Polyhedral Sampling for Multiattribute Preference Elicitation

Multiattribute auctions are now routinely used for B@B negotiations in electronic procurement. A basic requirement for running multiattribute auctions is a utility function of the buyer that trades off nonprice attributes against price. Such a utility function can then be used to design a (strategic) scoring function that communicates to the suppliers how the buyer will evaluate multtriatribute bids. One approach to eliciting the parameters and design a strategic scoring function that communicates to the suppliers how the buyer will evaluate multiattribute bids. One approach to eliciting the preference structure is to model it as polyhedra in the space of the parameters and design pair wise comparison to quickly narrow down the feasible region. In order to perform this in real time, we need efficient techniques for estimating the centroid and a cut that is perpendicular to the "longest axis" of the polyhedra thereby minimizing the feasible region for the parameters. In this paper, we present the use of a "hit-and-run" algorithm to also produce a cut that approximately minimizes the volume of feasible polyhedra. The advantage of this technique it its relative simplicity- it relies only on matrix algebra and avoids the use of nonlinear optimization techniques. Computational results suggest that this method is fast and accurate.