Data Envelopment Analysis With Dual-role Variables

Efficiency measurement and evaluation is the most common human activity and is the work of important significance and value with great difficulty. In general, any real production system should be fed up with inputs, and then generates one or more products or outputs. However, it is difficulty to measure efficiency for these systems. Especially, when the system has a complex network structure, the evaluation work will be more difficult. Data envelopment analysis, as the most popular and effective nonparametric statistical method for efficiency evaluation, is suitable for treating systems with multiple inputs and outputs. Theoretically, traditional data envelopment analysis regards decision making unit (DMU) as a black box, and ignores its internal structures. Recently, more and more literatures pay attention to the internal structure of DMU and efficiency measurement and evaluation of two-stage or multi-stage system. The presences of systems with two or more sequential stages lead to the recognition of a special variable which has the role of system input and output simultaneously. So we call it dual-role variable. Based on DEA theory, this paper studies dual-role variables and mainly evaluates two kinds of systems with dual-role variables.This paper is divided into six chapters, and its contents are as follows.The first chapter firstly introduces the basic concepts, the main models and research progress of data envelopment analysis. It is followed by reviewing and summarizing the classification of variables, especially the research status of dual-role variables. Finally, this chapter makes clear the research contents and the significance of this paper.The second chapter studies the two-stage sequential systems without feedback loop. The properties and characteristics of dual-role variables are discussed. Next, based on the operating mechanism of dual-role variables, this chapter proposes an efficiency evaluation model which can deal with dual-role variables. Then, expert weights on each stage are encoded into the model in some flexible manner. At the end of this chapter, the model is applied to efficiency evaluation of university departments. Then, the relationship of expert weights and efficiency scores is investigated. Also, the relationship of dual-role variable and efficiency scores is examined.The third chapter continues to study the two-stage sequential systems without feedback loop, and proposes six efficiency evaluation models. These models are assumed to subject to constant returns to scale. Three of them are based on the best practice frontier, while others based on the worst practice frontier. Obviously, DMU will obtain different efficiency scores from different model, and then obtains different ranking. In order to integrate these efficiency scores, an information entropy based procedure is proposed. The results of efficiency evaluation of university departments illustrate the validity and rationality of the procedure.The fourth chapter examines the two-stage sequential systems with feedback loop. The properties and characteristics of dual-role variables are discussed. Then, based on the operating mechanism of dual-role variables, an average model and two bi-level programming models are proposed. In fact, all models are nonlinear. Fortunately, a heuristic search algorithm can be used to solve these models. Although the objective function of the average model is unique, there may be two or more optimal solutions. In this situation, this paper provides three selection rules for allocating stage's efficiency scores, i.e. minimizing the gap of stage's efficiency score, maximizing the first stage's efficiency score and maximizing the second stage's efficiency score. Based on all solutions of the heuristic search algorithm, two algorithms for solving bi-level models are provided, while their validities are proved. In application section, the results indicate our models are more accurate and reasonable than standard CCR model in sequential systems.The fifth chapter evaluates research institutes. Firstly, research institute is deconstructed into two sequential stages, i.e. subsystem of resource allocation and subsystem of scientific research. Two stages are linked by dual-role variables and intermediate variables. The real dual-role variable is research income which is also regard as feedback variable in research institute. As follows, two models are provided. One adapts to subsystems with ambiguous or undefined weights, the other is used for subsystems with explicit weights. Finally, an empirical research on the efficiency evaluation of 50 universities shows that the method is reasonable.The sixth chapter summarizes all the work of this paper, and gives some useful suggestions for future research.The value of this paper includes: (1) digging out the properties, characteristics and operating mechanisms of dual-role variables; (2) examining and modeling two-stage sequential system without feedback loop and integrating flexible expert weights in models; (3) examining and modeling two-stage sequential system with feedback loop and first introducing bi-level programming into the framework of data envelopment analysis; (4) demonstration for the new application of data envelopment analysis methods.