A two-stage stochastic nonlinear integer-programming model for slot allocation of a liner container shipping service
Journal article, 2021

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.

Lagrangian relaxation and dual decomposition

Sample average approximation

Container slot allocation

Two-stage stochastic mixed-integer nonlinear programming


Tingsong Wang

Shanghai University

Qiang Meng

National University of Singapore (NUS)

Shuaian Wang

Hong Kong Polytechnic University

Xiaobo Qu

Chalmers, Architecture and Civil Engineering, Geology and Geotechnics

Transportation Research Part B: Methodological

0191-2615 (ISSN)

Vol. 150 143-160

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Control Engineering



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7/2/2021 8