Development of Dynamic Data Envelopment Analysis Models and their Applications in Some Real-life Problems

Abstract

Performance evaluation is vital for assessing the effectiveness of decision-making units (DMUs) such as banks, educational institutions, hospitals, airlines, etc., to determine the benchmarks and develop strategies for the improvement of underperforming units. Among all available techniques, data envelopment analysis (DEA) is found to be widely used technique for performance evaluation and ranking. DEA is a linear programming-based non-parametric technique for measuring relative efficiencies of homogeneous DMUs in terms of multiple inputsoutputs. It has been further extended to network DEA to incorporate internal structures of DMUs wherein a DMU is divided into different divisions based on their operations/functions. However, the DEA and network DEA models measure efficiency statically and lack in considering the interrelationships of periods. Dynamic DEA offers a more realistic framework by considering the interactions between periods, making it an emerging and crucial field. The development of models plays a significant role in the evolution of dynamic DEA, which is essential for incorporating dynamic factors and complex network structures to perform accurate efficiency analysis and recommend possible improvement paths. Moreover, the data for variables like customer satisfaction, environmental pollution and employees involved in different operations of a bank are not known precisely but need to be incorporated effectively in the production process while efficiency assessment. In view of the above observations, this research work extends the DEA to dynamic DEA by incorporating the dynamic effects of carryovers, different network structures and addressing imprecision in the data. It presents dynamic DEA models to evaluate technical, cost, and revenue efficiencies and demonstrates their applicability to real-world problems, in particular, the banking sector, providing a more comprehensive approach to performance assessment. The chapter-wise summary of the thesis is as follows: Chapter 1 of the thesis presents an overview of DEA, network DEA, and dynamic DEA models, along with literature on measuring technical, cost, and revenue efficiencies. It also presents some basic models in DEA and its extensions for different efficiency measures. The structure of the Indian banking sector and its efficiency evaluation using DEA models are discussed. Further, it reviews the literature on the application of dynamic DEA models to banks’ efficiency estimation. Chapter 2 presents a relational dynamic DEA approach to assess system and period efficiencies of DMUs with interval data, considering both good and bad carryovers as well as desirable and undesirable outputs. It utilizes the unified production frontier and a common set of weights methodology to derive interval efficiencies. It further derives the relationships between system and period efficiencies, and suggests targets for the performance improvement of inefficient DMUs. The approach is applied to the Indian banking sector, which offers valuable insights for banking experts. Chapter 3 develops an interval dynamic network DEA approach that incorporates the interval data and shared resources. It evaluates the interval efficiencies for divisions, periods, and the dynamic system by utilizing the unified production frontier and a common set of weights methodology. The proposed approach’s comparison with an existing approach and application to the Indian banking sector demonstrate its effectiveness and validity. Chapter 4 proposes a parabolic fuzzy dynamic DEA (PFDDEA) approach to measure fuzzy efficiencies in the presence of imprecise data represented by parabolic fuzzy numbers. The α cut approach and Pareto’s efficiency concept have been utilized to evaluate system and period efficiencies with shapes of their membership functions estimated as PFNs. Further, the relationships are derived for the system and period efficiencies at each α-level. Moreover, the proposed approach has been applied to evaluate the efficiencies of Indian banking sector in an uncertain environment. In Chapter 5, a relational dynamic network DEA approach is developed to measure the cost and revenue efficiencies in the presence of shared resources and undesirable outputs. Cost and revenue efficiencies are assessed by utilizing the production possibility set (PPS) for the dynamic system. Furthermore, the targets and reference sets are suggested for the improvement of cost-inefficient and revenue-inefficient DMUs. A case study in the Indian banking sector is performed to demonstrate the applicability of the presented approach. Chapter 6 measures the cost and revenue efficiencies by utilizing the value-based dynamic network DEA models in the presence of heterogeneous input/output prices. The performance model incorporates the shared resources and undesirable outputs along with inputs, desirable outputs, links, and carryovers while constructing the PPSs for divisions, periods, and the dynamic system. Value-based targets are proposed to improve the cost and revenue efficiencies of the inefficient DMUs. A case study on Indian banks identifies efficient DMUs that can serve as benchmarks for cost management and revenue maximization. In Chapter 7, a value-based dynamic network DEA approach is presented that utilizes the directional distance function approach to measure the cost-effectiveness of DMUs in the presence of shared resources, undesirable outputs, and heterogeneous input costs. The different direction vectors are presented to handle positive and negative data. The proposed approach also discusses properties like translation invariance, unit invariance, and strict monotonicity. It evaluates the cost efficiency of Indian domestic banks and demonstrates its significance through comparisons with the existing and static approaches. Chapter 8 summarizes the developments and findings of the presented dynamic DEA methodologies along with the possible directions for future research.