Inverse and Stochastic DEA: Models and Applications

Abstract

This thesis offers an in-depth investigation of Data Envelopment Analysis (DEA) models, encompassing classical DEA, inverse DEA, and stochastic DEA. The objective is to develop and apply inverse DEA models in the context of stochastic data. The research commences with a comprehensive introduction to classical DEA models, such as CCR, BCC, Additive, and SBM models. Subsequently, the study delves into inverse DEA and its application through a case study involving 15 hypothetical retail stores. Further, the thesis presents stochastic DEA models that account for data uncertainty and illustrates their practicality in real-world situations, as demonstrated by a case involving 20 bank branches. The primary contribution of this research lies in the analysis of the 15 hypothetical stores for budgeting and planning purposes, as well as the development of novel inverse DEA models that integrate stochastic data. This approach expands the applicability of DEA models in uncertain environments, assuming a symmetric error structure. For practical application and replication purposes, Python code implementations for each DEA model are provided in the Appendix. The proposed models hold potential for further research within dynamic and network DEA frameworks and have practical applications across various industries.