Two-stage distributionally robust optimization for maritime inventory routing

This work addresses uncertain sailing times and uncertain waiting times at ports in a maritime inventory routing problem (MIRP). As the probability distribution of these uncertain parameters is difficult to es-timate and hence not known exactly, we propose a two-stage distributionally robust optimization (DRO) approach in which the uncertainty is described by a Wasserstein ambiguity set. Our model is based on a continuous-time arc-flow mixed integer linear programming (MILP) formulation of the MIRP, and an equivalent robust counterpart of the two-stage DRO problem is derived under the 1-norm Wasser-stein metric. We also develop a tailored Benders decomposition algorithm that combines the strengths of Pareto-optimal and high-density cuts to solve large-scale model instances. Computational case stud-ies, including a real-world industrial case considering the maritime transportation of refined diesel along the east coast of China, demonstrate the benefits of the DRO model and the effectiveness of the pro-posed Benders decomposition algorithm. In general, compared to a traditional stochastic programming approach, the DRO model yields routing solutions that are significantly less sensitive to variations in sail-ing and port waiting times, and exhibit improved out-of-sample performance. ? 2021 Elsevier Ltd. All rights reserved.