The probabilistic traveling salesman problem with time windows

Abstract

With time-definite services occupying a large part of the delivery business, the explicit consideration of time windows into a route design has the potential to reduce transportation costs and the penalty costs associated with late deliveries. In this paper, we incorporate time windows into a priori routes by introducing the probabilistic traveling salesman problem with time windows (PTSPTW). The PTSPTW is an extension of the well-known probabilistic traveling salesman problem, where in addition to stochastic customer presence, each customer has an associated time window during which deliveries must be made. We present a recourse model and a variable neighborhood search with variable neighborhood descent algorithm to solve problem instances. We also present computational experiments that demonstrate the value of incorporating stochasticity into the problem.