ارائه یک مدل ترکیبی از DEA دو مرحله‌ای و PROMETHEE در محیط خاکستری جهت ارزیابی عملکرد
محورهای موضوعی : آمارعلیرضا علی نژاد 1 , امیر امینی 2
1 - گروه مهندسی صنایع، دانشکده مهندسی صنایع و مکانیک، واحد قزوین، دانشگاه آزاد اسلامی، قزوین، ایران، قزوین،ایران
2 - گروه مهندسی صنایع، دانشکده مهندسی صنایع، دانشگاه صنعتی ارومیه، ارومیه، ایران
کلید واژه: Two-Stage DEA, Promethee, Performance evaluation, MADM, Gray Numbers,
چکیده مقاله :
یکی از چالش‌های عمده ارزیابی عملکرد در سازمان‌ها و کلیه سیستم‌ها، غیرمنطقی بودن و دقیق نبودن روش‌ها و معیارهای بکار گرفته شده است. روش‌های سنتی ارزیابی عملکرد عمدتا یک سطحی بوده، لذا فاقد توان لازم بمنظور ارائه بازخورد کافی جهت شناسایی واحدهای ناکارا هستند. تحلیل پوششی داده‌ها، یک تکنیک برنامه‌ریزی ریاضی است که کارایی نسبی چندین واحد تصمیم‌گیرنده را بر مبنای ورودی‌ها و خروجی‌های مشاهده شده که ممکن است با انواع مقیاس‌های مختلف بیان شوند، محاسبه می‌کند. در عمل، بسیاری از واحدهای تصمیم‌گیری در درون خود به بخش‌های کوچک‌تری تقسیم می‌شوند و با مدل‌های استاندارد تحلیل پوششی داده‌ها که سازمان را به صورت یک بخش کلی در نظر می‌گیرند، نتایج منطقی حاصل نمی‌شود. بنابراین لازم است از مدل‌هایی همچون مدل DEA دومرحله‌ای متناسب با چنین شرایطی برای ارزیابی دقیق‌تر واحدهای تحت بررسی استفاده شود. همچنین در شرایطی که تعداد زیادی ورودی و خروجی وجود داشته باشد، این روش چندان کارآمد نمی‌باشد و تعداد زیادی از واحدها را کارا اعلام می‌کند لذا برای رفع این مشکل تحقیق حاضر با استفاده از روش PROMETHEE ، ورودی‌ها و خروجی‌ها رتبه‌بندی می‌کند، سپس با مهم‌ترین آنها کار ارزیابی ادامه خواهد یافت. از آنجایی که همواره اطلاعات در دسترس کامل و دقیق نیستند این مهم در فضای خاکستری انجام خواهد شد. یافته‌های به دست آمده نشان‌دهنده کاهش چشمگیر واحدهای شناسایی شده کاراست که در نتیجه بهبود قدرت تمایز روش DEA را نشان می‌دهد. در کنار این، استفاده از محیط عدم اطمینان به ارزیابی‌ها و برآوردهای دقیق‌تر نسبت به مدل‌های قطعی انجامیده است.
One of the main challenges of performance evaluation in organizations and all systems is the irrationality and inaccuracy of the methods and criteria used. Traditional performance evaluation methods are mostly one-level, so they usually fail to provide sufficient feedback to identify inefficient units. Data envelopment analysis is a mathematical programming technique that compares the relative efficiency of several decision-making units based on observed inputs and outputs expressed by a variety of different scales. In practice, since many decision-making units are subdivided into smaller parts, with standard data envelopment analysis models that consider the organization as a whole, logical results are not obtained. Therefore, it would be better to use developed models like the two-stage DEA model to more accurately evaluate under investigation units in these conditions. Moreover, in cases that there are a large number of inputs and outputs, traditional DEA is not very efficient and it may consider a large number of units as efficient one. To deal with the problem, this study uses PROMETHEE method to rank criteria. After that, the efficiency evaluation problem is continued with most important inputs and outputs. Since the available information is usually incomplete and inaccurate, the problem is solved in the gray environment. The findings indicate a significant decrease in the number of identified efficient units which shows the improvement in discrimination power of DEA method. Additionally, the use of uncertain environment has led to more accurate estimates than previous definite models.
[1] Akhlaghi, R., & Rostamy-Malkhalifeh, M. (2019). A linear programming DEA model for selecting a single efficient unit. International journal of industrial engineering and operational research, 1(1), 60-66.
[2] Shuai, S., & Fan, Z. (2020). Modeling the role of environmental regulations in regional green economy efficiency of China: Empirical evidence from super efficiency DEA-Tobit model. Journal of Environmental Management, 261, 110227.
[3] Kamyab, N. & Mozaffari, M.R. (2020). Cost efficiency in the three-step DEA-R network process, Journal of New Researches in Mathematics, 6 (23), 147-170.
[4] Guo, Y., Yu, Y., Ren, H., & Xu, L. (2020). Scenario-based DEA assessment of energy-saving technological combinations in aluminum industry. Journal of Cleaner Production, 121010.
[5] Sueyoshi, T., Yuan, Y., & Goto, M. (2017). A literature study for DEA applied to energy and environment. Energy Economics, 62, 104-124.
[6] Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444.
[7] Jalilzadehazhari, E., Vadiee, A., & Johansson, P. (2019). Achieving a trade-off construction solution using BIM, an optimization algorithm, and a multi-criteria decision-making method. Buildings, 9(4), 81.
