On the one-commodity pickup-and-delivery traveling salesman problem with stochastic demands

We study how to set the vehicle capacity for traveling Salesman Problems where some of the customer demands are stochastic. The analyses are done for the one-commodity pickup-and-delivery TSP, as this problem also includes the setting of the initial load. We first consider feasibility issues. This includes finding the smallest vehicle capacity and some initial load such that a given tour is feasible for all scenarios. Different variants are considered as a function of the time when information becomes available. We then analyze the case where some penalties are paid for routing a tour unable to handle customer demands. Various types of penalties are considered. We study properties of the minimal expected penalty of a given tour, which are then used to provide approaches to find near-optimal tours. Computational results are presented.