IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v150y2021icp143-160.html
   My bibliography  Save this article

A two-stage stochastic nonlinear integer-programming model for slot allocation of a liner container shipping service

Author

Listed:
  • Wang, Tingsong
  • Meng, Qiang
  • Wang, Shuaian
  • Qu, Xiaobo

Abstract

In this study, we propose a container slot allocation problem for a liner shipping service. A liner containership provides a regular shipping service with a fixed itinerary and schedule. In practice, the liner containership may not be fully loaded, which results in a loss of revenue. We therefore segment shippers into two classes: contract shippers and spot shippers. A contract shipper has a contract with the shipping company and negotiates a fixed minimum quantity, so that the shipping company can secure a steady revenue. The remaining containership slots are open to spot shippers, allowing the shipping company to obtain ad hoc revenue. The container slot allocation problem is investigated in this study using a two-stage stochastic mixed-integer nonlinear programming model. We use the sample average approximation based on Lagrangian relaxation and dual decomposition techniques to effectively solve the model. Finally, we conduct a case study to evaluate the applicability and effectiveness of the proposed model and the solution algorithm.

Suggested Citation

  • Wang, Tingsong & Meng, Qiang & Wang, Shuaian & Qu, Xiaobo, 2021. "A two-stage stochastic nonlinear integer-programming model for slot allocation of a liner container shipping service," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 143-160.
    • Handle: RePEc:eee:transb:v:150:y:2021:i:c:p:143-160
    DOI: 10.1016/j.trb.2021.04.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261521000795
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2021.04.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shih-Chan Ting & Gwo-Hshiung Tzeng, 2016. "Bi-criteria approach to containership slot allocation in liner shipping," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 18(2), pages 141-157, June.
    2. Peter P. Belobaba, 1987. "Survey Paper---Airline Yield Management An Overview of Seat Inventory Control," Transportation Science, INFORMS, vol. 21(2), pages 63-73, May.
    3. L. H. Lee & E. P. Chew & M. S. Sim, 2007. "A heuristic to solve a sea cargo revenue management problem," Springer Books, in: Kap Hwan Kim & Hans-Otto Günther (ed.), Container Terminals and Cargo Systems, pages 351-364, Springer.
    4. Marlow, Peter & Nair, Rawindaran, 2008. "Service contracts--An instrument of international logistics supply chain: Under United States and European Union regulatory frameworks," Marine Policy, Elsevier, vol. 32(3), pages 489-496, May.
    5. L.H. Lee & E.P. Chew & M.S. Sim, 2009. "A revenue management model for sea cargo," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 6(2), pages 195-222.
    6. Meng, Qiang & Lee, Chung-Yee, 2016. "Liner container assignment model with transit-time-sensitive container shipment demand and its applicationsAuthor-Name: Wang, Shuaian," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 135-155.
    7. Andrew Lim & Fan Wang & Zhou Xu, 2006. "A Transportation Problem with Minimum Quantity Commitment," Transportation Science, INFORMS, vol. 40(1), pages 117-129, February.
    8. Jeffrey I. McGill & Garrett J. van Ryzin, 1999. "Revenue Management: Research Overview and Prospects," Transportation Science, INFORMS, vol. 33(2), pages 233-256, May.
    9. 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.
    10. Huang, Kuancheng & Chang, Ko-chen, 2010. "An approximate algorithm for the two-dimensional air cargo revenue management problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(3), pages 426-435, May.
    11. Dong-Ping Song & Jing-Xin Dong, 2015. "Empty Container Repositioning," International Series in Operations Research & Management Science, in: Chung-Yee Lee & Qiang Meng (ed.), Handbook of Ocean Container Transport Logistics, edition 127, chapter 6, pages 163-208, Springer.
    12. Wang, Yadong & Meng, Qiang & Du, Yuquan, 2015. "Liner container seasonal shipping revenue management," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 141-161.
    13. S. L. Brumelle & J. I. McGill & T. H. Oum & K. Sawaki & M. W. Tretheway, 1990. "Allocation of Airline Seats between Stochastically Dependent Demands," Transportation Science, INFORMS, vol. 24(3), pages 183-192, August.
    14. Gharehgozli, Amir & Zaerpour, Nima, 2018. "Stacking outbound barge containers in an automated deep-sea terminal," European Journal of Operational Research, Elsevier, vol. 267(3), pages 977-995.
