Finding Efficient and Environmentally Friendly Paths for Risk-Averse Freight Carriers

Abstract

This paper aims to incorporate two important measures into a freight shortest path problem, namely reliability and sustainability. Reliability measure deals with the uncertainty of link travel time while sustainability measure tends to reduce the fuel consumption and emission along the path. Greenhouse gas (GHG) emission rates are generated from Motor Vehicle Emission Simulator (MOVES) model and approximated as a function of the average link travel speed. To model uncertainty, the link travel speed is treated as a discrete random variable with a given distribution. Freight carriers are assumed to be risk-averse; for example, given two paths with the same average cost, carriers prefer the one with less variability. The risk-averse behavior is captured by the second order stochastic dominance (SSD) relationship. Specifically, SSD constraints are introduced in our model to narrow down the feasible paths which dominate a chosen benchmark path. The reliable and sustainable routing model is formulated as an integer program that can be easily tailored to a variety of modeling preferences. The study experiments with eight variants of the base model, each corresponding to a different trade-off strategy between three objectives, namely, efficiency, reliability and sustainability. The numerical experiments illustrate the benefits of the models discussed in the paper.