by:

    1. Egon Balas & Giuseppe Lancia & Paolo Serafini & Alkiviadis Vazacopoulos, 1998. "Job Shop Scheduling With Deadlines," Journal of Combinatorial Optimization, Springer, vol. 1(4), pages 329-353, December.
    2. Da Col, Giacomo & Teppan, Erich C., 2022. "Industrial-size job shop scheduling with constraint programming," Operations Research Perspectives, Elsevier, vol. 9(C).
    3. Mukherjee, Saral & Chatterjee, A.K., 2006. "Applying machine based decomposition in 2-machine flow shops," European Journal of Operational Research, Elsevier, vol. 169(3), pages 723-741, March.
    4. Zoghby, Jeriad & Wesley Barnes, J. & Hasenbein, John J., 2005. "Modeling the reentrant job shop scheduling problem with setups for metaheuristic searches," European Journal of Operational Research, Elsevier, vol. 167(2), pages 336-348, December.
    5. Michael Pinedo & Marcos Singer, 1999. "A shifting bottleneck heuristic for minimizing the total weighted tardiness in a job shop," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(1), pages 1-17, February.
    6. Zijm, W. H. M. & Buitenhek, R., 1996. "Capacity planning and lead time management," International Journal of Production Economics, Elsevier, vol. 46(1), pages 165-179, December.
    7. Braune, R. & Zäpfel, G. & Affenzeller, M., 2012. "An exact approach for single machine subproblems in shifting bottleneck procedures for job shops with total weighted tardiness objective," European Journal of Operational Research, Elsevier, vol. 218(1), pages 76-85.
    8. Murat Güngör, 2023. "A note on the shifting bottleneck procedure for job shop scheduling," Journal of Scheduling, Springer, vol. 26(4), pages 399-402, August.
    9. Mukherjee, Saral & Chatterjee Ashis K, 2002. "Applying Machine Based Decomposition in 2-Machine Flow Shops," IIMA Working Papers WP2002-08-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
    10. Jain, A. S. & Meeran, S., 1999. "Deterministic job-shop scheduling: Past, present and future," European Journal of Operational Research, Elsevier, vol. 113(2), pages 390-434, March.
    11. C N Potts & J D Whitehead, 2007. "Heuristics for a coupled-operation scheduling problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(10), pages 1375-1388, October.
    12. Yiyo Kuo & Sheng-I Chen & Yen-Hung Yeh, 2020. "Single machine scheduling with sequence-dependent setup times and delayed precedence constraints," Operational Research, Springer, vol. 20(2), pages 927-942, June.
    13. Marc R. Lambrecht & Philip L. Ivens & Nico J. Vandaele, 1998. "ACLIPS: A Capacity and Lead Time Integrated Procedure for Scheduling," Management Science, INFORMS, vol. 44(11-Part-1), pages 1548-1561, November.
    14. El-Bouri, A. & Azizi, N. & Zolfaghari, S., 2007. "A comparative study of a new heuristic based on adaptive memory programming and simulated annealing: The case of job shop scheduling," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1894-1910, March.
    15. Mukherjee, Saral & Chatterjee, A.K., 2007. "On the representation of the one machine sequencing problem in the shifting bottleneck heuristic," European Journal of Operational Research, Elsevier, vol. 182(1), pages 475-479, October.
    16. Guidong Zhu & Jonathan F. Bard & Gang Yu, 2006. "A Branch-and-Cut Procedure for the Multimode Resource-Constrained Project-Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 18(3), pages 377-390, August.
    17. Sheen, Gwo-Ji & Liao, Lu-Wen, 2007. "A branch and bound algorithm for the one-machine scheduling problem with minimum and maximum time lags," European Journal of Operational Research, Elsevier, vol. 181(1), pages 102-116, August.
    18. Egon Balas & Alkis Vazacopoulos, 1998. "Guided Local Search with Shifting Bottleneck for Job Shop Scheduling," Management Science, INFORMS, vol. 44(2), pages 262-275, February.

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