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A Branch-and-Bound Algorithm for the Bi-Objective Quay Crane Scheduling Problem Based on Efficiency and Energy

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  • Hongming Li

    (College of Management and Economics, Tianjin University, Tianjin 300072, China)

  • Xintao Li

    (Zhou Enlai School of Government, Nankai University, Tianjin 300350, China
    Chinese Government and Policy Joint Research Center, Nankai University, Tianjin 300350, China)

Abstract

Motivated by the call of the International Maritime Organization to meet the emission targets of 2030, this study considers two important practical aspects of quay crane scheduling: efficiency and energy consumption. More precisely, we introduce the bi-objective quay crane scheduling problem where the objective is to minimize the vessel’s completion time and the crane’s energy consumption. This is done by formulating a bi-objective mixed-integer programming model. A branch-and-bound algorithm was developed as the exact solution approach to find the full set of Pareto-optimal solutions. We consider (i) various lower bounds for both objectives, (ii) specific upper bounds, (iii) additional branching criteria, and (iv) fathoming criteria to detect Pareto-optimal solutions. Numerical experiments on benchmark instances show that the branch-and-bound algorithm can efficiently solve small- and medium-sized problems.

Suggested Citation

  • Hongming Li & Xintao Li, 2022. "A Branch-and-Bound Algorithm for the Bi-Objective Quay Crane Scheduling Problem Based on Efficiency and Energy," Mathematics, MDPI, vol. 10(24), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4705-:d:1000352
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    References listed on IDEAS

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    1. Jiyin Liu & Yat‐wah Wan & Lei Wang, 2006. "Quay crane scheduling at container terminals to minimize the maximum relative tardiness of vessel departures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 60-74, February.
    2. Chen, Jiang Hang & Bierlaire, Michel, 2017. "The study of the unidirectional quay crane scheduling problem: complexity and risk-aversion," European Journal of Operational Research, Elsevier, vol. 260(2), pages 613-624.
    3. Markus Leitner & Ivana Ljubić & Markus Sinnl, 2015. "A Computational Study of Exact Approaches for the Bi-Objective Prize-Collecting Steiner Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 118-134, February.
    4. Bierwirth, Christian & Meisel, Frank, 2015. "A follow-up survey of berth allocation and quay crane scheduling problems in container terminals," European Journal of Operational Research, Elsevier, vol. 244(3), pages 675-689.
    5. Sophie N. Parragh & Fabien Tricoire, 2019. "Branch-and-Bound for Bi-objective Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 805-822, October.
    6. Bierwirth, Christian & Meisel, Frank, 2010. "A survey of berth allocation and quay crane scheduling problems in container terminals," European Journal of Operational Research, Elsevier, vol. 202(3), pages 615-627, May.
    7. Villalba, Gara & Gemechu, Eskinder Demisse, 2011. "Estimating GHG emissions of marine ports--the case of Barcelona," Energy Policy, Elsevier, vol. 39(3), pages 1363-1368, March.
    8. Daganzo, Carlos F., 1989. "The crane scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 23(3), pages 159-175, June.
    9. Chen, Gang & Govindan, Kannan & Golias, Mihalis M., 2013. "Reducing truck emissions at container terminals in a low carbon economy: Proposal of a queueing-based bi-objective model for optimizing truck arrival pattern," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 55(C), pages 3-22.
    10. Kim, Kap Hwan & Park, Young-Man, 2004. "A crane scheduling method for port container terminals," European Journal of Operational Research, Elsevier, vol. 156(3), pages 752-768, August.
    11. Chen, Jiang Hang & Lee, Der-Horng & Goh, Mark, 2014. "An effective mathematical formulation for the unidirectional cluster-based quay crane scheduling problem," European Journal of Operational Research, Elsevier, vol. 232(1), pages 198-208.
    12. Chang, Daofang & Jiang, Zuhua & Yan, Wei & He, Junliang, 2010. "Integrating berth allocation and quay crane assignments," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(6), pages 975-990, November.
    13. Kong, Lingrui & Ji, Mingjun & Gao, Zhendi, 2022. "An exact algorithm for scheduling tandem quay crane operations in container terminals," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    14. Shoufeng Ma & Hongming Li & Ning Zhu & Chenyi Fu, 2021. "Stochastic programming approach for unidirectional quay crane scheduling problem with uncertainty," Journal of Scheduling, Springer, vol. 24(2), pages 137-174, April.
    15. Mavrotas, G. & Diakoulaki, D., 1998. "A branch and bound algorithm for mixed zero-one multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 530-541, June.
    16. Xia, Jun & Wang, Kai & Wang, Shuaian, 2019. "Drone scheduling to monitor vessels in emission control areas," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 174-196.
    17. Natashia Boland & Hadi Charkhgard & Martin Savelsbergh, 2015. "A Criterion Space Search Algorithm for Biobjective Integer Programming: The Balanced Box Method," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 735-754, November.
    18. Natashia Boland & Hadi Charkhgard & Martin Savelsbergh, 2015. "A Criterion Space Search Algorithm for Biobjective Mixed Integer Programming: The Triangle Splitting Method," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 597-618, November.
    19. Mansouri, S. Afshin & Lee, Habin & Aluko, Oluwakayode, 2015. "Multi-objective decision support to enhance environmental sustainability in maritime shipping: A review and future directions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 78(C), pages 3-18.
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