Abstract: A system and method for processing bids of an auction by electricity market participants for electricity market commodities. The method includes retrieving model parameters and multiple bids for the electricity market commodities. The model parameters and bids are applied to equations representative of an electricity market, where the equations include at least one variable to be optimized. The equations are simultaneously solved for the variable(s). In simultaneously solving for the variable(s), the equations are iteratively solved to optimize the variable(s) according to a predetermined objective. Results of the auction are published to notify the market participants. The electricity market commodities include electric energy, reserve capacity, and transmission.