Summary: Day ahead electricity prices in European markets are determined by double-blind auctions. That is, both buyers and sellers may place anonymous orders with different prices and quantities. The market operator has to solve an optimization problem within an hour to clear the auction and determine the prices for the Day Ahead Market (DAM) which are used as a reference point for the other electricity contracts. All electricity traded at the same time period is traded at the same price, called market clearing price. The market operator has to end the algorithm with a feasible solution if the algorithm could not find the optimal solution within the time limit. In this paper, we develop an optimization model to solve the problem with day ahead electricity prices including all the practical considerations in the Turkish DAM. We present a mixed integer formulation and provide methods based on aggregation techniques and variable elimination to solve the problem within the limits of the practical requirements. Using real market data, we show that, aggregation reduces the problem size approximately 60 percent whereas variable elimination provides another 30 percent reduction. We also propose an IP-based large neighborhood search to obtain an initial solution. Empirical evidences coming from the Turkish DAM data indicate the heuristic has a substantial solution quality and the overall suggestions deliver remarkable solution time improvements. This is the first paper in terms of formulating DAM problem in Turkey, developing new approaches to solve it within the time limits of the market, and using real data.