Applying MCDEA Models to Rank Decision Making Units with Stochastic ‎Data

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

A. Ghofran ¹ , M. Sanei ² , G. Tohidi ³ , H. Bevrani ⁴

1 - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Islamic Azad University, Tehran-Center Branch, Tehran, Iran
3 - Department of Mathematics, Islamic Azad University, tehran-Center Branch, Tehran, Iran.
4 - Departments of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

تاریخ دریافت : 1398/02/08 تاریخ پذیرش : 1399/10/29 تاریخ انتشار : 1400/01/12

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.

چکیده انگلیسی:

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.

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