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Most of the liberalized electricity systems use the auction as a market model. The complexity of the underlying optimization formulation depends on the technical and regulatory constraints that must be considered. In Italy, the auction clearing should include not only congestion management limitations, but also a challenging regulatory constraint imposing that, while the zonal prices are allowed on the selling side, a uniform purchasing price has to be applied for all the zones of the Italian system. Such constraint introduces several complexities such as non-linearity and integrality. In this paper we discuss the modeling issues arising in the Italian context and we propose, in addition, a mechanism for the priority management of the offers/bids acceptance. We test the behavior of the models developed on a set of problems that represent all the possible scenarios that can be met in practice. The numerical results …