Network Data Envelopment Analysis with Fuzzy Data
Conventional data envelopment analysis (DEA) treats a system as a whole unit when measuring efficiency, ignoring the operations of the component processes. Network DEA, on the other hand, takes the component processes into consideration, with results that
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Network Data Envelopment Analysis with Fuzzy Data Chiang Kao
Abstract Conventional data envelopment analysis (DEA) treats a system as a whole unit when measuring efficiency, ignoring the operations of the component processes. Network DEA, on the other hand, takes the component processes into consideration, with results that are more representative and can be used to identify inefficient components. This paper discusses network DEA for fuzzy observations. Two approaches, the membership grade and the a-cut, are proposed for measuring the system and process efficiencies via two-level mathematical programming. The model associated with the latter approach is transformed into a conventional onelevel program so that the existing solution methods can be applied. Since the data is fuzzy, the measured efficiencies are also fuzzy. The property of the system efficiency slack being the sum of the process efficiency slacks, which holds in the deterministic case, was found to hold for the fuzzy case as well. A simple network system with three processes is used to illustrate the proposed idea. Keywords Network data envelopment analysis programming Extension principle
Fuzzy sets
Two-level
1 Introduction Data envelopment analysis (DEA) deals with the performance measurement of production systems which apply multiple inputs to produce multiple outputs. Conventionally, only the inputs consumed and outputs produced by the system are considered when measuring efficiency. However, in a production system, the inputs usually go through several processes, producing a number of intermediate C. Kao (&) Department of Industrial and Information Management, National Cheng Kung University, Taiwan, Tainan, Republic of China e-mail: [email protected]
A. Emrouznejad and M. Tavana (eds.), Performance Measurement with Fuzzy Data Envelopment Analysis, Studies in Fuzziness and Soft Computing 309, DOI: 10.1007/978-3-642-41372-8_9, Springer-Verlag Berlin Heidelberg 2014
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products, before being converted into the final outputs. If the operations of the component processes are ignored, the resulting efficiency can be misleading. Kao and Hwang [13] provided an example showing that a system can be efficient even if all the component processes are not. It is also possible that when the process efficiencies of one DMU are dominated by another, the system efficiency of the former is still greater than that of the latter. The operations of component processes must therefore be considered to obtain meaningful results. The methodology that takes the operations of component processes into account has been called network DEA [7]. The basic idea is to embed the production technology of individual processes into the conventional DEA model when calculating system efficiency. Several models have been developed under this framework (see the review of Kao and Hwang, [13]). One of which is the relational model [10], where two processes connected by an intermediate product are related using the same multiplier. The rationale is that if
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