Ranking of decision making units based on cross efficiency by undesirable outputs and uncertainity

Document Type : research paper


1) louvain school of management and CORE, university catholique de louvain, louvain-la- neuve, belgium 2) Department of mathematics, Islamic azad university, Ardebil branch, Ardebil, iran


Cross efficiency is one of the useful methods for ranking of decision making units (DMUs) in data envelopment analysis (DEA). Since the optimal solutions of inputs and outputs weights are not unique so the selection of them are not simple and the ranks of DMUs can be changed by the difference weights. Thus, in this paper, we introduce a method for ranking of DMUs which does not have a unique problem. In the real life, the outputs can be shown as desirable and undesirable outputs. So it is important to provide models for the ranking of DMUs in present of desirable and undesirable outputs. The classic DEA models deals with certain data. But, in the real word, all data are not necessarily certain. For solve of this problem, we present a new method that compute the ranks of all DMUs by uncertain data and calculate the lower and upper bounds for the ranks of DMUs. Finally, the results of a simple example are given.


Article Title [فارسی]

رتبه‌بندی واحدهای تصمیم‌گیرنده با استفاده از کارایی متقاطع در حضور خروجی‌های نامطلوب و عدم قطعیت داده‌ها

Author [فارسی]

  • نازیلا آقایی
1) گروه مدیریت، مرکز تحقیق در عملیات و اقتصاد، دانشگاه کاتولیک لوون، لوون لنو، بلژیک 2) گروه ریاضی، واحد اردبیل، دانشگاه آزاد اسلامی، اردبیل، ایران
Abstract [فارسی]

کارایی متقاطع یک ابزار سودمند برای رتبه­بندی واحدهای تصمیم­گیرنده (DMU) در تحلیل پوششی دادها (DEA) می­باشد. اما از انجا که ممکن است در ارزیابی DMUها وزن­های بهینه منحصر بفرد نباشد لذا انتخاب یکی از آنها کار ساده­ای نخواهد بود و ممکن است نتایج حاصل از جواب­های بهینه دگرین، متفاوت باشد. برای این منظور، در این مقاله، روشی برای رتبه بندی DMUها که مشکل غیر یکتایی را ندارد، ارایه می­شود. از آنجا که خروجی­ها به دوصورت مطلوب و نامطلوب به کار
می­روند. پس ارایه مدل­هایی برای رتبه­بندی واحدهای تصمیم­گیرنده در حضور خروجی­های مطلوب ونامطلوب حایز اهمیت است. ازطرفی مدل­های DEA کلاسیک باداده­های قطعی سروکار دارد. ولی دردنیای واقعی، لزوماً همه داده­ها قطعی
نمی­باشند. در نتیجه، به دنبال رویکردی هستیم که کارایی DMU را در شرایط عدم قطعیت محاسبه کند. لذا واحدهای تصمیم­گیرنده باخروجی­های مطلوب ونا مطلوب بازه­ای رتبه­بندی می­شوند. برای رویارویی با این مسئله، یک کران پایین و یک کران بالا برای کارایی براساس رویکرد بازه­ای پیشنهاد می­شود. نتایج حاصل در یک مثال عددی ساده مورد تحلیل قرار می­گیرد.

Keywords [فارسی]

  • تحلیل پوششی داده‌ها
  • کارایی متقاطع
  • رتبه‌بندی
  • عدم قطعیت
  • خروجی نامطلوب
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