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

Abstract

D ue 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 CO 2 emissions costs. Specifically, we propose a framework for modeling CO 2 emissions in a time-dependent vehicle routing context. The model is solved via a tabu search procedure. As the amount of CO 2 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 timedependent 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 CO 2 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.

A review of recent research on green road freight transportation

“…Another application of MEET is due to Jabali et al (2012) who have investigated travel times and CO 2 emissions in the context of the TDVRP by analyzing the effect of limiting vehicle speed. The authors also addressed the issue of congestion, where the vehicle is forced to drive slower and therefore emits more CO 2 .…”

A Lagrangian Relaxation-Based Solution Method for a Green Vehicle Routing Problem to Minimize Greenhouse Gas Emissions

“…Constraints (14) and (15) ensure that each customer is visited only once by a single vehicle. Constraint (16) states that each vehicle carries no more than the vehicle capacity. By Constraint (17), each vehicle's duration of trip must be less than the maximum vehicle operating time.…”

“…Thus, the problem becomes how to find the "hard" constraints and calculate the Lagrangian multipliers. In our formulation, the "hard" constraints are Constraints (16) and (17). If those constraints are lifted into the objective function, the Lagrangian relaxed formulation for GVRP can be transformed as follows.…”

“…In the above Lagrangian-relaxed formulation, the amount of violations in the hard constraints (Constraints (16) and (17)) is multiplied by their dual variables (Lagrangian multipliers) and included in the objective function. Since the original problem is relaxed, it is easier to solve and provides a lower bound of the optimum (in the case of the minimization problem).…”

A bi-objective mathematical model for two-dimensional loading time-dependent vehicle routing problem

“…However, they did not develop any mathematical model based on this property, as their focus was on the use of heuristic methods to solve the problem. The mathematical model developed by Jabali et al (2012) for time-dependent vehicle routing problem relied on FIFO property. But the disadvantage of that model is the presence of instant jumps in the speeds of different time periods, which is not realistic.…”