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Description
This article studies iterative multi-attribute auctions for multi-unit procurement. Order splitting among suppliers is allowed in auctions to improve efficiency and take advantage of suppliers' cost structures. Suppliers are also allowed to provide discriminative prices over units based on their cost structures. A mechanism called iterative multi-attribute multi-unit reverse auction (IMMRA) is proposed based on the assumption of the modified myopic best-response strategies. Results from numerical experiments show that the IMMRA achieves market efficiency in most instances. The inefficiency occurs occasionally in special cases when cost structures are significantly different among suppliers. Numerical results also show that the IMMRA results in lower buyer payments than the traditional Vickrey-Clarke-Grove (VCG) payments in most cases without significantly hurting market efficiency.
INTRODUCTION
With the rapid growth of Internet technologies, online reverse business-to-business (B2B) auctions have become common. Online reverse auction mechanisms in the literature fall into three categories: multi-item auctions, multi-unit auctions, and multi-attribute auctions. Between the first two auction forms, multi-item auctions deal with heterogeneous items to be auctioned off while multi-unit auctions treat multiple units of homogeneous goods. Both multi-item auctions and multi-unit auctions focus on price-only negotiations and their optimal solutions find the supplier(s) with the lowest cost. The value of the goods or services for the buyer is assumed to be predetermined and the same, no matter which supplier is chosen as the winner. In reality, in addition to price, other attributes such as quality and other specifications may influence the buyer's value of the goods or services. In this setting, multi-attribute reverse auctions are proposed as electronic request for quotation (eRFQ) buying processes in the auction literature (Strecker and Seifert, 2004) to consider multiple attributions. In an RFQ process, a corporate buyer announces a set of negotiable attributes, such as quality, lead-time, and technical specifications, for the bidding product. Each attribute has several possible levels; for example, lead-time could be one week, half a month, or two months. Potential suppliers are invited to submit bids on one or several attribute-level bundles. The attribute-level bundle is defined as a combination of selections with one and only one level for each product attribute. The traditional RFQ process terminates with an outcome of one winner and a single selected attribute-level bundle. There are two computational challenges in traditional RFQ buying processes: the evaluation of bids for suppliers and the winner determination for the auctioneer (or the buyer) (Parkes and Kalagnanam 2005; Bichler and Kalaganam, 2005).
If the suppliers' marginal costs of each attribute-level bundle are fixed and independent from the quantity, a multi-attribute reverse auction with multiple units is reduced to the single-unit procurement, and a single supplier wins the entire sourcing contract. However, the marginal costs of suppliers, especially in various manufacturing and power industries, are variable because of setup costs, variable costs, capacity constraints, or other factors. Therefore, economies and diseconomies of scale cannot be ignored in analysis of online procurements (Jin et al., 2006). Economies of scale justify procurement agreements with quantity discounts, which are widely considered in the procurement literature (Tenorio, 1999). Hohner et al., (2003) give a realistic case with quantity discounts in procurement auctions. With variable marginal costs, allowing the split of the sourcing contract among multiple suppliers may achieve more cost-efficient outcomes for both the buyer and the overall system. Jin et al. (2006) provide examples with splitting among suppliers in multiple-unit auctions.
In this article, auctions with multiple attributions and multiple units are considered. An iterative multi-unit, multi-attribute reverse auction mechanism is proposed for multi-attribute procurements with suppliers' variable marginal costs. The mechanism allows the contract to be split among winning suppliers. However, the mechanism requires all winners to provide the products or services with the same attribute-level bundle. Most corporate buyers have this homogeneous requirement (the same level for all attributes) to simplify management, reduce future maintenance cost, and preserve the same add-on values for their customers. Parkes and Kalagnanam (2005) designed an iterative additive and discrete (AD) auction for a special case of the multi-attribute allocation problem with the assumption of additive structure on the buyer's valuation and suppliers' costs. The AD auction quotes prices on each attribute. We generalize it into the auction with bidding on each attribute-level bundle by relaxing the assumptions of additive structure and preferential independence (Keeney and Raiffa, 1993). Introducing the concept of attribute-level bundle increases the computational complexity for suppliers to evaluate their bids but extends the auction to a more general setting. This article formulates a mathematical programming model to optimize the market allocation. The results of computer-based numerical experiments are used to compare the performance of the multi-attribute reverse auction with the reverse Vickrey-Clarke-Grove (VCG) auctions.
The following section reviews related work on multi-attribute reverse auctions and multi-unit auctions. The mathematical programming model that solves the winner allocation problem in the proposed multi-attribute multi-unit reverse auction is presented in the following section, followed by a discussion of the details of the mechanism design and theoretical analysis and an example to illustrate the proposed mechanism. Numerical experiment results are presented next and the article concludes with a discussion of the advantages and disadvantages of the proposed auction mechanism and provides future work directions.
LITERATURE REVIEW
In the literature of multi-attribute auctions, Che (1993) first presents two-dimensional reverse auctions in which a group of suppliers bid on both price and quality. The bids are evaluated by an ex ante scoring rule announced by the buyer. By defining each supplier's cost structure as an independent increasing function in quality with an unknown parameter, three sealed-bid auction mechanisms are developed to maximize the expected buyer profits. With her strong commitment power, the buyer can implement the optimal scoring rule. Branco (1997) relaxes Che's assumption of independent supplier cost functions and studies the impact of cost correlation on the multi-attribute auctions. Considering three product attributes--price, quality, and lead time--Chen Ritzo et al. (2005) compare the multi-attribute auctions with the price-only auctions. If the quality and lead-time utility functions are known to the auctioneer, the multi-attribute auctions outperform the price-only auctions always on the buyer's profit and occasionally on sellers' profits in the standard English auctions. Beil and Wein (2003) extend Che's auction to a more general iterative mechanism. In their paper, a supplier's cost function of each attribute is assumed to have P parameters. It is also assumed that the structure of suppliers' cost functions is exposed to the auctioneer while the P parameters are private information held by the suppliers. An iterative auction mechanism with P + 1 rounds is designed for the auctioneer (the buyer) to derive the P parameters in suppliers' cost functions of attributes. With all revealed information, the buyer determines the optimal scoring functions in the [(P+ l).sup.st] round to maximize her expected profit. Parkes and Kalagnanam (2005) developed an iterative price-based reverse auction that provides an equilibrium outcome of the modified Vickrey-Clarke-Groves (VCG) auctions. Instead of focusing on the buyer's profits, they consider an efficient design for the market that includes the buyer and all the suppliers. Under the assumptions of additive cost components (Bichler and Kalagnanam 2005) and preferential independence (Keeney and Raiffa 1993), all suppliers submit bids in the forms of additive price parts for each attribute level after evaluating the ask price from the buyer and their own cost structures. By assuming fixed marginal costs, Parkes and Kalagnanam (2005) proposed a single-item multi-attribute auction that can be easily extended to homogeneous multi-unit procurement. For heterogeneous items, the combinatorial allocation problem (CAP) is studied as multi-item auctions in Benoit and Krishna (2001), Rothkopf et al. (1998), Bikhchandani (1999), and others. Bichler et al. (2003) studied multi-attribute reverse auctions in the case of multiple sourcing rather than one single supplier. They also extended the multi-attribute reverse auctions to the concept of configurable offers and developed mathematical models for the winner determination problems under different situations and analyzed the computational complexity.... |
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