Impact of travel time uncertainties on the solution cost of a two-echelon vehicle routing problem with synchronization

Two-echelon vehicle routing problems which contain synchronization between vehicles can be deeply impacted by time uncertainty, because one vehicle’s delay can propagate to other vehicles. In this paper, we evaluate the deterministic solution of such a problem based on simulated travel time scenarios. The information obtained by simulation is incorporated in the optimization procedure iteratively. Computational results show that the degree of synchronization in an instance is directly correlated with the potential improvements by reoptimization. We present findings on the number of travel time scenarios required to obtain a representative picture of the stochastic solutions. In addition, we demonstrate that time dependent travel times can be aggregated on a city-wide level and linearized as a function of free flow times without major loss of reliability.