Vessel deployment with limited information: Distributionally robust chance constrained models

This paper studies the fundamental vessel deployment problem in the liner shipping industry, which decides the numbers of mixed-type ships and their sailing frequencies on fixed routes to provide sufficient vessel capacity for fulfilling stochastic shipping demands with high probability. In reality, it is usually difficult (if not impossible) to acquire a precise joint distribution of shipping demands, as they may fluctuate heavily due to the fast-changing economic environment or unpredictable events. To address this challenge, we leverage recent advances in distributionally robust optimization and propose distribution-free robust joint chance constrained models. In the first model, we only assume support, mean as well as lower order dispersion information of the shipping demands and provide high-quality solutions via a sequential convex optimization algorithm. Comparing with existing literature that chiefly studies individual chance constraints based on concentration inequalities and the union bound, our approach yields solutions that are less conservative and less vulnerable to the magnitude of demand dispersion. We also extend to a data-driven model based on the Wasserstein distance, which suits well in situations where limited historical demand samples are available. Our distributionally robust chance constrained models could serve as a baseline model for vessel deployment, into which we believe additional practical constraints could be incorporated seamlessly.