Approximation approach for robust vessel fleet deployment problem with ambiguous demands

This paper studies the vessel fleet deployment problem for liner shipping under uncertain shipment demands. The aim is to minimize the sum of vessel chartering cost and route operating cost, while controlling the risk of shipment demand overflow, i.e., the risk of demand exceeding the shipping capacity. We use moment knowledge to construct an ambiguous set to portray the unknown probability distributions of the demands. We establish chance constraints with risk tolerance for shipping service routes, in a distributionally robust (DR) framework. We propose a mixed integer programming reformulation to approximate the concerned problem with DR chance constraints. We show that the state-of-the-art approach is a special case of our designed approximation method, and we prove the sufficient and necessary conditions such that our approximation method outperforms the state-of-the-art approach, respecting the given risk level. We conduct numerical experiments to demonstrate the advantages of our approximation method. We also show that our novel approximation approach can significantly save the total cost.