No abstract

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. Model 1 requires minimizing the due date subject to a service level constraint. Model 2 addresses a weighted trade-off between the due date and the expected tardiness. Both models require safety time and therefore the distribution of the tour length is important. In alternate formulations the due date is given and we maximize the service level for Model 1 or minimize the expected tardiness for Model 2. In an unpublished working paper (available as a web resource), we addressed normal travel times. In this paper we recap some of those results and extend them to lognormal travel times. In general, we show that Alternate 1 is equivalent to Model 1, but Alternate 2 is different to Model 2. For the normal distribution, we solve optimally for Model 2 and for Model 1 with service level 50% and higher by solving few deterministic TSP derived models. For other instances, including all lognormal models, we provide effective heuristics and tight performance guarantee certificates. As a by-product of our TSP analysis, we obtain comparable results for the shortest route problem.