Integrated data envelopment analysis: Global vs. local optimum
- Authors
- Lim, Sungmook; Zhu, Joe
- Issue Date
- 16-8월-2013
- Publisher
- ELSEVIER
- Keywords
- Integrated data envelopment analysis; Efficiency; Two-stage; Local optimum; Global optimum
- Citation
- EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, v.229, no.1, pp.276 - 278
- Indexed
- SCIE
SCOPUS
- Journal Title
- EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
- Volume
- 229
- Number
- 1
- Start Page
- 276
- End Page
- 278
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/102438
- DOI
- 10.1016/j.ejor.2013.02.023
- ISSN
- 0377-2217
- Abstract
- Chiou et al. (2010) (A joint measurement of efficiency and effectiveness for non-storable commodities: integrated data envelopment analysis approaches. European journal of Operational Research 201, 477-489) propose an integrated data envelopment analysis model in measuring decision making units (DMUs) that have a two-stage internal network structure with multiple inputs, outputs, and consumptions. They claim that any optimal solutions determined by their DEA model are a global optimum, not a local optimum. We show that such a conclusion is a false statement due to their misuse of Hessian matrix in examining the concavity of the objective function, and their DEA model is actually a non-convex optimization problem. As a result, their DEA model is unusable in practice due to a lack of efficient algorithm for this particular non-convex DEA model. We further show that Chiou et al.'s (2010) model is a special case of a well-known two-stage network DEA model, and it can be transformed into a parametric linear program for which an approximate global optimal solution can be obtained by solving a sequence of linear programs in combination with a simple search algorithm. (C) 2013 Elsevier B.V. All rights reserved.
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