In our knowledge society, where universities are key players, the assessment of higher education institutions should meet the new demands of the present complex environment. This calls for the use of techniques that are able to manage this complexity. In this paper, we propose a novel combination of methodologies, jointly using a multi-criteria reference point scheme and the data envelopment analysis (DEA) for the assessment of universities. This combination allows us to take into account all the aspects regarded as relevant to assess university performance, and use them as outputs in the efficiency analysis. Our findings highlight the convenience to assess the university performance by using both compensatory and non-compensatory schemes. This way, the information provided allows to detect the actions needed to improve the performances of the universities, rather than just giving an overall performance measure. Furthermore, combining the use of composite indicators with the DEA analysis provides a more complete picture of the institutions assessed, allowing universities to check their efficiency and to detect their weaknesses and strengths accordingly. The approach is illustrated using data of 47 Spanish public universities for the academic year, 2016–2017.