    15. Sebastian Zurheide & Kathrin Fischer, 2012. "A revenue management slot allocation model for liner shipping networks," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 14(3), pages 334-361, September.
    16. Bell, Michael G.H. & Liu, Xin & Rioult, Jeremy & Angeloudis, Panagiotis, 2013. "A cost-based maritime container assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 58-70.
    17. Moussawi-Haidar, Lama, 2014. "Optimal solution for a cargo revenue management problem with allotment and spot arrivals," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 173-191.
    18. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    19. Mikhail A. Bragin & Peter B. Luh & Joseph H. Yan & Nanpeng Yu & Gary A. Stern, 2015. "Convergence of the Surrogate Lagrangian Relaxation Method," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 173-201, January.
    20. Wen He & Lawrence C. Leung & Yer Van Hui & Gang Chen, 2019. "An air freight forwarder’s resource planning and revenue management," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(2), pages 294-309, February.
    21. 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.
    22. Meng, Qiang & Zhao, Hui & Wang, Yadong, 2019. "Revenue management for container liner shipping services: Critical review and future research directions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 128(C), pages 280-292.
    23. Cheng-Min Feng & Chia-Hui Chang, 2008. "Optimal Slot Allocation in Intra-Asia Service for Liner Shipping Companies," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 10(3), pages 295-309, September.
    24. Bell, Michael G.H. & Liu, Xin & Angeloudis, Panagiotis & Fonzone, Achille & Hosseinloo, Solmaz Haji, 2011. "A frequency-based maritime container assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1152-1161, September.
    25. Huang, Kuancheng & Liang, Yu-Tung, 2011. "A dynamic programming algorithm based on expected revenue approximation for the network revenue management problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(3), pages 333-341, May.
    26. Yadong Wang & Qiang Meng, 2019. "Integrated method for forecasting container slot booking in intercontinental liner shipping service," Flexible Services and Manufacturing Journal, Springer, vol. 31(3), pages 653-674, September.
    27. Yuri Levin & Mikhail Nediak & Huseyin Topaloglu, 2012. "Cargo Capacity Management with Allotments and Spot Market Demand," Operations Research, INFORMS, vol. 60(2), pages 351-365, April.
    28. Shin-Chan Ting * & Gwo-Hshiung Tzeng, 2004. "An optimal containership slot allocation for liner shipping revenue management," Maritime Policy & Management, Taylor & Francis Journals, vol. 31(3), pages 199-211, July.
    29. Faiz A. Al-Khayyal & James E. Falk, 1983. "Jointly Constrained Biconvex Programming," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 273-286, May.
    30. Sumit Kunnumkal & Huseyin Topaloglu, 2011. "A stochastic approximation algorithm to compute bid prices for joint capacity allocation and overbooking over an airline network," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(4), pages 323-343, June.
    31. Wang, Shuaian & Liu, Zhiyuan & Bell, Michael G.H., 2015. "Profit-based maritime container assignment models for liner shipping networks," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 59-76.
    32. X. Zhao & P. B. Luh & J. Wang, 1999. "Surrogate Gradient Algorithm for Lagrangian Relaxation," Journal of Optimization Theory and Applications, Springer, vol. 100(3), pages 699-712, March.
    33. King-Wah Pang & Jiyin Liu, 2014. "An integrated model for ship routing with transshipment and berth allocation," IISE Transactions, Taylor & Francis Journals, vol. 46(12), pages 1357-1370, December.
    34. Marshall L. Fisher, 2004. "Comments on ÜThe Lagrangian Relaxation Method for Solving Integer Programming ProblemsÝ," Management Science, INFORMS, vol. 50(12_supple), pages 1872-1874, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hu, Qiaolin & Gu, Weihua & Wang, Shuaian, 2022. "Optimal subsidy scheme design for promoting intermodal freight transport," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 157(C).
    2. Liang, Jinpeng & Li, Liming & Zheng, Jianfeng & Tan, Zhijia, 2023. "Service-oriented container slot allocation policy under stochastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 176(C).
    3. Ksciuk, Jana & Kuhlemann, Stefan & Tierney, Kevin & Koberstein, Achim, 2023. "Uncertainty in maritime ship routing and scheduling: A Literature review," European Journal of Operational Research, Elsevier, vol. 308(2), pages 499-524.
