Optimal pricing in iterative flexible combinatorial procurement auctions

In a combinatorial procurement auction with large demand volumes, bidders can find it challenging to carefully combine, evaluate and price different units of items in a package while at the same time considering their internal capacity and production costs. As opposed to static combinatorial procurement auctions, flexible procurement combinatorial auctions provide the bidders with the ability to reveal their price functions and therefore more efficiently communicate numerous variations of pricing for multiple units of items via concise bids. In this paper we propose a fully expressive bidding language for flexible combinatorial auctions. We define its associated winner determination problem, show that it is NP-hard and propose a Lagrangian-based approach to solve it. Optimal Lagrangian multipliers are used as proxies for auction item prices. The multipliers are also used in formulating the suppliers’ profit maximization problem to find their optimal bid quantities and prices while taking into account various levels of suppliers’ risk-taking attitudes. We analytically show the convergence of the iterative flexible auction. Our numerical experiments show that on average flexible iterative auctions generate lower market prices, require less computational effort and converge faster than their static counterpart. At termination, while the auctioneer secures lower procurement costs in a flexible auction, the total winning-suppliers’ profit slightly reduces due to price reduction in the auction.