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Minimizing the makespan in a two-machine cross-docking flow shop problem

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  • Chen, Feng
  • Lee, Chung-Yee

Abstract

This paper studies a two-machine cross-docking flow shop scheduling problem in which a job at the second machine can be processed only after the processing of some jobs at the first machine has been completed. The objective is to minimize the makespan. We first show that the problem is strongly NP-hard. Some polynomially solvable special cases are provided. We then develop a polynomial approximation algorithm with an error-bound analysis. A branch-and-bound algorithm is also constructed. Computational results show that the branch-and-bound algorithm can optimally solve problems with up to 60 jobs within a reasonable amount of time.

Suggested Citation

  • Chen, Feng & Lee, Chung-Yee, 2009. "Minimizing the makespan in a two-machine cross-docking flow shop problem," European Journal of Operational Research, Elsevier, vol. 193(1), pages 59-72, February.
    • Handle: RePEc:eee:ejores:v:193:y:2009:i:1:p:59-72
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    References listed on IDEAS

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    1. A.A. Gladky & Y.M. Shafransky & V.A. Strusevich, 2004. "Flow Shop Scheduling Problems Under Machine–Dependent Precedence Constraints," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 13-28, March.
    2. Kevin R. Gue, 1999. "The Effects of Trailer Scheduling on the Layout of Freight Terminals," Transportation Science, INFORMS, vol. 33(4), pages 419-428, November.
    3. Clyde L. Monma, 1979. "The Two-Machine Maximum Flow Time Problem with Series-Parallel Precedence Constraints: An Algorithm and Extensions," Operations Research, INFORMS, vol. 27(4), pages 792-798, August.
    4. John J. Bartholdi & Kevin R. Gue, 2004. "The Best Shape for a Crossdock," Transportation Science, INFORMS, vol. 38(2), pages 235-244, May.
    5. Clyde L. Monma, 1980. "Sequencing to Minimize the Maximum Job Cost," Operations Research, INFORMS, vol. 28(4), pages 942-951, August.
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