On the Sensitivity of Incremental Algorithms for Combinatorial Auctions

Despite the large amounts of runtime needed to adequately solve a combinatorial auction (CA), existing iterative CA auction protocols require winner determination during every round of bid submissions. Using existing algorithms for winner determination will cause a timing bottleneck during the winner determination phase. Furthermore, there has recently been work which models the formation of supply chains through auctions. Both traditional, single item auction protocols (e.g. English, Dutch, Vickrey auctions and their variants) and combinatorial auctions can be used as negotiation tools. Here, winner determination is used for supply chain formation. As supply chains become more dynamic, there is a need for incremental algorithms that quickly and accurately restructure the supply chain while keeping the initial supplier/producer/consumer constraints satisfied. In this work, we look into the process of quickly and efficiently handling incremental changes in combinatorial auctions (CA). We develop an ILP formulation that preserves the initial solution while maximizing the solution quality. We illustrate the tradeoff between preserving the solution while maximizing the valuation of the auction. Additionally, we show that a simple, fast algorithm can be used to handle incremental changes in CAs with a large number of bids.