Dynamic Slot Allocation for Spot Containers under Stochastic Demand and Time-Varying Freight Rates

Container shipping demands are classified into contract and spot demands. Shipping companies typically reserve slots for long-term contracts, while spot bookings must be made before departure. This paper examines the dynamic slot allocation problem for spot containers on a scheduled liner service, formulating it as a dynamic programming (DP) model aimed at maximizing total revenue from accepted slot booking requests. This paper incorporates the variability of freight rates over time and develops a decision period segmentation method grounded in the dynamics of demand arrivals. The stochastic nature of demand arrivals is effectively captured using a non-homogeneous Poisson process. To overcome the curse of dimensionality in solving the DP model, affine and dual techniques transform it into an approximate linear programming model. Given the complexity of solving this model across multiple decision periods, a dynamic disaggregation approach based on time-varying freight rates is proposed. Numerical experiments validate the effectiveness of the methodology. The results show that the dynamic slot allocation strategy significantly outperforms the first-come, first-served, bid-price control, and static booking limits, particularly in high-demand, capacity-constrained scenarios. These findings offer valuable insights for revenue optimization in container shipping.