[8] Driscoll, D. A., Bode, M., Bradstock, R. A., Keith, D. A., Penman, T. D., & Price, O. F. (2016). Resolving future fire management conflicts using multi-criteria decision making. Conservation Biology, 30(1), 196-205.
[9] Jaini, N. I., & Utyuzhnikov, S. V. (2018). A fuzzy trade-off ranking method for multi-criteria decision-making. Axioms, 7(1), 1.
[10] Yazdani, M. (2018). New approach to select materials using MADM tools. International Journal of Business and Systems Research, 12(1), 25-42.
[11] Baghban, A., Amiri, M., Efat, L. & Sharafiavarzaman, Z. (2012). Evaluation and ranking of contractors and upgrade inefficient contractors with DEA gray, Operations research and its applications, 9, 21-38.
[12] Ekiz, M. K., & Tuncer Şakar, C. (2020). A new DEA approach to fully rank DMUs with an application to MBA programs. International Transactions in Operational Research, 27(4), 1886-1910.
[13] Peykani, P., Mohammadi, E., Emrouznejad, A., Pishvaee, M. S., & Rostamy-Malkhalifeh, M. (2019). Fuzzy data envelopment analysis: an adjustable approach. Expert Systems with Applications, 136, 439-452.
[14] Ju-Long, D. (1982). Control problems of grey systems. Systems & control letters, 1(5), 288-294.
[15] Malek, A. and Dabaghi, A. (2011). Foundations of gray systems theory with an overview of the methods of uncertainty, Terme Publications, Tehran, Iran (in Persian).
[16] Kao, C., & Hwang, S. N. (2008). Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan. European journal of operational research, 185(1), 418-429.
[17] Lotfi, F. H., Jahanshahloo, G. R., Soltanifar, M., Ebrahimnejad, A., & Mansourzadeh, S. M. (2010). Relationship between MOLP and DEA based on output-orientated CCR dual model. Expert Systems with Applications, 37(6), 4331-4336.
[18] Tavana, M., & Khalili-Damghani, K. (2014). A new two-stage Stackelberg fuzzy data envelopment analysis model. Measurement, 53, 277-296.
[19] Liu, W., Zhou, Z., Ma, C., Liu, D., & Shen, W. (2015). Two-stage DEA models with undesirable input-intermediate-outputs. Omega, 56, 74-87.
[20] Ma, J., Qi, L., & Deng, L. (2017). Efficiency measurement and decomposition in hybrid two-stage DEA with additional inputs. Expert Systems with Applications, 79, 348-357.
[21] Barak, S., & Dahooei, J. H. (2018). A novel hybrid fuzzy DEA-Fuzzy MADM method for airlines safety evaluation. Journal of Air Transport Management, 73, 134-149.
[22] Zhang, J., Wu, Q., & Zhou, Z. (2019). A two-stage DEA model for resource allocation in industrial pollution treatment and its application in China. Journal of Cleaner Production, 228, 29-39.
[23] Sarrico, C. S., & Dyson, R. G. (2004). Restricting virtual weights in data envelopment analysis. European Journal of Operational Research, 159(1), 17-34.
[24] Dimitrov, S., & Sutton, W. (2010). Promoting symmetric weight selection in data envelopment analysis: A penalty function approach. European Journal of Operational Research, 200(1), 281-288.
[25] Hatami-Marbini, A., Rostamy-Malkhalifeh, M., Agrell, P. J., Tavana, M., & Mohammadi, F. (2015). Extended symmetric and asymmetric weight assignment methods in data envelopment analysis. Computers & Industrial Engineering, 87, 621-631.
[26] Bagherikahvarin, M., & De Smet, Y. (2016). A ranking method based on DEA and PROMETHEE II (a rank based on DEA & PR. II). Measurement, 89, 333-342.
[27] Zhou, H., Wang, J. Q., & Zhang, H. Y. (2019). Stochastic multicriteria decision‐making approach based on SMAA‐ELECTRE with extended gray numbers. International Transactions in Operational Research, 26(5), 2032-2052.
[28] Brans, J. P., & De Smet, Y. (2016). PROMETHEE methods. In Multiple criteria decision analysis (pp. 187-219). Springer, New York, NY.
[29] Chen, T. Y. (2018). A novel PROMETHEE-based outranking approach for multiple criteria decision analysis with Pythagorean fuzzy information. Ieee Access, 6, 54495-54506.
[30] Ahadzadeh Namin, M., & Khamseh, E. (2017). Ranking Efficient DMUs in Two-stage Network DEA with Common Weights method. Journal of New Researches in Mathematics, 3(11), 5-18.
[31] Javaherian, N., Hamzeei, A., Sayyadi Toranlo, H. & Soleymani Damaneh, R. (2020). Evaluating the efficiency of two-
stage data envelopment analysis model based on intuitive triangular fuzzy numbers and auxiliary variables, Journal of New Researches in Mathematics (Article in press).
[32] Kao, C., & Liu, S. T. (2011). Efficiencies of two-stage systems with fuzzy data. Fuzzy Sets and Systems, 176(1), 20-35.
[33] Entani, T., & Tanaka, H. (2006). Improvement of efficiency intervals based on DEA by adjusting inputs and outputs. European Journal of Operational Research, 172(3), 1004-1017.