Container slot allocation and dynamic pricing of time-sensitive cargoes considering port congestion and uncertain demand

This paper studies the container slot allocation problem for time-sensitive cargoes with consideration of dynamic pricing and port congestion under uncertain demand. Time-sensitive cargoes call for express delivery. However, port congestion is a non-negligible factor to affect the delivery time. Hence, a new freight rate function with respect to the delivery time considering port congestion is proposed for time-sensitive cargoes, and two different slot allocation strategies are proposed: Loyal Strategy and Expansive Strategy. Accordingly, we formulate the problem as a one-stage container slot allocation model and a two-stage container slot allocation model, respectively. Both of the two models are stochastic mixed-integer quadratic programming models with chance constraints due to the involvement of dynamic pricing, port congestion, and uncertain demand. To solve the proposed models, a tailored algorithm that combines the Sample Average Approximation approach and the Reformulation Linearization Technique (SAA-RLT) is developed in this paper. Finally, numerical experiments are carried out to verify the applicability and effectiveness of the proposed models and the solution algorithm.