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

Tingsong Wang, Qiang Meng, Shuaian Wang, Xiaobo Qu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)143-160
Number of pages18
JournalTransportation Research Part B: Methodological
Publication statusPublished - Aug 2021


  • Container slot allocation
  • Lagrangian relaxation and dual decomposition
  • Sample average approximation
  • Two-stage stochastic mixed-integer nonlinear programming

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation

Cite this