Analysis of Travel Times and CO2 Emissions in Time‐Dependent Vehicle Routing

Due to the growing concern over environmental issues, regardless of whether companies are going to voluntarily incorporate green policies in practice, or will be forced to do so in the context of new legislation, change is foreseen in the future of transportation management. Assigning and scheduling vehicles to service a pre‐determined set of clients is a common distribution problem. Accounting for time‐dependent travel times between customers, we present a model that considers travel time, fuel, and CO₂ emissions costs. Specifically, we propose a framework for modeling CO₂ emissions in a time‐dependent vehicle routing context. The model is solved via a tabu search procedure. As the amount of CO₂ emissions is correlated with vehicle speed, our model considers limiting vehicle speed as part of the optimization. The emissions per kilometer as a function of speed are minimized at a unique speed. However, we show that in a time‐dependent environment this speed is sub‐optimal in terms of total emissions. This occurs if vehicles are able to avoid running into congestion periods where they incur high emissions. Clearly, considering this trade‐off in the vehicle routing problem has great practical potential. In the same line, we construct bounds on the total amount of emissions to be saved by making use of the standard VRP solutions. As fuel consumption is correlated with CO₂ emissions, we show that reducing emissions leads to reducing costs. For a number of experimental settings, we show that limiting vehicle speeds is desired from a total cost perspective. This namely stems from the trade‐off between fuel and travel time costs.