Stochastic Traveling Salesperson Models with Safety Time

We address the stochastic traveling salesperson problem (TSP) with distances measured by travel time. We study how to select the best tour and due date for the minimization of fundamental safe scheduling objectives. In Model 1 the objective is minimizing the due date subject to a service level constraint. In Model 2 the objective reflects a trade-off between the due date and the expected weighted tardiness. Both models involve safety time and therefore the distribution of the tour length is important. We also consider an alternate formulation of Model 1 in which the due date is given. We show that the model 1 alternate is equivalent to model 1. We solve for a large subset of parameters, and for other instances, we provide an effective heuristic and tight performance guarantee certificates. Acknowledgement: We are grateful to the developers of the Concorde software for making it freely available for academic research. In particular, Bill Cook has generously provided useful advice and insights. We also wish to thank Ken Baker for detailed and helpful comments.