Solving Truckload Procurement Auctions Over an Exponential Number of Bundles

Truckload carriers provide hundreds of billions of dollars worth of services to shippers in the United States alone each year. Internet auctions provide these shippers with a fast and easy way to negotiate potential contracts with a large number of carriers. Combinatorial auctions have the added benefit of allowing multiple lanes to be considered simultaneously in a single auction. This is important because it enables carriers to connect multiple lanes in continuous moves or tours, decreasing the empty mileage that must be driven, and therefore increasing overall efficiency. On the other hand, combinatorial auctions require bidding on an exponential number of bundles to achieve full economies of scope and scale, which is not tractable except for very small auctions. In most real-world auctions, bidding is instead typically limited to a very small subset of the potential bids. We present an implicit bidding approach to combinatorial auctions for truckload procurement that enables the complete set of all possible bids to be considered implicitly, without placing the corresponding burden of an exponential number of bids on the bidders or the auctioneer. We present the models needed to solve this problem. We then provide extensive computational results to demonstrate the tractability of our approach. Finally, we conclude with numerical analysis to assess the quality of the solutions that are generated and to demonstrate the benefits of our approach over existing bidding methods in practice.