Applying MCDEA Models to Rank Decision Making Units with Stochastic Data
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
A. Ghofran
1
(
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
)
M. Sanei
2
(
Department of Mathematics, Islamic Azad University, Tehran-Center Branch, Tehran, Iran
)
G. Tohidi
3
(
Department of Mathematics, Islamic Azad University, tehran-Center Branch, Tehran, Iran.
)
H. Bevrani
4
(
Departments of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
)
کلید واژه: Data envelopment analysis (DEA), Stochastic Data, Ranking, Probability, Multiple criteria DEA (MCDEA),
چکیده مقاله :
As a technique based on mathematical programming, Data Envelopment Analysis (DEA) is used for evaluating the efficiency of homogeneous Decision Making Units (DMUs). DEA models need accurate input and output data. In many situations, on the one hand, accurate measurement of inputs and outputs is difficult due to their volatility and complexity. This conflict results in uncertain DEA models. Its main problem is transformation of deterministic equivalent of stochastic model into quadratic programming, time-consuming and complexity and it requires presuppositions. By means of Bi-objective multiple criteria DEA (Bio-MCDEA) model that considers stochastic data, our proposed model reduces some of these problems and facilitates problem solving through presenting primary presupposition and final linear model. The efficiency score of DMUs is determined by applying stochastic Bio- MCDEA model. Eventually, we used the data of seventeen Iranian electricity distribution companies to illustrate the methods developed in the present paper.
تحلیل پوششی داده‌ها به عنوان تکنیکی که بر پایه برنامه‌ریزی ریاضی است، برای ارزیابی کارایی واحدهای تصمیم‌گیری همگن استفاده می‌شود. مدل‌های DEA نیاز به داده‌های ورودی و خروجی دقیق دارند. در بسیاری از شرایط، اندازه‌گیری دقیق ورودی‌ها و خروجی‌ها به خاطر نوسان و پیچیدگی آن‌ها امری دشوار است. این تضاد منجر به مدل‌های DEA نامطمئن می‌شود. تغییر شکل معادل قطعی مدل تصادفی به مساله برنامه‌ریزی درجه دوم، به منزله حل این مشکل اصلی است که کدام یک زمان‌بر و پیچیده و نیازمند پیش فرض است. با استفاده از مدل MCDEA دو هدفه که داده تصادفی را در نظر می‌گیرد، مدل ارائه شده ما برخی از این مشکلات را کاهش داده و حل مشکل را از طریق ارائه پیش فرض اولیه و مدل خطی نهایی تسهیل می‌کند. نمره کارایی DMUs با به کارگیری مدل MCDEA دو هدفه تصادفی تعیین می‌شود. در نهایت، از داده‌های مربوط به هفده شرکت توزیع برق ایران برای نشان دادن روش‌های به کار گرفته شده در این مقاله استفاده کردیم.
[1] Y. Liu, M. Wang , M, The upper and lower bound evaluation based on the quintile efficiency in stochastic data envelopment analysis, Expert system with Application 3 (2017) 14-24.
[2] M. Tavana, R. Kiani Mavi, An extended VIKOR method using stochastic data and subjective judgments, Computers & Industrial Engineering 6 (2016) 240-247.
[3] A. Emrouznejad, M. Ghasemi, A Biobjective weighted model for improving the discrimination power in MCDEA, European Journal of operational Research 12 (2014) 640-650.
[4] H. Bal, H. Orkcu, Improving the discrimination power and weight dispersion in the data envelopment analysis (DEA), Computer and Operation research 3 (2010) 99-107.
[5] H. Bal, H. Orkcu, H. Celebioglu, A new method based on the dispersion of weights in data envelopment analysis, Computers and Industrial Engineering (2008) 502-512 .
[6] A. Charnes, W. Cooper, A chance constrained programming approaches to congestion in stochastic data envelopment analysis, European Journal of Operational Research 13 (2004) 487-501.
[7] F. Hosseinzadeh Lotfi, N. ,Nematollahi, Centralized resource allocation with stochastic data, Computational and Applied mathematics 21 (2012) 1783-1788.
[8] Y. Chen, J. Huo, Super efficiency based on Modified directional distance function, Omega 41 (2013) 621-625.
[9] Y. Chen, M, Chang, Multi objective data envelopment analysis, European Journal of Operational Research Society 60 (2009) 1556-1566.
[10] X. Li, G. R Reeves, A Multiple Criteria approach to data envelopment analysis, European Journal of Operational Research 115 (1999) 507-517.
[11] W. W. Cooper, H. Deng, M. Huang, X. Li, Chance Constrained Programming Approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis, European Journal of Operational Research Society 60 (2002) 1346-1356
[12] M. Khodabakhshi, M. Asgharian, An Input relaxation measure of efficiency in Stochastic data envelopment analysis, Applied Mathematical Modeling 33 (2009) 2010-2023.
[13] M. Khodabakhshi, M. Asgharian, An input-Oriented super-efficiency measure in Stochastic data envelopment analysis: Evaluating chief executive officers of US public banks and thrifts, Expert system with applications 32 (2009) 325-329
[14] M. Asgharian, M. Khodabakhshi, Congestion in stochastic data envelopment analysis, International Journal of Statistics and Management System 23 (2010) 584-106.
[15] M. Khodabakshi, An output- oriented superefficiency measure in stochastic data envelopment analysis: Considering Iranian electricity distribution companies, Computers and Industrial Engineering 12 (2010) 663-
671.
[16] J. Jinglian, D. Zhou, Measuring environmental performance with stochastic environmental DEA:The case of APEC economies, Economic Modeling 38 (2014) 80-86.
[17] T. Sueyoshi, Stochastic DEA for restructure strategy: an application to a Japanese petroleum company, Omega 28 (2000) 385-398.
[18] A. Udhayakumar, V. Charles, Stochastic simulation based genetic algorithm for chance constrained Data Envelopment Analysis, Omega 39 (2010) 387-397.
[19] T. Sueyoshi, Stochastic DEA for restructure strategy: an application to a Japanese petroleum company,Omega 28 (2000) 385-398.
[20] A. Udhayakumar, V. Charles, Stochastic simulation based genetic algorithm for chance constrained Data Envelopment Analysis, Omega 39 (2010) 387-397.
