Dynamic trucking equilibrium through a freight exchange

This paper proposes a new hyperpath-based dynamic trucking equilibrium (DTE) assignment model. Unlike existing freight assignment models, we focus on the interactions between individual truck operators that solely compete for loads advertised on an online freight exchange. The competitors are assumed to follow optimal bidding and routing strategies – represented using a hyperpath – to maximize their expected profit. The proposed DTE model (1) predicts system-wide truck flows (including empty truck flows), (2) identifies efficiency improvements gained by network-wide visibility, and (3) lays the foundation for building a system optimal model. We rewrite the DTE conditions as a variational inequality problem (VIP) and discuss the analytical properties of the formulation, including solution existence. A heuristic solution algorithm is developed to solve the VIP, which consists of three modules: a dynamic network loading procedure for mapping hyperpath flows onto the freight network, a column generation scheme for creating hyperpaths as needed, and a method of successive average for equilibrating profits on existing hyperpaths. The model and the solution algorithm are validated by numerical experiments constructed from empirical data collected in China. The results show that the DTE solutions outperform with wide margin the benchmark solutions that either ignore inter-truck interactions or operate trucks according to suboptimal routing and bidding decisions.