Demirel, E., van Ommeren, J.N. and Rietveld, P. (2010). A matching model for the backhaul problem Transportation Research. Part B, Methodological, 44:549--561.

The 'backhaul problem' is characterized by an imbalance in transport flows between locations. In a perfectly competitive framework with perfect information, the price of transport from low demand locations to high demand locations, the so-called backhaul price, drops to zero when the imbalance is sufficiently large. However, this result is inconsistent with empirical observations for many competitive transport markets (e.g. taxi and inland navigation markets). In this paper, we develop a matching model to show that a deviation from perfect information may address this inconsistency. We argue that carriers' search time to locate customers plays an important role in the determination of prices. We demonstrate that carriers are compensated for a part of the transport cost and for the time they search for customers. This implies positive backhaul prices. The matching model is numerically applied to the inland navigation shipping market in the Rhine river area in Western-Europe. We find that backhaul prices are substantial. {\textcopyright} 2009 Elsevier Ltd. All rights reserved.