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Modeling data envelopment analysis by chance method in hybrid uncertain environments

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  • Qin, Rui
  • Liu, Yan-Kui

Abstract

This article first presents several formulas of chance distributions for trapezoidal fuzzy random variables and their functions, then develops a new class of chance model (C-model for short) about data envelopment analysis (DEA) in fuzzy random environments, in which the inputs and outputs are assumed to be characterized by fuzzy random variables with known possibility and probability distributions. Since the objective and constraint functions contain the chance of fuzzy random events, for general fuzzy random inputs and outputs, we suggest an approximation method to compute the chance. When the inputs and outputs are mutually independent trapezoidal fuzzy random variables, we can turn the chance constraints and the chance objective into their equivalent stochastic ones by applying the established formulas for the chance distributions. In the case when the inputs and the outputs are mutually independent trapezoidal fuzzy random vectors, the proposed C-model can be transformed to its equivalent stochastic programming one, in which the objective and the constraint functions include a number of standard normal distribution functions. To solve such an equivalent stochastic programming, we design a hybrid algorithm by integrating Monte Carlo (MC) simulation and genetic algorithm (GA), in which MC simulation is used to calculate standard normal distribution functions, and GA is used to solve the optimization problems. Finally, one numerical example is presented to demonstrate the proposed modeling idea and the efficiency in the proposed model.

Suggested Citation

  • Qin, Rui & Liu, Yan-Kui, 2010. "Modeling data envelopment analysis by chance method in hybrid uncertain environments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 922-950.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:5:p:922-950
    DOI: 10.1016/j.matcom.2009.10.005
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    1. Coelho, Leandro dos Santos & Souza, Rodrigo Clemente Thom & Mariani, Viviana Cocco, 2009. "Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3136-3147.
    2. Wu, Ling-Yun & Li, Zhenping & Wang, Rui-Sheng & Zhang, Xiang-Sun & Chen, Luonan, 2009. "Self-organizing map approaches for the haplotype assembly problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3026-3037.
    3. Azadivar, F. & Talavage, J., 1980. "Optimization of stochastic simulation models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 22(3), pages 231-241.
    4. Konstantinos Triantis & Olivier Girod, 1998. "A Mathematical Programming Approach for Measuring Technical Efficiency in a Fuzzy Environment," Journal of Productivity Analysis, Springer, vol. 10(1), pages 85-102, July.
    5. Horne, Jocelyn & Hu, Baiding, 2008. "Estimation of cost efficiency of Australian universities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(2), pages 266-275.
    6. O. B. Olesen & N. C. Petersen, 1995. "Chance Constrained Efficiency Evaluation," Management Science, INFORMS, vol. 41(3), pages 442-457, March.
    7. Chuanwen, Jiang & Bompard, Etorre, 2005. "A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(1), pages 57-65.
    8. Golenko-Ginzburg, Dimitri & Gonik, Aharon & Laslo, Zohar, 2003. "Resource constrained scheduling simulation model for alternative stochastic network projects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(2), pages 105-117.
    9. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    10. Laabidi, Kaouther & Bouani, Faouzi & Ksouri, Mekki, 2008. "Multi-criteria optimization in nonlinear predictive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(5), pages 363-374.
    11. Kangas, Jari & Kohonen, Teuvo, 1996. "Developments and applications of the self-organizing map and related algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 41(1), pages 3-12.
    12. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    13. Menipaz, Ehud & Ben-Yair, Avner, 2002. "Harmonization simulation model for managing several stochastic projects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(1), pages 61-66.
    14. Kao, Chiang & Liu, Shiang-Tai, 2003. "A mathematical programming approach to fuzzy efficiency ranking," International Journal of Production Economics, Elsevier, vol. 86(2), pages 145-154, November.
    15. Hibiki, Norio & Sueyoshi, Toshiyuki, 1999. "DEA sensitivity analysis by changing a reference set: regional contribution to Japanese industrial development," Omega, Elsevier, vol. 27(2), pages 139-153, April.
    16. Shklyar, A. & Arbel, A., 2009. "Accelerated convergence of the numerical simulation of incompressible flow in general curvilinear co-ordinates by discretizations on overset grids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2476-2489.
    17. Sarper, Hüseyin, 1993. "Monte Carlo simulation for analysis of the optimum value distribution in stochastic mathematical programs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(6), pages 469-480.
    18. Nedjalkov, M. & Dimov, I., 1998. "Convergency of the Monte Carlo algorithms for linear transport modeling1This work was supported by the Ministry of Science, Education and Technology of Bulgaria under grants # I501/95 MM449/94 as well," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 383-390.
    19. Dellino, G. & Lino, P. & Meloni, C. & Rizzo, A., 2009. "Kriging metamodel management in the design optimization of a CNG injection system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2345-2360.
    20. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, December.
    21. Khlaifi, Anis & Ionescu, Anda & Candau, Yves, 2009. "Pollution source identification using a coupled diffusion model with a genetic algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3500-3510.
    22. Entani, Tomoe & Maeda, Yutaka & Tanaka, Hideo, 2002. "Dual models of interval DEA and its extension to interval data," European Journal of Operational Research, Elsevier, vol. 136(1), pages 32-45, January.
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