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A mixed-integer programming formulation and Lagrangean relaxation for the cross-dock door assignment problem

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Listed:
  • W. Nassief
  • I. Contreras
  • R. As’ad

Abstract

In a cross-dock, goods are unloaded from incoming trucks, consolidated according to their destinations, and then, loaded into outgoing trucks with little or no storage in between. In this paper, we study the cross-dock door assignment problem in which the assignment of incoming trucks to strip doors, and outgoing trucks to stack doors is determined, with the objective of minimising the total material handling cost. We present a new mixed integer programming formulation which is embedded into a Lagrangean relaxation that exploits the special structure of the problem to obtain bounds on the optimal solution value. A primal heuristic is used at every iteration of the Lagrangean relaxation to obtain high quality feasible solutions. Computational results obtained on benchmark instances (with up to 20 origins and destinations, and 10 strip and stack doors) and on a new and more difficult set of instances (with up to 50 origins and destinations, and 30 strip and stack doors) confirm the efficiency of the algorithm.

Suggested Citation

  • W. Nassief & I. Contreras & R. As’ad, 2016. "A mixed-integer programming formulation and Lagrangean relaxation for the cross-dock door assignment problem," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 494-508, January.
    • Handle: RePEc:taf:tprsxx:v:54:y:2016:i:2:p:494-508
    DOI: 10.1080/00207543.2014.1003664
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    Cited by:

    1. Wolff, Pascal & Emde, Simon & Pfohl, Hans-Christian, 2021. "Internal resource requirements: The better performance metric for truck scheduling?," Omega, Elsevier, vol. 103(C).
    2. Gelareh, Shahin & Glover, Fred & Guemri, Oualid & Hanafi, Saïd & Nduwayo, Placide & Todosijević, Raca, 2020. "A comparative study of formulations for a cross-dock door assignment problem," Omega, Elsevier, vol. 91(C).
    3. Feifeng Zheng & Yaxin Pang & Yinfeng Xu, 2022. "Heuristics for cross-docking scheduling of truck arrivals, truck departures and shop-floor operations," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1571-1601, July.
    4. Li, Mingjie & Hao, Jin-Kao & Wu, Qinghua, 2024. "A flow based formulation and a reinforcement learning based strategic oscillation for cross-dock door assignment," European Journal of Operational Research, Elsevier, vol. 312(2), pages 473-492.
    5. Guemri, Oualid & Nduwayo, Placide & Todosijević, Raca & Hanafi, Saïd & Glover, Fred, 2019. "Probabilistic Tabu Search for the Cross-Docking Assignment Problem," European Journal of Operational Research, Elsevier, vol. 277(3), pages 875-885.
    6. Wang, Haibo & Alidaee, Bahram, 2019. "The multi-floor cross-dock door assignment problem: Rising challenges for the new trend in logistics industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 132(C), pages 30-47.
    7. Sayed Ibrahim Sayed & Ivan Contreras & Juan A. Diaz & Dolores E. Luna, 2020. "Integrated cross-dock door assignment and truck scheduling with handling times," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 705-727, October.

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