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 %.

中文翻译：

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一种近似动态规划方法，用于随机到达、取消和未出现的现货集装箱的动态舱位分配


集装箱运输需求通常分为大型托运人的长期合同需求和现货发货人的临时需求。与稳定的长期合同需求相比，现货集装箱运输需求往往不稳定，因为在船期订舱期间取消的频率很高，而且到货情况不确定，甚至没有出现。这给航运公司带来了挑战，他们需要为这些现货需求做出精确且有利可图的船位分配决策，以避免船位利用率和航运利润的损失。因此，本文关注现货集装箱的动态舱位分配问题，考虑它们在订舱期间的随机到达和取消，以最大限度地提高预期的航运利润，并将其表述为马尔可夫决策过程 （MDP） 模型。由于 MDP 模型的维数诅咒是众所周知的，本文使用近似动态规划 （ADP） 方法来近似我们的 MDP 模型，并因此开发了一系列随机规划模型，可以产生近乎最优的时隙分配策略。进行了数值实验以检验通过 ADP 方法获得的模型的有效性和优越性。计算结果表明，我们的动态 Slot 分配策略可以使船公司实现较高的 Slot 利用率，高达 91.36 %。此外，与航运公司在实践中常用的各种舱位分配策略相比，本文所用方法得到的策略在利润方面表现最好，提高了 33.26 %。