Simulation of Stichastic Data Envelopment Analysis in Selection of Research and Development Projects

Subject Areas : Statistics

Mehdi Namazi ¹ , Emran Mohammadi ²

1 - Ph.D. Student، Department of Philosophy and Management of Technology، Faculty of Progress Engineering، Iran University of Science and Technolog، Tehran، Iran.
2 - Assistant Professor، Faculty of Industrial Engineering، Iran University of Science and Technolog، Tehran، Iran

Received: 2019-07-20 Accepted : 2019-11-05 Published : 2022-03-21

Keywords: انتحاب پروژه, اولویت بندی, تحقیق و توسعه, عدم قطعیت, نوآوری,

Abstract :

Uncertainty is the obvious attribute of any activity in the real world, and performance analysis of units in terms of uncertainty is one of the most important concerns of managers and planners of companies. Various approaches to data envelopment analysis have been presented so far to provide a good tool for evaluating the efficiency of units in uncertain situations, including random, fuzzy and robust approaches. In a situation where the probability distribution function of random variables is known, stochastic approach is a precise solution for problem solving. Nevertheless, previous research in this field has focused on the transformation of a random problem into a definite problem. In this research, a method for modeling data envelopment analysis is presented using computer programming. In this method, random processes are simulated, and finally, the performance distribution function is presented instead of a definite number as the unit's efficiency. In this model, a new concept is presented as the probability of efficiency, which represents the probability that the unit will be located on the efficient boundary. The proposed method is empirically applied in a real case of selecting research and development projects.

References:

[1] M. J. Farrell، “The Measurement of Productive Efficiency،” Journal of Royal Society ، vol. 120، no. A، pp. 253-281، 1957.

[2] A. Charnes، W. W. Cooper and E. Rhodes، “Measuring the Efficiency of decision Making Units،” European Journal of Operational Research، vol. 2، pp. 429-444، 1978.

[3] H. Dyckhoff and K. Allen، “Measuring ecological efficiency with data envelop analysis،” European Journal of Operation Research، vol. 132، pp. 312-325، 2001.

[4] N. Adler and B. Golnay، “Evaluation of deregulated airline networks using data envelop analysis combined with principal component analysis with in Western Europe،” European Journal of Operation Research، vol. 132، pp. 260-273، 2001.

[5] W. C. A. Charnes، “Chance Constrained Programming،” Management Science، pp. 73-79، 1959.

[6] K. K. L. ،. S. T. Land، “Chance-Constrained Data Envelopment Analysis،” Journal of Managerial and Decision Economics، vol. 14، 1993.

[7] Z. H. S. X. L. WW Cooper، “Satisficing DEA models under chance constraints،” Annals of operations research، vol. 66، no. 4، pp. 279-295، 1996.

[8] A. C. a. W. W. C. Banker R.، “Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis،” Management Science، vol. 30، pp. 1078-1092 ، 1984.

[9] H. D. Z. H. S. L. WW Cooper، “Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis،” Journal of the Operational Research Society، vol. 53، no. 12، pp. 1347-1356، 2002.

[10] M. D. J. P. M. ،. T. W. J. Fethi، “An Empirical Study of Stochastic DEA and Financial Performance: the Case of the Turkish Commercial Banking Industry،” Efficiency and Productivity Research Unit، University of Leicester.، 2001.

[11] M. D. J. P. M. ،. T. W. J. Fethi، “European Airlines: A Stochastic DEA Study of Efficiency With Market Liberalisation،” Efficiency and Productivity Research Unit، University of Leicester، 2001.

[12] T. W. Jones، “Stochastic Non-parametric Efficiency Measurement and Yardstick Competition in Electricity Regulation،” Loughborough University Working Papers، 2001.

[13] J. a. S. Shang، “A unified framework for the selection of a flexible manufacturing system،” European Journal of Operation Research، vol. 85، no. 2، pp. 297-315، 1995.

