Incorporating decision-makers’ perspectives into DEA models by means of weight restrictions

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Date

2023

Authors

Γκουβίτσος, Ιωάννης

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Abstract

This thesis discusses an important issue in the field of Operational Research, particularly in the efficiency assessment of DMUs by means of the Data Envelopment Analysis method. In fact, we investigate the field of DEA weight restrictions and their use as a means of incorporating managerial decisions, priorities, or decision makers’ perceptions into the relevant DEA models. The thesis consists of two parts, each of which explores the use of weight restrictions in a different context, with the objective to provide decision-makers with flexibility regarding the determination of DEA weights. The first part proposes a new approach that performs a complete ranking of decision-making units (DMUs), by employing Data Envelopment Analysis (DEA) models with virtual weight restrictions. It is a multi-stage process that employs the super-efficiency DEA model (AP Model) at each stage of the process. In each stage, the virtual weight bounds could be different and are obtained by means of the MACBETH methodology. Our approach has been applied in a real-life application, where three decision-makers need to perform a complete ranking of 33 Greek general hospitals. The empirical results indicate that the proposed multi-stage ranking approach increases the discrimination power of the conventional super-efficiency DEA model and provides an improved DMUs ranking. The importance of such an improvement is more prominent in situations where a decision related to funds or other resource allocation should be made. Thus, the proposed approach not only contributes to the relevant literature but also is quite important from a decision-making perspective, as it is the first (to the best of our knowledge) allowing decision-makers to adjust the DEA weights at each stage of the ranking process. The second part proposes the incorporation of fuzzy numbers into the production trade-off weight restrictions approach. The key idea of the discussed approach is that in real-life DEA applications, existing production trade-offs among inputs and/or outputs may be extremely difficult to express with crisp numbers. The proposed approach allows decision-makers to restrict the weights of DEA models, by expressing complex production trade-offs in fuzzy terms. With this approach, the obtained efficiency scores remain meaningful from a production perspective and more compatible with real-life applications that often involve ambiguity or uncertainty. Based on the fuzzification of production trade-offs, we introduce DEA models that consider the ambiguity inherent in realistic processes and determine appropriate efficiency scores and targets for the DMUs.

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Keywords

Super-efficiency DEA Model, Data Envelopment Analysis (DEA), MACBETH, Virtual weight restrictions, Production trade-offs, Triangular fuzzy numbers

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