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This paper presents a market clearing tool for the market operator of a pool-based electricity market for energy. This tool is transparent and fair for the market participants, and simple to implement and to interpret. It preserves the privacy of the corporate information of the participants and provides the right signals to achieve economic efficiency. Furthermore, it recognizes and properly models the technical (physical and inter-temporal) constraints of the participant thermal power generators. From a mathematical point of view, the proposed tool results in a mixed-integer linear programming problem that can be efficiently solved using currently available branch and cut software. To illustrate the adequate functioning of the proposed market clearing procedure different realistic case studies are analyzed in detail.