Coordinating Multi-Attribute Reverse Auctions Subject to Temporal and Capacity Constraints Jiong Sun and Norman M. Sadeh e-Supply Chain Management Laboratory – ISRI – School of Computer Science Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213-3891, USA jiongs@andrew.cmu.edu and sadeh@cs.cmu.edu Abstract Over the past few years, reverse auctions have attracted a lot of attention in the AI community. They offer the prospect of more efficiently matching suppliers and producers in the face of changing market conditions. Prior research has generally ignored the temporal and finite capacity constraints under which reverse auctioneers typi- cally operate. In this paper, we consider the problem faced by a reverse auctioneer (e.g. a manufacturer) that can procure key components or services from a number of possible suppliers through multi-attribute reverse auctions. This problem can also be viewed as a static abstraction of the procurement problem faced by agents in the new TAC’03 Supply Chain Trading Competition. Bids submitted by prospective suppliers include a price and a delivery date. The reverse auctioneer has to select a combination of supplier bids that will maximize its overall profit, taking into ac- count its own finite capacity and the prices and delivery dates offered by different suppliers for the same components/services. The auctioneer’s profit is determined by the revenue generated by the products it sells, the costs of the compo- nents/services it purchases as well as late delivery penalties it incurs if it fails to deliver prod- ucts/services in time to its own customers. We provide a formal model of this important class of problems, discuss its complexity and introduce rules that can be used to efficiently prune the resulting search space. We also introduce a branch-and-bound algorithm and an efficient heuristic search procedure for this class of prob- lems. Empirical results show that our heuristic procedure typically yields solutions that are within 10 percent of the optimum. They also in- dicate that taking into account finite capacity considerations can significantly improve the re- verse auctioneer’s bottom line. Keywords: Supply Chain Formation, Procurement, Reverse Auction, Finite Capacity Scheduling, Branch-and-Bound, Heuristic Search 1 Introduction Today’s global economy is characterized by fast changing market demands, short product lifecycles and increasing pressures to offer high degrees of customization, while keeping costs and lead times to a minimum. In this con- text, the competitiveness of both manufacturing and ser- vice companies will increasingly be tied to their ability to identify promising supply chain partners in response to changing market conditions. Today, however dynamic supply chain practices are confined to relatively simple scenarios such as those found in the context of MRO (Maintenance, Repair and Operations) procurement. The slow adoption of these practices and the failure of many early electronic marketplaces can in part be attributed to the one-dimensional nature of early solutions that forced suppliers to compete solely on the basis of price. Similarly, research in the area has generally ignored key temporal and capacity constraints under which most re- verse auctioneers operate. For instance, a PC manufacturer can only assemble so many PCs at once and not all PCs are due at the same time. Such considerations can be used to help the PC manufacturer select among bids from com- peting suppliers. In this paper, we summarize research aimed at exploiting these temporal and capacity con- straints to help a reverse auctioneer select among com- peting multi-attribute procurement bids that differ in prices and delivery dates. We refer to this problem as the Finite Capacity Multi-Attribute Procurement (FCMAP) problem. It is representative of a broad range of practical reverse auctions, whether in the manufacturing or service industry. We start by providing a formal definition of the FCMAP problem, discuss its complexity and introduce several rules that can be used to prune its search space. We then present a branch-and-bound algorithm and a heuristic search procedure along with empirical results showing that accounting for the reverse auctioneer’s finite capacity can significantly improve its bottom line. The balance of this paper is organized as follows. Section 2 provides a brief review of the literature. In section 3, we introduce a formal model of the FCMAP problem. Section 4 identifies three rules that can help the reverse auctioneer eliminate non-competitive bids or bid combinations. Sec-