Reliable vehicle routing problem in stochastic networks with correlated travel times

This study is motivated by the fact that travel times on road networks are correlated. However, all existing studies on the vehicle routing problem share a common simplifying assumption that arc travel times are independently distributed. In this paper, we address a variant of the vehicle routing problem with soft time windows in which travel times are treated as correlated random variables. To this end, correlations among arc travel times are modeled by a variance-covariance matrix. We use a mathematical model in which penalties are incurred for early and late arrival at each customer (violation of time window constraints). A Max-Min ant colony system is hybridized with a tabu search algorithm to solve the model. Results show that ignorance of correlations among arc travel times can significantly lead to inefficient solutions to the vehicle routing problem in stochastic networks. We also conduct an exploratory analysis of real travel time data. The results of the analysis demonstrate that travel times are significantly correlated and the shifted log-normal distribution is an appropriate candidate for modeling travel time uncertainty.