A novel multi-objective green vehicle routing and scheduling model with stochastic demand, supply, and variable travel times

We propose an optimization approach to the routing and scheduling problem for a heterogeneous transportation network that considers (i) stochastic values of demand and supply at the nodes, (ii) variable travel times between nodes conditioned by the fatigue of drivers, (iii) maximum allowed continuous driving time, and (iv) soft service time windows per customer at the nodes. The problem minimizes energy consumption and maximizes customer satisfaction. The subsequent stochastic multi-objective mixed integer programming model is solved using a hybrid approach based on chance- and epsilon-constraint methods. Given the NP-hard quality of the model, we introduce a hybrid meta-heuristic method based on genetic algorithm (GA) and simulated annealing (SA). This novel technique, named MOGASA, combines the global and local search capacities of both meta-heuristic algorithms, providing an intuitive solution approach that allows to solve problem instances considering large distribution networks with multiple types of vehicles in reasonable CPU time. We illustrate how MOGASA improves upon the hybrid chance- and epsilon-constraint exact solution method, particularly when dealing with large problem instances that cannot be solved by the latter. A medium instance scenario is used to analyze the reaction of the objective functions and the subsequent Pareto frontiers to modifications in the main structural parameters defining the transportation network. Potential applications of our stochastic framework to different types of logistic structures and retail supply chains are highlighted.