    4. Ming Liu & Yueyu Ding & Lihua Sun & Runchun Zhang & Yue Dong & Zihan Zhao & Yiting Wang & Chaoran Liu, 2023. "Green Airline-Fleet Assignment with Uncertain Passenger Demand and Fuel Price," Sustainability, MDPI, vol. 15(2), pages 1-22, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Moussawi-Haidar, Lama & Nasr, Walid & Jalloul, Maya, 2021. "Standardized cargo network revenue management with dual channels under stochastic and time-dependent demand," European Journal of Operational Research, Elsevier, vol. 295(1), pages 275-291.
    2. Wang, Tingsong & Xing, Zheng & Hu, Hongtao & Qu, Xiaobo, 2019. "Overbooking and delivery-delay-allowed strategies for container slot allocation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 433-447.
    3. Wang, Shuaian & Wang, Hua & Meng, Qiang, 2015. "Itinerary provision and pricing in container liner shipping revenue management," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 77(C), pages 135-146.
    4. Wang, Yadong & Meng, Qiang & Du, Yuquan, 2015. "Liner container seasonal shipping revenue management," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 141-161.
    5. Meng, Qiang & Zhao, Hui & Wang, Yadong, 2019. "Revenue management for container liner shipping services: Critical review and future research directions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 128(C), pages 280-292.
    6. Wang, Yadong & Gu, Yuyun & Wang, Tingsong & Zhang, Jun, 2022. "A risk-averse approach for joint contract selection and slot allocation in liner container shipping," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    7. Wang, Tingsong & Tian, Xuecheng & Wang, Yadong, 2020. "Container slot allocation and dynamic pricing of time-sensitive cargoes considering port congestion and uncertain demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).
    8. Liang, Jinpeng & Li, Liming & Zheng, Jianfeng & Tan, Zhijia, 2023. "Service-oriented container slot allocation policy under stochastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 176(C).
    9. Liu, Ming & Chu, Feng & Zhang, Zizhen & Chu, Chengbin, 2015. "A polynomial-time heuristic for the quay crane double-cycling problem with internal-reshuffling operations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 81(C), pages 52-74.
    10. Wang, Yadong & Meng, Qiang, 2021. "Optimizing freight rate of spot market containers with uncertainties in shipping demand and available ship capacity," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 314-332.
    11. Liu, Ming & Lee, Chung-Yee & Zhang, Zizhen & Chu, Chengbin, 2016. "Bi-objective optimization for the container terminal integrated planning," Transportation Research Part B: Methodological, Elsevier, vol. 93(PB), pages 720-749.
    12. Klein, Robert & Koch, Sebastian & Steinhardt, Claudius & Strauss, Arne K., 2020. "A review of revenue management: Recent generalizations and advances in industry applications," European Journal of Operational Research, Elsevier, vol. 284(2), pages 397-412.
    13. Lee, Chung-Yee & Song, Dong-Ping, 2017. "Ocean container transport in global supply chains: Overview and research opportunities," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 442-474.
    14. Wang, Shuaian, 2015. "Optimal sequence of container ships in a string," European Journal of Operational Research, Elsevier, vol. 246(3), pages 850-857.
    15. Hui Zhao & Qiang Meng & Yadong Wang, 2022. "Robust container slot allocation with uncertain demand for liner shipping services," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 551-579, September.
    16. Shuai Jia & Chung-Lun Li & Zhou Xu, 2019. "Managing Navigation Channel Traffic and Anchorage Area Utilization of a Container Port," Transportation Science, INFORMS, vol. 53(3), pages 728-745, May.
    17. Meng, Qiang & Lee, Chung-Yee, 2016. "Liner container assignment model with transit-time-sensitive container shipment demand and its applicationsAuthor-Name: Wang, Shuaian," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 135-155.
    18. Goh, Shao Hung & Chan, Yuxian, 2016. "Operational shadow pricing in back haul container shipping," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 92(C), pages 3-15.
    19. Hua-An Lu & Wen-Hung Mu, 2016. "A slot reallocation model for containership schedule adjustment," Maritime Policy & Management, Taylor & Francis Journals, vol. 43(1), pages 136-157, January.
    20. Azadian, Farshid & Murat, Alper & Chinnam, Ratna Babu, 2015. "Integrated production and logistics planning: Contract manufacturing and choice of air/surface transportation," European Journal of Operational Research, Elsevier, vol. 247(1), pages 113-123.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:150:y:2021:i:c:p:143-160. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.