Time constraints in mixed multi-unit combinatorial auctions

We extend the framework of mixed multi-unit combinatorial auctions to include time constraints, present an expressive bidding language, and show how to solve the winner determination problem for such auctions using integer programming. Mixed multi-unit combinatorial auctions are auctions where bidders can offer combinations of transformations of goods rather than just simple goods. This model has great potential for applications in the context of supply chain formation, which is further enhanced by the integration of time constraints. We consider different kinds of time constraints: they may be based on either time points or intervals, they may determine a relative ordering of transformations, they may relate transformations to absolute time points, and they may constrain the duration of transformations.