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JACIII Vol.19 No.6 pp. 880-891
doi: 10.20965/jaciii.2015.p0880
(2015)

Paper:

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Marginal Model Synthesization Algorithm for Data Envelopment Analysis and its Application

Koki Kyo* and Hideo Noda**

*Department of Human Sciences, Obihiro University of Agriculture and Veterinary Medicine
Inada-cho, Obihiro, Hokkaido 080-8555, Japan

**School of Management, Tokyo University of Science
500 Shimokiyoku, Kuki, Saitama 346-8512, Japan

Received:
May 19, 2015
Accepted:
October 7, 2015
Published:
November 20, 2015
Creative Commons License
Keywords:
marginal model synthesization algorithm, data envelopment analysis (DEA), BCC models, linear programming (LP), economic efficiency analysis
Abstract
In this paper, we propose a new approach for determining the unknown quantities in Banker–Charnes–Cooper models for data envelopment analysis by developing the marginal model synthesization algorithm. In this algorithm, several marginal fractional programming models are first constructed based on a simple numeric optimization. Then, a set of synthetic Banker–Charnes–Cooper models is obtained by compounding the marginal fractional programming models. A comparison of the proposed and existing approaches in terms of computational cost and stability of results shows that the former approach has distinct advantages. We also present an application of the proposed approach for analyzing the efficiency of industries in Japanese prefectures.
Cite this article as:
K. Kyo and H. Noda, “Marginal Model Synthesization Algorithm for Data Envelopment Analysis and its Application,” J. Adv. Comput. Intell. Intell. Inform., Vol.19 No.6, pp. 880-891, 2015.
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References
  1. [1] W. W. Cooper, L. M. Seiford, and K. Tone, “Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software (2nd ed.),” Springer, 2007.
  2. [2] A. Charnes, W. W. Cooper, and E. Rhodes, “Measuring the efficiency of decision making units,” European J. of Operational Research, Vol.2, pp. 429-444, 1978.
  3. [3] A. Charnes, W. W. Cooper, and E. Rhodes, “Short communication: measuring efficiency of decision making units,” European J. of Operational Research, Vol.3, pp. 339, 1979.
  4. [4] R. E. Steuer, “Multiple Criteria Optimization: Theory, Computation, and Application,” Wiley, 1986.
  5. [5] K. Tone, “An ε-free DEA and a new measure of efficiency,” J. of the Operations Research Society of Japan, Vol.36, pp. 167-174, 1993.
  6. [6] C. A. K. Lovell and J. T. Pastor, “Units invariant and translations invariant DEA,” Operations Research Letters, Vol.18, pp. 147-151, 1995.
  7. [7] C. A. K. Lovell, J. T. Pastor, and J. A. Turner, “Measuring macroeconomic performance in the OECD: A comparison of European and non-European countries,” European J. of Operational Research, Vol.87, pp. 507-518, 1995.
  8. [8] J. T. Pastor, “Translations invariant in data envelopment analysis: a generation,” Annals of Operations Research, Vol.66, pp. 93-102, 1996.
  9. [9] A. L. Ali, “Streamlined computation for data envelopment analysis,” European J. of Operational Research, Vol.64, pp. 61-67, 1993.
  10. [10] J. H. Dulámboxa and R. V. Helgason, “A new procedure for identifying the frame of the convex hull of a finite collection of points in multidimensional space,” European J. of Operational Research, Vol.92, pp. 352-367, 1996.
  11. [11] J. H. Dulámboxa, R. V. Helgason, and N. Venugopal, “An algorithm for identifying the frame of a pointed finite conical hull,” J. of Computing, Vol.10, pp. 323-330, 1997.
  12. [12] R. S. Barr and M. L. Durchholz, “Parallel and hierarchical decomposition approaches for solving large-scale data envelopment analysis models,” Annals of Operations Research, Vol.73, pp. 339-372, 1997.
  13. [13] P. J. Korhonen and P. A. Siitari, “Using lexicographic parametric programming for identifying efficient units in DEA,” Computer and Operations Research, Vol.34, pp. 2177-2190, 2007.
  14. [14] P. J. Korhonen and M. Halme, “Using lexicographic parametric programming for searching a nondominated set in multiple objective linear programming,” J. of Multi-Criteria Decision Analysis, Vol.5, pp. 291-300, 1996.
  15. [15] K. Kyo and H. Noda, “A new approach to data envelopment analysis and its application to industries in Japan prefectures,” Proc. of SCIS&ISIS 2014, pp. 518-525, 2014.
  16. [16] R. D. Banker, A. Charnes, and W. W. Cooper, “Some models for estimating technical and scale inefficiencies in data envelopment analysis,” Management Science, Vol.30, pp. 1078-1092, 1984.
  17. [17] J. Tokui, T. Makino, K. Fukao, T. Miyagawa, N. Arai, S. Arai, T. Inui, K. Kawasaki, N. Kodama, and N. Noguchi, “Compilation of the regional-level Japan industrial productivity database (R-JIP) and analyses of productivity differences across prefectures,” The Economic Review (in Japanese), Vol.64, pp. 218-239, 2013.

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