  The European power grid can be divided into several market areas where the
price of electricity is determined in a day-ahead auction. Market participants
can provide continuous hourly bid curves and combinatorial bids with associated
quantities given the prices. The goal of our auction is to maximize the
economic surplus of all participants subject to quantity constraints and price
constraints. The price constraints ensure that no one incurs a loss. Only
traders who submitted a combinatorial bid might miss a not-realized profit. The
resulting problem is a large scale mathematical program with equilibrium
constraints (MPEC) and binary variables that cannot be solved efficiently by
standard solvers. We present an exact algorithm and a fast heuristic for this
type of problem. Both algorithms decompose the MPEC into a master problem (a
MIQP) and pricing subproblems (LPs). The modeling technique and the algorithms
are applicable to a wide variety of combinatorial auctions that are based on
mixed integer programs.
