A Continuous Approximation Model for the Vehicle Routing Problem for Emissions Minimization at the Strategic Level

This paper presents a continuous approximation model for the Vehicle Routing Problem for Emissions Minimization (EVRP) and demonstrates the model’s applicability and usefulness with numerical studies based on implementations of the Solomon test instances. The EVRP is a variant of the Time Dependent Vehicle Routing Problem (TDVRP) in which minimizing emissions is an additional objective of the model. The continuous approximation model presented in this paper will facilitate strategic planning of one-to-many distribution systems and evaluate the effects of emissions costs. Furthermore, results from the continuous model can provide guidelines for constructing solutions for the discrete EVRP. Furthermore, results from a sensitivity analysis indicated that the optimal number of dispatches during the peak period is smaller than the optimal number of dispatches during the off-peak period when considering the temporal effects of congestion. Results revealed that the potential cost savings due to incorporating emissions in distribution problems are considerable. Incorporating emissions costs in distribution problems will contribute toward having more environmentally sustainable distribution systems. The proposed continuous approximation model can be extended for other specific conditions, e.g. when considering pipeline inventory, storage restrictions, different customers, random demand, discriminating strategies, etc.