Modeling Uncertain Travel Times in Distribution Logistics

Uncertainty quantification is a critical aspect of distribution logistics, particularly unpredictable travel times caused by traffic congestion and varying transportation conditions. This paper explores the modeling of uncertainty in dealing with travel times in the context of distribution logistics using the collocation method. First, we employ Monte Carlo simulations to assess the efficacy of the collocation method in modeling the variability and uncertainty associated with travel times. Second, we implement the collocation method in Casablanca, Morocco, a city renowned for its extensive distribution logistics operations and its dynamic traffic. Four distinct scenarios are considered: morning peak, inter-peak, evening peak, and off-peak periods. Our study explores two scenarios: one with recurrent congestion, representing typical daily conditions, and the other with unpredictable uncertainties in travel times, accounting for unexpected events that may occur during a distribution day. Our research findings enhance our understanding of the probabilistic nature of travel times in distribution logistics. This knowledge provides valuable insights applicable to both routine situations with recurrent congestion and non-recurrent congestion. The results' findings contribute to a better understanding of the probabilistic nature of travel times in distribution logistics, offering valuable insights for optimizing route planning and scheduling.