Profit-based maritime container assignment models for liner shipping networks

Shuaian Wang, Zhiyuan Liu, Michael G H Bell

Research output: Contribution to journalArticleResearchpeer-review

50 Citations (Scopus)


We propose the problem of profit-based container assignment (P-CA), in which the container shipment demand is dependent on the freight rate, similar to the elastic demand in the literature on urban transportation networks. The problem involves determining the optimal freight rates, the number of containers to transport and how to transport the containers in a liner shipping network to maximize the total profit. We first consider a tactical-level P-CA with known demand functions that are estimated based on historical data and formulate it as a nonlinear optimization model. The tactical-level P-CA can be used for evaluating and improving the container liner shipping network. We then address the operational-level P-CA with unknown demand functions, which aims to design a mechanism that adjusts the freight rates to maximize the profit. A theoretically convergent trial-and-error approach, and a practical trial-and-error approach, are developed. A numerical example is reported to illustrate the application of the models and approaches.
Original languageEnglish
Pages (from-to)59 - 76
Number of pages18
JournalTransportation Research Part B: Methodological
Publication statusPublished - Feb 2015


  • Liner shipping network
  • Maritime transportation
  • Profit-based container assignment (P-CA)
  • Container routing
  • Nonlinear programming
  • Trial-and-error

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