This chapter focuses on a scheduling problem that considers various constraints as a complex real world problem. Constraints on scheduling can be expressed as combinations of items (time slots) in a combinatorial auction. Agents bid for necessary combinations of time slots to satisfy users’ preferences. We formalize a combinatorial auction for scheduling as an MIP (mixed integer programming) problem, which integrates the constraints on items and bids to express complex problems. This integration solves the trade-off between the computation time to find the solution and the expressiveness to represent a scheduling problem. This chapter presents a new formalization of a combinatorial auction with constraints. We have experimentally confirmed that our method can obtain a socially preferable schedule in practical time.