A matching model for the backhaul problem

The ‘backhaul problem’ is characterized by an imbalance in transport flows between locations. This problem is usually studied in a perfectly competitive framework, which essentially predicts that when the imbalance is sufficiently large, the freight price of transport from low demand regions to high demand regions, the so-called backhaul price, drops to zero. This result is inconsistent with empirical observations. In this paper, we develop a matching model to address this inconsistency. We argue that market friction, through search imperfections due to lack of information by carriers on the (future) demand for transport by customers, may play an important role in the determination of backhaul prices. We demonstrate that carriers are at least compensated for the time they search for customers, so the backhaul price is in general positive. The matching model is numerically applied to the inland navigation shipping market in the Rhine river area in Western-Europe. We also analyse the effects of increases in transport costs on transport flows and backhaul prices, e.g. due to climate changes.