Robust and Distributionally Robust Shortest Path problems: A survey

The availability of frequently updated and reliable data on traversal times of arcs in a network makes the study of non-deterministic Shortest Path problems of high importance nowadays. A large body of literature on robust and distributionally robust models is emerging, allowing reliable decisions to be taken that consider the worst-case condition. The literature differs in the assumptions made on the uncertainty of the traversal times, on the information available, and on the objective function that guides the optimization. In this paper, we review this literature with the goal of identifying open and relevant research directions. We present robust Shortest Path and Distributionally Robust Shortest Path problems including: static, with recourse, and dynamic robust problems; absolute and relative robust problems. For each area, a description of the models and solution approaches is given, with concise excerpts of the related works. Trends and possible research directions are outlined. We review 29 papers on this subject, classifying them in terms of problem description, model characteristics and proposed solution methods. • Arc traversal data supports the study of non-deterministic shortest path problems. • Literature on robust models enables decisions accounting for worst-case scenarios. • The literature is reviewed to classify approaches and identify key research gaps. • The most relevant papers are reviewed, classified by problems, models, and solution methods.