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A BB&R algorithm for minimizing total tardiness on a single machine with sequence dependent setup times

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  • Edward Sewell
  • Jason Sauppe
  • David Morrison
  • Sheldon Jacobson
  • Gio Kao

Abstract

This paper presents a Branch, Bound, and Remember (BB&R) exact algorithm using the Cyclic Best First Search (CBFS) exploration strategy for solving the $${1|ST_{sd}|\sum T_{i}}$$ scheduling problem, a single machine scheduling problem with sequence dependent setup times where the objective is to find a schedule with minimum total tardiness. The BB&R algorithm incorporates memory-based dominance rules to reduce the solution search space. The algorithm creates schedules in the reverse direction for problems where fewer than half the jobs are expected to be tardy. In addition, a branch and bound algorithm is used to efficiently compute tighter lower bounds for the problem. This paper also presents a counterexample for a previously reported exact algorithm in Luo and Chu (Appl Math Comput 183(1):575–588, 2006 ) and Luo et al. (Int J Prod Res 44(17):3367–3378, 2006 ). Computational experiments demonstrate that the algorithm is two orders of magnitude faster than the fastest exact algorithm that has appeared in the literature. Computational experiments on two sets of benchmark problems demonstrate that the CBFS search exploration strategy can be used as an effective heuristic on problems that are too large to solve to optimality. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Edward Sewell & Jason Sauppe & David Morrison & Sheldon Jacobson & Gio Kao, 2012. "A BB&R algorithm for minimizing total tardiness on a single machine with sequence dependent setup times," Journal of Global Optimization, Springer, vol. 54(4), pages 791-812, December.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:4:p:791-812
    DOI: 10.1007/s10898-011-9793-z
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    References listed on IDEAS

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    1. Thomas L. Morin & Roy E. Marsten, 1976. "Branch-and-Bound Strategies for Dynamic Programming," Operations Research, INFORMS, vol. 24(4), pages 611-627, August.
    2. Tan, K. C. & Narasimhan, R., 1997. "Minimizing tardiness on a single processor with sequence-dependent setup times: a simulated annealing approach," Omega, Elsevier, vol. 25(6), pages 619-634, December.
    3. C Gagné & M Gravel & W L Price, 2005. "Using metaheuristic compromise programming for the solution of multiple-objective scheduling problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 687-698, June.
    4. Luo, Xiaochuan & Chu, Chengbin, 2007. "A branch-and-bound algorithm of the single machine schedule with sequence-dependent setup times for minimizing maximum tardiness," European Journal of Operational Research, Elsevier, vol. 180(1), pages 68-81, July.
    5. Gupta, Skylab R. & Smith, Jeffrey S., 2006. "Algorithms for single machine total tardiness scheduling with sequence dependent setups," European Journal of Operational Research, Elsevier, vol. 175(2), pages 722-739, December.
    6. C Gagné & W L Price & M Gravel, 2002. "Comparing an ACO algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(8), pages 895-906, August.
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    Citations

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    Cited by:

    1. Wenda Zhang & Jason J. Sauppe & Sheldon H. Jacobson, 2023. "Results for the close-enough traveling salesman problem with a branch-and-bound algorithm," Computational Optimization and Applications, Springer, vol. 85(2), pages 369-407, June.
    2. David R. Morrison & Edward C. Sewell & Sheldon H. Jacobson, 2016. "Solving the Pricing Problem in a Branch-and-Price Algorithm for Graph Coloring Using Zero-Suppressed Binary Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 67-82, February.
    3. David R. Morrison & Jason J. Sauppe & Edward C. Sewell & Sheldon H. Jacobson, 2014. "A Wide Branching Strategy for the Graph Coloring Problem," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 704-717, November.
    4. Yolmeh, Abdolmajid & Baykal-Gürsoy, Melike, 2021. "Weighted network search games with multiple hidden objects and multiple search teams," European Journal of Operational Research, Elsevier, vol. 289(1), pages 338-349.
    5. David R. Morrison & Jason J. Sauppe & Wenda Zhang & Sheldon H. Jacobson & Edward C. Sewell, 2017. "Cyclic best first search: Using contours to guide branch‐and‐bound algorithms," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 64-82, February.
    6. Geert De Maere & Jason A. D. Atkin & Edmund K. Burke, 2018. "Pruning Rules for Optimal Runway Sequencing," Transportation Science, INFORMS, vol. 52(4), pages 898-916, August.
    7. Morrison, David R. & Sewell, Edward C. & Jacobson, Sheldon H., 2014. "An application of the branch, bound, and remember algorithm to a new simple assembly line balancing dataset," European Journal of Operational Research, Elsevier, vol. 236(2), pages 403-409.

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