Combinatorial Auctions: A Survey Sven de Vries and Rakesh Vohra summarize the design of combinatorial auctions, which allow bidders to bid on combinations of assets. These auctions are more efficient than traditional ones because bidders can express preferences for sets of items, not just individual ones. The paper discusses the challenges of designing such auctions, including the Combinatorial Auction Problem (CAP), which involves selecting the winning bids. The CAP can be formulated as an integer program, and the paper explores various methods for solving it, including exact and approximate approaches. It also covers decentralized methods, such as Lagrangean relaxation and column generation, which help reduce computational complexity. The paper highlights the importance of integer programming in auction design and discusses the complexity of the Set Packing Problem (SPP), which is central to the CAP. It also addresses incentive issues and computational experiments, showing that combinatorial auctions can be implemented in real-world scenarios like logistics and transportation. The paper concludes that while solving the CAP is computationally challenging, integer programming techniques and approximation methods can be effective in practice.Combinatorial Auctions: A Survey Sven de Vries and Rakesh Vohra summarize the design of combinatorial auctions, which allow bidders to bid on combinations of assets. These auctions are more efficient than traditional ones because bidders can express preferences for sets of items, not just individual ones. The paper discusses the challenges of designing such auctions, including the Combinatorial Auction Problem (CAP), which involves selecting the winning bids. The CAP can be formulated as an integer program, and the paper explores various methods for solving it, including exact and approximate approaches. It also covers decentralized methods, such as Lagrangean relaxation and column generation, which help reduce computational complexity. The paper highlights the importance of integer programming in auction design and discusses the complexity of the Set Packing Problem (SPP), which is central to the CAP. It also addresses incentive issues and computational experiments, showing that combinatorial auctions can be implemented in real-world scenarios like logistics and transportation. The paper concludes that while solving the CAP is computationally challenging, integer programming techniques and approximation methods can be effective in practice.