In this paper we extend the notion of multi-unit combinatorial reverse auction by adding a new dimension to the goods at auction. In such a new type of combinatorial auction a buyer can express substitutability relationships among goods: some goods can be substituted with others at a substitution cost. Substitutability relationships allow a buyer to introduce his uncertainty as to whether it is more convenient to buy some goods or others. We introduce such uncertainty in the winner determination problem (WDP) so that not only does the auction help allocate the optimal set of offers —taking into account substitutability relationships—, but also assesses the substitutability relationships that apply. In this way, the buyer finds out what goods to buy, to whom, and what operations (substitutions) to apply to the acquired goods in order to obtain the initially required ones.
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