In this paper we address optimal routing problems in networks where travel times are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. Nevertheless, in some particular cases an origin–destination path must be chosen a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is an NP-hard problem. In this paper, we propose a solution method for the a priori shortest path problem, and we show that it can be easily extended to the ranking of the first K shortest paths. Our method exploits the solution of the time-adaptive routing problem as a relaxation of the a priori problem. Computational results are presented showing that, under realistic distributions of travel times and costs, our solution methods are effective and robust.
European Journal of Operational Research, 2014, Vol 236, Issue 3, p. 903-914