An approximate dynamic programming approach to dynamic slot allocation of spot containers with random arrivals, cancellations, and no-shows

Container shipping demands are usually classified into long-term contract demands from large shippers and ad hoc demands from spot shippers. Compared with stable long-term contract demands, spot container shipping demands are often unstable due to their high frequent cancellations during the slot booking period and their uncertain arrivals even no-shows. This poses a challenge for shipping companies in making precise and profitable decisions on slot allocations for these spot demands, to avoid the loss of slot utilization and shipping profit. This paper thus focuses on a dynamic slot allocation problem for spot containers with consideration of their random arrivals and cancellations during the booking period to maximize the expected shipping profit, and formulates it as a Markov decision process (MDP) model. Due to the well-known curse of dimensionality of MDP models, this paper uses the approximate dynamic programming (ADP) approach to approximate our MDP model, and consequently develops a series of stochastic programming models, which can yield a near-optimal slot allocation policy. Numerical experiments are conducted to examine the effectiveness and superiority of our models obtained by the ADP approach. The computational results show that our dynamic slot allocation strategy can make shipping companies achieve a high slot utilization rate, up to 91.36 %. Furthermore, compared with various slot allocation policies commonly used by shipping companies in practice, the policy obtained by the approach used in this paper performs best in terms of profit, with an improvement of up to 33.26 %.