Value based and network Data Envelopment Analysis : new models and applications
Σωτήρος, Δημήτριος - Γεώργιος Π.
Sotiros, Dimitrios - Georgios
KeywordsData Envelopment Analysis (DEA) ; Value judgments ; Value based DEA ; Max column normalization ; Network DEA ; Composition paradigm in network DEA ; Academic research activity ; Higher Education ; Περιβάλλουσα ανάλυση δεδομένων ; Περιβάλλουσα ανάλυση αξιών ; Κανονικοποίηση των δεδομένων ; Πολυσταδιακή περιβάλλουσα ανάλυση δεδομένων ; Ερευνητική δραστηριότητα ακαδημαϊκών ; Ανώτατη Εκπαίδευση
Performance measurement of production units is a critical aspect for their improvement. Performance assessment can be achieved either by parametric approaches, when specific parametric functional forms that transform particular inputs to outputs are assumed or by non-parametric approaches, when no assumptions on the production functions are made. Data Envelopment Analysis (DEA) is a non-parametric technique for measuring the performance of Decision Making Units that use multiple inputs to produce multiple outputs and has been established as the leading technique in performance measurement. Recent extensions of DEA, among others, include value based DEA and network DEA. Value based DEA is a recent development that resorts to value assessment protocols from Multiple Criteria Decision Analysis (MCDA) to transform the original input/output data to a value scale so as to incorporate individual prior views according to the value functions of the inputs and/or outputs in the efficiency assessment. Although the existing value based DEA models are flexible, they fail to provide a measure of efficiency. Network DEA is one of the major extensions of the conventional DEA. Specifically, conventional DEA models assume one stage production processes. However, there are cases where the internal flow of the production process is known and it plays a crucial role in the efficiency assessment. Network DEA conceives the production process that characterizes the DMUs as a network of sub-processes (stages, divisions), which are linked with intermediate measures. However, the proposed models in network DEA do not necessarily provide unique divisional efficiency scores. In addition, the estimation of the overall and the divisional efficiency scores is achieved by unduly and implicitly assigning different priority to the sub-processes. These issues question the neutrality of the results, which generally can be biased and to lead to erroneous interpretation.In this dissertation, we provide critical reviews on the value based and network DEA models proposed in the literature and we develop new models which deal with the aforementioned defects. Specifically, in the first part of this dissertation we introduce a data transformation – variable alteration technique as a means to transformation enhances the conventional DEA models with additional properties and that it treats successfully the discontinuity issue of the value functions in DEA, when non-linear value functions for the inputs and the outputs are assumed (non-linear virtual inputs/outputs). These findings allow us to develop a novel value based DEA model, which unlikely the value based DEA models proposed in the literature, provides a measure of efficiency for the evaluated units. Moreover, we develop a two-phase approach to incorporate individual preferences in a DEA assessment framework by means of Ordinal Regression. The effectiveness and the applicability of the novel value based DEA model is further illustrated by revisiting a case study drawn from the literature and by providing an application concerning the assessment of the research performance of academics which takes into account both the quantity as well as the quality of the research output. In the second part of this dissertation, we deal with network DEA. Specifically, we introduce a multi-objective programming approach for general series multi-stage processes, which employs the L∞ norm as a distance measure to locate the stage efficiency scores as close as possible to their ideal values that are obtained independently through standard DEA models. Our new approach overcomes the defects of the basic network DEA models as it provides unique and unbiased stage efficiency scores. When data are available in the literature, the effectiveness of our approach is illustrated by comparing the results obtained by our method with those obtained by other methods presented in the literature. When data are not available in the literature, synthetic data are used for testing and validation. The effectiveness and the applicability of our approach, is further illustrated by providing an application for the assessment of the academic research activity in higher education viewed as a two stage network process.