Combinatorial clock-proxy exchange for carrier collaboration in less than truck load transportation

•A carrier collaboration problem in LTL transportation is studied.•Combinatorial clock-proxy exchange is applied to the problem for the first time.•This mechanism is better adapted to the problem than combinatorial auctions.•Experimental results are quite promising.•They show the indispensability of the proxy phase of the mechanism.

A carrier collaboration problem in less-than-truck load transportation is considered, where multiple carriers exchange their pickup and delivery requests in order to improve their operational efficiency. We extend the clock-proxy auction proposed by Ausubel et al. (2006) to a combinatorial clock-proxy exchange for the problem. This mechanism combines the price discovery of the clock exchange designed based on Lagrangian relaxation with the efficiency of the proxy exchange determined based on the information observed in the clock phase. Numerical experiments on randomly generated instances demonstrate the necessity of the proxy phase and the effectiveness of the clock-proxy exchange.