Network Flow Methodology for Estimating Empty Trips in Freight Transportation Models

Abstract

Commodity-based freight transportation models, for example, the Freight Analysis Framework, transform volumes of commodities into traffic flow by the application of vehicle use factors. However, these models cannot accurately capture the number of empty trips that result as a consequence of the movement of these commodities. Previous research has proposed a number of methodologies to incorporate empty trips as a function of loaded trips and some assumptions about the trip chains. Parameters in these models are calibrated with extensive origin–destination surveys. However, freight transportation data are usually scarce or not available in proper form for use in models. This paper presents a novel methodology to estimate the number of empty trips on the basis of a time-expanded network flow approach that captures the behavioral and operational characteristics of the carriers. The model was formulated as a linear optimization problem that minimized the system costs associated with truck trips. The model was validated with a commercial vehicle survey from Colombia. The results showed that under some operational assumptions, the model appropriately represented the amount of empty vehicle hours in a freight transportation network.