Corruption Robust Dynamic Pricing in Liner Shipping under Capacity Constraint

The shipping industry has irreplaceable importance in international trade and commerce. How to dynamically price different containers has long been a hot topic due to its direct connection to the final revenue. Two critical observations have been made after a comprehensive survey within a top liner company, China Ocean Shipping Company (COSCO). (1) Each type of container carried on a liner ship has its maximum capacity. (2) The sales volume is occasionally subject to huge fluctuations due to rare uncontrollable factors, such as COVID. Based on the above two points and the liner routine's periodic nature, we model the dynamic pricing problem as an episodic MDP model integrating with both capacity constraints and adversarial corruption, named C3-MDP. To maximize the cumulative revenue in the C3-MDP setting, we propose a programming framework, Bonus-Exploration based Episodic Programming (BEEP). This framework can directly accommodate the linear programming algorithm to form the algorithm BEEP-LP, which provides the episode-wise greedy optimal strategy. Furthermore, a detailed regret analysis is provided, showing that BEEP-LP has a regret that is sublinear in the number of episodes. Combining deep techniques, we also present an approximation algorithm BEEP-DQN in the case of large state-action space to strike a balance between the running time and the performance. Abundant experiments based on real container sales data exhibit the rationality of C3-MDP and the effectiveness of BEEP.