Modeling correlation in vehicle routing problems with makespan objectives and stochastic travel times

The majority of stochastic vehicle routing models consider travel times to be independent. However, in reality, travel times are often stochastic and correlated, such as in urban areas. We examine a vehicle routing problem with a makespan objective incorporating both stochastic and correlated travel times. We develop an approach based on extreme-value theory to estimate the expected makespan (and standard deviation) and embed this within a routing heuristic. We present results that demonstrate the impact of different correlation patterns and levels of correlation on route planning.