Continuous Approximation Model for the Vehicle Routing Problem for Emissions Minimization at the Strategic Level
Publication: Journal of Transportation Engineering
Volume 138, Issue 11
Abstract
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. 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 attributable 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.).
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Acknowledgments
The authors gratefully thank Karen Smilowitz, Timothy Sweda, and Madison Fitzpatrick from Northwestern University for their review and feedback. Also, the authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.
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Information
Published In
Journal of Transportation Engineering
Volume 138 • Issue 11 • November 2012
Pages: 1368 - 1376
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Oct 7, 2011
Accepted: Apr 25, 2012
Published online: Oct 15, 2012
Published in print: Nov 1, 2012
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