DEA Models In The Presence Of Decision Making Units’Heterogeneity And The Applications

Efficiency evaluation and improvement are very significant and interesting in the research field of decision-making science, and play an important role in promoting both the theoretical development and the practical application. With the further development of economic globalization and regional economic integration and unity, efficiency issues are critical to competitive status and influence of various countries and their companies in the market.Data envelopment analysis (DEA) is a decision analysis method used to evaluate the relative efficiency of the decision making units (DMUs) by utilizing the input to obtain the output. DEA has drew a lot of attention from many scholars and numerous research results in the theoretical study and practical application are achieved since it was first proposed in1978. DEA has several significant features in the field of efficiency assessment:firstly, the calculation process of the DEA model does not require preset parameters and only needs the input and output of the process of production; secondly, the functional relationship between input and output needn’t to be taken into consideration in the practical application of DEA. Therefore, with its unique features, DEA can give an objective and fair assessment on the DMUs and hence provide efficiency information for decision-makers as well as the direction of improving the efficiency of production for decision-makers. However, with the theoretical and practical expansion of the DEA, the traditional DEA method also revealed some problems to be solved:first, the calculation results of the DEA model can distinguish between efficient and inefficient units, but the unit in the production frontier cannot be further distinguished; second, the traditional DEA method of conducting efficiency evaluation has an implicit assumption that the homogeneity of the decision-making unit must be satisfied. In general, the DMUs must meet the following conditions:(1) each DMU should have the same or similar external environment;(2) each unit shall have the same or similar goals and mission;(3) the input and output indexes should be the same. However, the outstanding issue is that, when the heterogeneous DMUs occurs in reality, how to do a fair evaluation? To solve this problem, scholars and experts have proposed a number of new theories and methods to solve the non-homogeneity problems in practical evaluation. Based on previous research achievements, this paper aims to further expand the heterogeneity problem and enrich the theory and practice of decision-making analysis. To this end, this paper will introduce the basic problem of heterogeneity, the factors affecting the efficiency evaluation, the expanding research of heterogeneity evaluation methods and the related research status of DEA at home and abroad respectively, which will be further analyzed and summarized. This paper will consider the efficiency evaluation of non-homogeneous DMUs, specifically the following scenarios:the efficiency evaluation of the DMUs under different circumstances; efficiency evaluation of multi-stage DEA model; the research on congestion considering the presence of undesirable outputs; and performance evaluation with multiple department employees. Specifically, this paper carried out a detailed argument and analysis in the following aspects:The first chapter is the introduction. In this paper, with the basic DEA model as a starting point we introduce its basic model, related concepts and some applications. The paper describes the main issues, existing solutions and future directions under the present circumstances and their relationship with the theme of the current research are discussed. Then, the research framework is raised and the heterogeneity situations are highlighted in the paper:(1) the DMUs under different external environment lead to environmental heterogeneity;(2) the DMUs with different inputs and outputs indexes result in structural heterogeneity;(3) the DMUs with different production scale lead to scale heterogeneity. Finally, we present the basic method and expand the theoretical model and apply it into practice under the problem-driven objective.The second chapter discusses the inefficiency and congestion problem when undesirable outputs are yielded. This chapter distinguishes between inefficiency and congestion and constructs the mathematical expressions at first according to the characteristics of them. Then it proposes the models which can identify managerial inefficiency, technical inefficiency and congestion. We also illustrate the problem that cannot be distinguished between technical inefficiency and congestion in previous paper with a practical example. Based on this rationale, the paper calculates the inefficiency and congestion and further differentiates the congestion into desirable and undesirable congestion when undesirable output and desirable output are co-existed. The desirable congestion is defined as occurring between undesirable outputs and inputs, which is expected by the managers; and instead undesirable congestion occurs between the desirable output and input, and the manager expected to avoid this kind of congestion. Finally, the proposed approach is applied and verified by identifying resource congestion and environmental inefficiencies of China’s economic development.The third chapter discusses the problem of environmental nonhomogeneity. The external environmental variable is an important issue that makes an indispensable impact on the productivity of decision making units (DMUs). In this paper, we first investigate whether and how these variables influence performances of the DMUs based on slack-based measurement. We extend the implicit assumption of prior studies and suggest that environmental variables can be a catalyst to increase productivity. Impact and error factors, which are derived from regression analysis and stochastic frontier analysis (SFA), are defined to better represent the composition of two contradictory impacts, catalyst and depressant, of contextual variables. A statistical analysis is provided to identify the significance of such impacts and recognize multicollinearity among contextual variables. The two factors are also moderated flexibly by decision makers in accordance with various production scenarios. Accordingly, original inputs and outputs are appropriately adjusted to well depict individual, contextual, and statistical error inefficiencies. Further, modified slack-based DEA models are proposed to incorporate DEA and regression methodology within an integral framework. Several properties are presented to better describe the characteristics of the models. An empirical example is shown to verify the feasibility of the proposed approach.The fourth chapter further expands the theory and practice of non-homogeneous problem. In this research, we study the performance of the employees in heterogeneous departments with distinctly different key performance indicators (KPIs). We begin with the identification of the characteristics of KPIs and explore widely accepted criteria to collect the appropriate indicators for each department in a consistent way. We then make a classification of the departmental indicators and orient various KPI indices to a framework composed of four unified dimensions. An approach incorporating data envelopment analysis (DEA) and common weights is proposed to integrate various KPIs and obtain objective scores for each employee. Since the KPI scores of employees are also significantly related to the "technology" of a department and may be preferred by the managers of department, we propose a Malmquist productivity index alike (MPI-alike) model to evaluate the performance of an employee in different departments which represent different technology and identify the employee’s efficiency based on the idea of cross efficiency. In this way, the inconsistency caused by different frontier facets is eliminated when estimating the employees’performance. Specifically, the subjective preference and inconsistence of the managers are also eliminated or reduced. Further, we propose a modified meta-frontier model to estimate the technology heterogeneity among departments.The final chapter is a summary and outlook. This chapter summarizes all research contents of the full text, and gives the detailed analysis and evaluation of the content of each chapter. We also identify shortcomings of the present study. At last, we propose future research methods and research areas based on the current research situation.Innovation of this paper is mainly reflected in the following aspects:(1) We first classify conventional congestion into a new congestion and technical inefficiency based on priori researches and real applications. Modified definitions and mathematical expression of congestion, managerial and technical inefficiencies are proposed to better illustrate the differences among them. The proposed approach is applied and verified by identifying resource congestion and environmental inefficiencies of China’s economic development.(2) In this paper, we apply the SBM-DEA model to calculate slack variables which can make the inefficiency more comprehensive when considering the impact of the external environment variable on the DMUs efficiency. At the same time, through the new adjustment method, the amount of the adjustment can be controlled properly. We also consider the relationship between the impact factor (IF) and error factor (EF). In reality, environment variables will not only affect inputs, but also have the impact on outputs, so the adjustment in this paper is more comprehensive. Numerical analysis validates the influence of environment variables on productivity.(3) This paper discusses the performance assessment methods and models indifferent departments and incorporates the different evaluation and examination index into a unified framework based on the enterprise level. In order to obtain a more reasonable employee performance, the proposed models considers the impact of the technological heterogeneity on the employee’s efficiency among multiple departments. Numerical analysis of an auto company validates the proposed models.