Copula-Based Joint Discrete–Continuous Model of Road Vehicle Type and Shipment Size

Abstract

A major issue in freight modeling is the interrelationship between logistics choices that can be seen as a learning process that shippers or carriers undertake to optimize their logistics process, with the aim of minimizing their cost, maximizing their level of service, or both. This study looked at the interrelated decisions of vehicle type choice and shipment size in urban freight transportation by formulating a model that considered ( a) the nature of these two dependent variables via a joint discrete–continuous model, ( b) the correlation between the two decisions via a copula-based approach, ( c) the differences in decision making between carriers and shippers via the estimation of two models, and ( d) the relaxation of the assumption of pure utility maximization via a hybrid utility–regret specification. Results show differences between shippers’ and carriers’ preferences. These differences were logical because many urban shippers owned an efficient fleet of commercial vehicles, whereas carriers evaluated alternatives to maximize their aggregated utility and minimize their direct costs. Results also show the importance of considering jointly the two decisions as well as the relevance of using a hybrid utility–regret formulation for the cost. Practical findings emerge from the model: ( a) when faced with night delivery and intercity trips, carriers were more likely to use heavier vehicles and more voluminous shipments, whereas smaller shipments were preferred during the afternoon peak hour; ( b) urban shippers tended to deliver larger shipments during night by light trucks but preferred trailers for longer distances; and ( c) commodity types played a role in these joint decisions because some commodities were more likely to be transported by for-hire carriers and others were more likely to be transported by shippers.