روشی جدید برای رتبه بندی واحدهای تصمیم گیرنده کارا در تحلیل پوششی داده ها با استفاده از نظریه بازی همکارانه

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده ریاضی، آمار و علوم کامپیوتر، دانشگاه سمنان، سمنان، ایران

چکیده

رتبه‌بندی واحدهای تصمیم گیرنده (DMU) موضوعی مهم در تحلیل پوششی داده‌ها (DEA) است. هنگامی که DMUهای کارا نمرات کارایی یکسانی دارند، مدل‌های سنتی DEAمعمولا در رتبه‌بندی DMUهای کارا شکست می‌خورند. در سال‌های اخیر برای مقایسه و بهبود قدرت تمایز DMUهای‌کارا، از نظریه بازی‌ همکارانه استفاده شده است. در این تحقیق، روش جدیدی از بازی همکارانه پیشنهاد می‌شود. ایده این روش بدین‌صورت است که ابتدا با حذف زیرمجموعه معینی از واحدهای تصمیم گیرنده کارا از مجموعه واحدها، کارایی همه واحدها محاسبه، و سپس واحدهای کارا با استفاده از ارزش شپلی در نظریه بازی همکارانه، رتبه بندی می شوند. یک مثال عددی برای نشان دادن کارکرد روش پیشنهادی و مقایسه آن با روش‌های رتبه بندی اخیر ارائه می‌شود. در مطالعه تجربی، رتبه بندی DMUهای‌کارا مفید و معقول است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

A new approach for ranking efficient DMUs in Data Envelopment Analysis by using cooperative game theory

نویسندگان [English]

  • Ali Ashrafi
  • Mahdie Amiri
Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
چکیده [English]

Ranking of decision making units (DMU) is an important issue in data envelopment analysis (DEA). When efficient DMUs have the same efficiency scores, traditional DEA models usually fail to rank efficient DMUs. In recent years, cooperative game theory has been used to compare and improve the discrimination power of efficient DMUs. In this research, a new method of cooperative game is proposed. The idea of this method is that first, by removing a certain subset of efficientِDMUs from the set of units, the efficiency of all units is calculated, and then, using the Shepley value in cooperative game theory, the efficient units are ranked. A numerical example is presented to show the performance of the proposed method and its comparison with recent ranking methods. In the empirical study, the ranking of efficient DMUs is useful and reasonable.

کلیدواژه‌ها [English]

  • Data Envelopment Analysis (DEA)
  • Decision Making Unit (DMU)
  • Game Theory
  • Cooperative Game
  • Ranking efficient DMUs
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