The New Neutral Secondary Goal based on Ideal DMU Evaluation in‏‎‎ Cross-Efficiency

Document Type: Research Paper


Department of Mathematics, University of Mazandaran, Babolsar, Iran


Cross-efficiency is a famous ranking method for data envelopment analysis (DEA) that deletes unrealistic weights pattern with no need to a priori information ‎related ‎to ‎weights ‎restrictions. ‎This‎ method analyzes each decision making unit (DMU) taking into account the best weights resulted from assessing other DMUs. In cross-efficiency evaluation, secondary goals such as aggressiveness, benevolence and neutrality are used because there are alternative optimal solutions. The neutral secondary goal makes the decision maker have no problem in selecting the aggressive and benevolent secondary goals. In the article at hand, a new secondary purpose is introduced which ‎selects the ‎ ‎optimal ‎weight ‎among the ‎multiple‎ optimal ‎weights based on the evaluation of ideal virtual DMUs corresponding ‎to ‎each ‎DMU. Since this kind of ‎weight selection does not lead to any increase or decrease in other DMUs’ cross-efficiency, the new secondary goal is neutral. The advantage of this method over other methods is that the selected ‎weights are the best ‎possible weights, because it maximizes the ideal virtual DMUs’ efficiciency score corresponding ‎to ‎each ‎DMU. ‎For this purpose‎, some examples are used to illustrate  its difference with other methods‎.


Main Subjects

Article Title [Persian]

هدف ثانویه بی طرف جدید بر مبنای ارزیابی واحد تصمیم گیرنده ایده آل در کارایی متقاطع

Authors [Persian]

  • سید هادی ناصری
  • حمید کیایی
دانشکده علوم ریاضی، دانشگاه مازندران، بابلسر، ایران
Abstract [Persian]

کارایی متقاطع روش رتبه بندی معروفی در تحلیل پوششی داده ها است که الگوی وزن های غیرواقعی را بدون نیاز به اطلاعات برتر مرتبط با محدودیت های وزنی حذف می کند. این روش، هر واحد را از دیدگاه بهترین وزن های حاصل از ارزیابی واحدهای دیگر، مورد سنجش قرار می دهد. در ارزیابی کارایی متقاطع به دلیل وجود جواب های بهینه دگرین از هدف های ثانویه ای چون خوش بینانه، بدبینانه و بی طرف استفاده شده است. هدف ثانویه بی طرف باعث می شود تا تصمیم گیرنده، مشکلی برای انتخاب هدف های ثانویه خوش بینانه و بدبینانه نداشته باشد. در مقاله حاضر هدف ثانویه جدیدی معرفی می گردد که بر مبنای ارزیابی واحدهای مجازی ایده آل نظیر هر واحد، وزن های بهینه ای از میان وزن های بهینه دگرین انتخاب می کند و از آن جایی که این نوع گزینش وزن ها، تاثیری در افزایش یا کاهش کارایی متقاطع دیگر واحد ها ندارد، هدف ثانویه جدید بی طرف است. حسن این روش در مقایسه با روش های دیگر آن است که وزن های انتخاب شده، بهترین وزن های ممکن است چرا که نمره کارایی واحدهای مجازی ایده آل متناظر هر واحد را ماکزیمم می کند.

Keywords [Persian]

  • تحلیل پوششی داده ها
  • کارایی متقاطع
  • هدف ثانویه بی طرف
  • واحدهای مجازی ایده آل
  • رتبه بندی

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