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


  • Chen, Feng
  • Lee, Chung-Yee


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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    Cited by:

    1. Bruno, Giuseppe & Genovese, Andrea & Piccolo, Carmela, 2014. "The capacitated Lot Sizing model: A powerful tool for logistics decision making," International Journal of Production Economics, Elsevier, vol. 155(C), pages 380-390.
    2. Hermel, Dror & Hasheminia, Hamed & Adler, Nicole & Fry, Michael J., 2016. "A solution framework for the multi-mode resource-constrained cross-dock scheduling problem," Omega, Elsevier, vol. 59(PB), pages 157-170.
    3. Saeid Rezaei & Amirsaman Kheirkhah, 0. "A comprehensive approach in designing a sustainable closed-loop supply chain network using cross-docking operations," Computational and Mathematical Organization Theory, Springer, vol. 0, pages 1-48.
    4. Lin, Bertrand M.T. & Lin, Y.-Y. & Fang, K.-T., 2013. "Two-machine flow shop scheduling of polyurethane foam production," International Journal of Production Economics, Elsevier, vol. 141(1), pages 286-294.
    5. Boysen, Nils & Emde, Simon & Hoeck, Michael & Kauderer, Markus, 2015. "Part logistics in the automotive industry: Decision problems, literature review and research agenda," European Journal of Operational Research, Elsevier, vol. 242(1), pages 107-120.
    6. Maknoon, M.Y. & Soumis, F. & Baptiste, P., 2016. "Optimizing transshipment workloads in less-than-truckload cross-docks," International Journal of Production Economics, Elsevier, vol. 179(C), pages 90-100.
    7. repec:spr:comaot:v:24:y:2018:i:1:d:10.1007_s10588-017-9247-3 is not listed on IDEAS
    8. Fateme Heidari & Seyed Hessameddin Zegordi & Reza Tavakkoli-Moghaddam, 0. "Modeling truck scheduling problem at a cross-dock facility through a bi-objective bi-level optimization approach," Journal of Intelligent Manufacturing, Springer, vol. 0, pages 1-16.
    9. M. H. Fazel Zarandi & H. Khorshidian & M. Akbarpour Shirazi, 2016. "A constraint programming model for the scheduling of JIT cross-docking systems with preemption," Journal of Intelligent Manufacturing, Springer, vol. 27(2), pages 297-313, April.
    10. Shi, Wen & Shang, Jennifer & Liu, Zhixue & Zuo, Xiaolu, 2014. "Optimal design of the auto parts supply chain for JIT operations: Sequential bifurcation factor screening and multi-response surface methodology," European Journal of Operational Research, Elsevier, vol. 236(2), pages 664-676.
    11. Buijs, Paul & Vis, Iris F.A. & Carlo, Héctor J., 2014. "Synchronization in cross-docking networks: A research classification and framework," European Journal of Operational Research, Elsevier, vol. 239(3), pages 593-608.
    12. Liao, T.W. & Egbelu, P.J. & Chang, P.C., 2013. "Simultaneous dock assignment and sequencing of inbound trucks under a fixed outbound truck schedule in multi-door cross docking operations," International Journal of Production Economics, Elsevier, vol. 141(1), pages 212-229.
    13. Shi, Wen & Liu, Zhixue & Shang, Jennifer & Cui, Yujia, 2013. "Multi-criteria robust design of a JIT-based cross-docking distribution center for an auto parts supply chain," European Journal of Operational Research, Elsevier, vol. 229(3), pages 695-706.
    14. repec:eee:proeco:v:194:y:2017:i:c:p:102-112 is not listed on IDEAS
    15. Konrad Stephan & Nils Boysen, 2011. "Cross-docking," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 22(1), pages 129-137, September.
    16. Ladier, Anne-Laure & Alpan, Gülgün, 2016. "Cross-docking operations: Current research versus industry practice," Omega, Elsevier, vol. 62(C), pages 145-162.


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