[14] T. Y. Chen، “A Comparision of Chance-Constrianed DEA and Stochastic Frontier Analysis: Bank Efficiency in Taiwan،” Journal of The Operational Research Society، vol. 53، 20025.

[15] J. B. ،. K. G. Alam، “Stochastic Data Envelopment Analysis Based on Choice Theoretic Approach to Analyze Interaction between Transportation and Economic Development،” in 86th Annual Meeting of Transportation Research Board، Washington، USA.، 2005.

[16] A. ،. E. T. Kasman، “A Comparison of Chance-Constrained Dea and Stochastic Frontier Analysis: an Application to the Turkish Life Insurance Industry،” in 8. Türkiye Ekonometri ve İstatistik Kongresi ، Malatya، Turkey، 2007.

[17] J. a. S. Shang، “A unified framework for the selection of a flexible manufacturing system،” European Journal of Operation Research، vol. 85، no. 2، pp. 297-315، 1995.

[18] ص. م. و. ا. خویینی، “تعیین و پیش بینی کارایی شعب بانک ملت استان قزوین با استفاده از روش تحلیل پوششی داه تصادفی،” دانش مدیریت،vol. 64، 1383.

[19] F. H. e. a. Lotfi، “Congestion in Stochastic DEA for Restructure Strategy:An Application to Iranian Commercial Banks،” International Mathematical Forum، vol. 2، 2007.

[20] C.-G. L. Desheng Wua، “Stochastic DEA with ordinal data applied to a multi-attribute pricing problem،” European Journal of Operational Research، vol. 207، p. 1679–1688، 2010.

[21] M. E. B. P. Beraldi، “Data Envelopment Analysis under Uncertainty and Risk،” International Journal of Computer، Electrical، Automation، vol. 6، no. 6، pp. 811-816، 2012.

[22] M. K. A. P. M. N. Abbas Ali Noora، “Common Set of Weights Approach in Stochastic DEA and its Application to Chief Executive Officers of US Public Banks and Thrifts،” in The First Regional Conference on the Advanced Mathematics and Its Applications، Mobarakeh، Iran، 2012.

[23] Y. L. ،. Q. L. ،. K. W. Chong Wua، “A stochastic DEA model considering undesirable outputs with weak disposability،” Mathematical and Computer Modelling، vol. 8، p. 980–989، 2013.

[24] M. E. B. &. P. B. Gianpaolo Iazzolino، “Using DEA and financial ratings for credit risk evaluation: an empirical analysis،” Applied Economics Letters، 2013.

[25] N. C. P. OleB Olesen، “Stochastic Data Envelopment Analysis—A review،” European Journal of Operational Research، vol. 251، pp. 2-21، 2016.

[26] T. Linsmeier and N. D. Pearson، “Value at Risk.،” Financial Analysts Journal، vol. 56، no. 2، pp. 47-67، 2000.

[27] R. Rockafellar and S. Ursayev، “Optimization of Conditional Value-at-Risk،” The Journal of Risk،، vol. 2، no. 3، pp. 21-41، 2000.

[28] J. Aparicio، J. Pastor and J. Zofio، “How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies،” Journal of Operational Research، vol. 3، pp. 822-891، 2015.

[29] S. Hora، “Probability judgments for continuous quantities: Linear combinations and calibration،” Management Science، vol. 50، no. 5، pp. 597-604، 2004.

[30] S. C. Hora، “Eliciting probabilities from experts،” in Advances in Decision Analysis: From Foundations to Applications، W. Edwards، R. F. Miles and D. Von Winterfeldt، Eds.، Cambridge، Cambridge University Press، 2007، pp. 53-129.

[31] M. Namazi، "Technological Capability Building in the Satellite Communications Industry in Iran،" in The Development of Science and Technology in Iran: Policies and Learning Frameworks، New York، Palgrave Macmillan، 2017، pp. 203-224.