A decomposition based approach for design of supply aggregation and demand aggregation exchanges

Combinatorial exchanges are double sided marketplaces with multiple sellers and multiple buyers trading with the help of combinatorial bids. The allocation and other associated problems in such exchanges are known to be among the hardest to solve among all economic mechanisms. In this paper, we study combinatorial exchanges where (1) the demand can be aggregated, for example, a procurement exchange or (2) the supply can be aggregated, for example, an exchange selling excess inventory. We show that the allocation problem in such exchanges can be solved efficiently through decomposition when buyers and sellers are single minded. The proposed approach decomposes the problem into two stages: a forward or a reverse combinatorial auction (stage 1) and an assignment problem (stage 2). The assignment problem in Stage 2 can be solved optimally in polynomial time and thus these exchanges have computational complexity equivalent to that of one sided combinatorial auctions. Through extensive numerical experiments, we show that our approach produces high quality solutions and is computationally efficient