A relative robust optimization for a vehicle routing problem with time-window and synchronized visits considering greenhouse gas emissions

The Paris Agreement appeals to all countries around the world for reducing greenhouse gas emissions. Nowadays, logistics companies do not only consider improving service quality and reducing operating costs but also should take a particular corporate social responsibility: reducing greenhouse gas emissions. Minimizing greenhouse gas emissions has been emerged in vehicle routing problems in many investigations, while most of the models are deterministic. The feedback from logistics practice reveals that the workers often encounter uncertainties when providing services to customers. The decisions made without considering uncertainties show less robustness when carrying the logistics activities according to the given scheduling. Consequently, in this study, this is the first attempt to develop a relative robust optimization model for a vehicle routing problem with synchronized visits and uncertain scenarios considering greenhouse gas emissions. In this study the greenhouse gas emissions is evaluated by the fuel consumption cost. Due to the NP-hard of the studied model, a hybrid tabu search and simulated annealing is proposed to solve it. The experimental results on the popularly used benchmark instances demonstrate that the proposed algorithm is efficient and effective. The comparison performed among the solutions obtained by different types of models has highlighted the importance of considering uncertainties. Then, the sensitivity analysis is performed to observe the change of fuel consumption cost with varying types of vehicles. Statistical analysis is carried out to further validate the different models. Finally, two bi-objective optimization based scenarios have been established to demonstrate the trade-off between GHG emissions and robustness indicators. The proposed models can be applied to some practical applications, such as logging truck routing planing.