Multicomponent Data Envelopment Analysis and Its Basic Models

Abstract

Data Envelopment Analysis (DEA) [10] is a linear programming based methodology to measure the relative efficiencies of multiple decision-making units (DMUs) when the production process presents a structure of multiple inputs and outputs. DMU is an entity whose performance is to be evaluated and who is responsible for converting all inputs into outputs. DMU is an entity whose performance is to be evaluated and who is responsible for converting all inputs into outputs. DEA is a popular management tool which is commonly used to evaluate the efficiency of a number of DMUs. It is a linear programming based technique. It compares each DMU with only the ”best” DMU(s). It has been used for both production and cost data. Multicomponent DEA (MCDEA) is a popular technique which can be used for mea- suring the aggregate performance of DMUs along with the efficiencies of their components. The components in MCDEA are the decision making sub-units (DMSUs). The DMSUs can be categorized as: interdependent DMSUs, independent DMSUs and Mixed DMSUs. The DMSUs in which the output produced by one DMSU is used as the input by the other DMSU is known as interdependent DMSUs which constitute Series Structure in MCDEA. The DMSUs in which each DMSU has its own set of inputs and outputs is known as independent DMSUs which constitute Parallel Structure in MCDEA. Further, mixed DMSUs consist of both interdependent and independent DMSUs. The produc- tion process of a DMU consisting of mixed DMSUs is known as Mixed Structure in MCDEA/network DEA. Chapter 1 is based on mathematical models which are used for efficiency evaluations of DMUs in DEA. The basic DEA models [50] are: fractional DEA model, CCR model and BCC model. The CCR models has two forms: output maximization CCR model and input minimization CCR model. This chapter includes the mathematical formulations of all basic models in DEA. Chapter 2 is a literature review on DEA and MCDEA. It includes the review of existing literature on the series, parallel and mixed structures in MCDEA. In Chapter 3, we have discussed about series structure in MCDEA. This chapter is a review of Kordrostami and Amirteimoori [33] work on series structured MCDEA. It includes the formulation of MCDEA model in series structure for measuring aggregate performance of all DMUs and the efficiencies of their DMSUs. Chapter 4 includes parallel structureMCDEA which consists of the components/DMSUs that operate independently. In this structure, each DMSU has its own set of inputs and outputs. In this chapter, we have extended the work of Jahashahloo et al. [25] by con- sidering discretionary inputs, non-discretionary inputs, desirable outputs and undesirable outputs in MCDEA model. The shared resources are also considered to deal with real sit- uations. The parallel structure MCDEA model has been developed to measure aggregate efficiencies of each DMU along with the efficiencies of its components. In Chapter 5, we have discussed about mixed structure in MCDEA/network DEA. The mixed structured network system is a combination of both series and parallel pro- cesses/DMSUs. This chapter is a review of the work presented by Hsieh and Lin [24]. It includes the formulation of a relational network DEA model for measuring the overall performance of the DMUs and the efficiencies of their DMSUs.