They have been used recently for truckload transportation, bus routes, industrial procurement, and in the allocation of radio spectrum for wireless communications.
Since construction procurement often involves negotiations over multiple components, combinatorial reverse auctions are suggested to reduce costs in this industry.
Specifically, it is NP-hard, meaning that it is conjectured that there does not exist a polynomial-time algorithm which finds the optimal allocation.
For example, Hsieh (2010) proposed a Lagrangian relaxation approach for combinatorial reverse auction problems.
Many of these aspects of combinatorial auctions, including some real-world examples, are also discussed in the comprehensive book edited by Cramton, Shoham and Steinberg (2006).