Simplified Bidding and Solution Methodology for Truckload Procurement and Other Vcg Combinatorial Auctions

Abstract

In theory, combinatorial auctions can provide significant benefits in many real-world applications, such as truckload procurement. In practice, however, the use of such auctions has been greatly limited by the need for bidders to bid on an exponential number of bundles and for the auctioneer to solve an exponentially large winner-determination problem. We address these challenges for VCG combinatorial procurement auctions in which a bidder's cost for each bundle is determined by a cost function with an amenable structure. For example, the cost to a trucking company of servicing a bundle of loads is based on the least-cost set of tours covering all of these loads, which can be found by solving a simple minimum cost flow problem. Leveraging the fact that true-cost bidding is a dominant strategy in VCG auctions, we suggest that the bidders' challenges can be overcome by specifying this true-cost function explicitly as a bid, rather than computing and communicating each bid individually. Moreover, we propose to embed this true-cost function directly within the winner-determination problem, using the strength of mathematical programming to solve this problem without ever explicitly enumerating the bids. The research challenge is then to identify this cost function, and formulate and solve the corresponding winner-determination problem. We focus primarily on how this can be done for the truckload procurement problem, outline a more general framework for the approach, and identify a number of other promising applications.

Keywords: Combinatorial Auction, Procurement, Mathematical Programming, Truthful Bidding, Mechanism Design

JEL Classification: D44, C61