Embracing fairness within a cross-efficiency hierarchical network DEA system

Abstract

Several scholars have utilized hierarchical network Data Envelopment Analysis modeling techniques to assess the performance of complex structures. However, there has been limited consideration given to the integration of a peer-appraisal setting within a self-evaluation hierarchical context. This aims to enhance discriminatory power and mitigate the issue of unrealistic weighting scheme. To this end, our study extends the single-stage hierarchical additive self-evaluation model of Kao (Omega 51:121–127, 2015. https://doi.org/10.1016/j.omega.2014.09.008), by integrating the well-established cross-efficiency method. An original combination of a maxmin secondary goal model and the Criteria Importance Through Inter-criteria Correlation (CRITIC) method is proposed, to expand the basic hierarchical self-evaluation model. The maxmin model addresses the issue of the non-unique optimal multipliers obtained from the self-evaluation model, ensuring a more realistic weight scheme. The CRITIC method, that tackles the aggregation problem by objectively determining weights of criteria, rewards the minority and is conducive to a fairer evaluation. Results indicate that the proposed approach is more likely to obtain a unique efficiency and ranking score for the units under consideration. This study entails a numerical experimentation aimed at evaluating the efficiency of a set of 20 universities while validating the applicability of our proposed approach. To conclude, the practical applications of this methodological framework could encompass assessing services within the higher education sector or fostering sustainable development across various operations within a hierarchical structure.