The conventional data envelopment analysis (DEA) models consider the input and output data features to be continuous ignoring the natural presence of integer characteristic inherited by the input and output data in many real-life problems. In this study, we propose a directional distance function (DDF) for solving DEA problems with positive and nonpositive integer and continuous data. The super efficiency (SE) evaluation process aimed in this study incorporates integer characteristics into the SE analysis and resolves the infeasibility drawback often encountered in the SE-DEA models. The proposed model is dynamic and can measure the efficiency change over time in the presence of the carryover activities connecting successive time periods. The dynamic SE analysis provides a mechanism for discriminating between the efficient Decision Making Units (DMUs) over a period. We highlight the need for both efficiency and SE models to classify inefficient, efficient, and super-efficient DMUs correctly. Finally, we present an efficiency evaluation illustration of 13 Indian Institute of Technology institutes to demonstrate the applicability and efficacy of the proposed models.