Bid Evaluation in Procurement Auctions with Piecewise Linear Supply Curves

Abstract

Consider a marketplace operated by a buyer who wishes to procure large quantities of several heterogeneous products. Suppliers submit price curves for each of the commodities indicating the price charged as a function of the supplied quantity. The total amount paid to a supplier is the sum of the prices charged for the individual commodities. It is assumed that the submitted supply curves are piecewise linear as they often are in practice. The bid evaluation problem faced by the procurer is to determine how much of each commodity to buy from each of the suppliers so as to minimize the total purchase price. In addition to meeting the demand, the buyer may impose additional business requirements that restrict which contracts suppliers may be awarded. These requirements may result in interdependencies between the commodities which lead to suboptimal results if the commodities are traded in independent auctions rather than simultaneously. Even without the additional business constraints the bid evaluation problem is NP-hard. The main contribution of our study is a flexible column generation based heuristics that provides near-optimal solutions to the procurer's bid evaluation problem. Our method scales very well due to the Branch-and-Price technology it is built on. We employ sophisticated rounding and local improvement heuristics to obtain quality solutions. We also developed a test data generator that produces realistic problems and allows control over the difficulty level of the problems using parameters.

Agent-based formation of virtual organisations

“…Using our correlation function, this can be expressed by adding segments t 1 and t 2 ; which contain only 100 and 50, to the functions P This means of representing bids is novel and superior to popular bid representations. Compared with other work in this area [9,19] it is more expressive as it allows bidders to detail the correlation between separate items. Compared to XOR atomic proposition presentations, it is nearly as expressive but much more compact.…”

“…Compared to XOR atomic proposition presentations, it is nearly as expressive but much more compact. Moreover, this case is important to consider because piecewise linear curves are commonly used in industrial trading applications [9] and any general curve can be approximated arbitrarily closely by a family of such functions [19].…”

Compact bidding languages and supplier selection for markets with economies of scale and scope

“…Their bidding language requires suppliers to specify continuous supply curves for each item. Eso et al (2001) further advance the ideas described in Davenport and Kalagnanam (2000) and allow for discontinuities and decreasing slopes in the bids. They use a branch-and-price approach to solve the winner determination problem.…”

Auction-Based Mechanisms for Electronic Procurement

“…See [55] for a comprehensive tabulation of business constraints that are observed in practice. With inclusion of business constraints, the winner determination problem becomes a mixed integer programming problem (MIP) [17], [56]. In the following subsection, we first present the mathematical formulation of a volume discount auction problem adapted from [54], [56] and then discuss the computational issues that arise in determining the winning bids.…”