An Ascending Auction for Freight Forwarder Collaboration in Capacity Sharing

In the highly competitive transportation market, small freight forwarders can form an alliance to secure capacity in advance and then share the capacity to fulfill their shipping requests during the freight season. Because not all the requests can be accepted, the rejected requests can be outsourced to the spot market typically at low profit margins. The forwarders are self-interested and have private information on the revenues and outsourcing profit margins of their requests. The centralized capacity-allocation problem is NP -hard, and its optimal solution may erode the profits of some forwarders. We propose an ascending auction mechanism to achieve truthful and approximately optimal capacity sharing. At each iteration of the auction, the set of bundles of capacity for each request is updated. The mechanism then determines a provisional capacity allocation and updates dual prices. Each request is allocated with a convex combination of bundles because a continuous capacity resource is considered. Strategy-proofness is ensured because all the winning bundles for an accepted request have the same payment, and the payment is ascending during the iterations. The mechanism iteratively expands the set of bundles and approximates the revenue loss to search optimal allocations, using the dual solution derived from minimizing primal-dual slackness. Social welfare is significantly improved compared with the no-collaboration case. We prove that the mechanism is strategy-proof, individually rational, weakly budget balanced, and finitely convergent. Extensive computational experiments show that the mechanism has efficiency loss less than 3% and budget surplus less than 10% in most cases. To achieve high system efficiency and small budget surplus with a reasonable computational time, it is better to select an appropriately small bid increment, especially for large-scale problems.