Robust container slot allocation with uncertain demand for liner shipping services

Container slot allocation for liner shipping services is to allocate the limited container slots of ships to different segments of demands in order to maximize the total revenue over a shipping network. This study focuses on a planning-level container slot allocation problem with uncertain demand, which is essential in container shipping revenue management. Due to the challenge of calibrating/formulating a specific probability distribution of uncertain container slot demand, we can rely on its fundamental descriptive statistics, namely, mean, upper/lower bounds as well as variance to tackle the container slot allocation problem. We, therefore, develop a robust optimization model using the fundamental descriptive statistics, which is approximated by a solvable second-order cone programming model. A numerical example based on a real shipping network demonstrates that the optimal solution from the second-order cone programming model outperforms the models using the expectation of uncertain demand data and the normally distributed demand. The numerical results indicate that the robust optimization model can well deal with the large fluctuations of uncertain container slot demand. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.