Design of progressive auctions for procurement based on Lagrangian relaxation

Auction mechanisms have been found successful in implementing e-procurement, with the buyer as the auctioneer and the sellers as the bidders. Single round auctions are prevalently used in e-procurement, in which the suppliers submit sealed bids in response to the buyer's request-for-quote. The bid evaluation problem faced by the buyer is an optimization problem that selects the winning bids to minimize the cost of procurement. Though these auction types are advantageous in many scenarios, progressive auctions (multiple rounds) are preferred in terms of information elicitation and bid preparation. This paper demonstrates the design of progressive auctions, from their single-round counterparts, using Lagrangian relaxation. In particular, we show that an appropriate algorithm for a judiciously selected Lagrangian relaxation of the bid evaluation problem, can help in designing a progressive auction. The procurement of multiple units of a single item is considered with linear and piecewise linear supply curves.