Challenges and Advances in A Priori Routing

An a priori route is a route which specifies an ordering of all possible customers that a particular driver may need to visit. The driver may then skip those customers on the route who do not receive a delivery. Despite the prevalence of a priori routing, construction of these routes still presents considerable challenges. Exact methods are limited to small problem sizes, and even heuristic methods are intractable in the face of real-world-sized instances. In this chapter, we will review some of the ideas that have emerged in recent years to help solve these larger instances. We focus on the probabilistic traveling salesman problem and the recently introduced probabilistic traveling salesman problem with deadlines and discuss how objective-function approximations can reduce computation time without significantly impacting solution quality. We will also present several open research questions in a priori routing.