A bi-objective time-dependent vehicle routing problem with delivery failure probabilities

This work presents a bi-objective time-dependent vehicle routing problem with delivery failure probabilities (TDVRPDFP). Two objectives are jointly minimized: operational costs and delivery failure rates. Both travel times and costs, as well as the probabilities of delivery failure and service times and costs, are considered time-dependent. A mixed-integer linear programming model is proposed to obtain sets of non-dominated solutions for small-size instances, while a multi-objective genetic algorithm, NSGA-II, is implemented to obtain approximate sets of non-dominated for large-size instances. Five sets of instances are proposed and used to evaluate the solution approaches. Our results indicate that the implemented NSGA-II algorithm can optimally solve small and large instances and find large Pareto fronts for instances with more than 25 nodes and 40-time intervals.