Determining the Exact Stability Region and Radius Through Efficient Hyperplanes

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran

Abstract

The main goal of this study was to address the sensitivity analysis fora specific efficient decision-making unit (DMU), which is under evaluation, by the variable returns to scale (VRS) technology to extend the efficiency stability region. Variations in inputs or outputs of any DMU can change the efficiency classification of that DMU as well as other DMUs, i.e., an efficient DMU can become inefficient and vice versa. This study considered the largest performance stability region for an extreme efficient DMU whose data could be changed in all directions of input/output space, including both directions of improving the situation and worsening the situation such that under these changes, the efficiency classification of all extreme DMUs would be preserved. We found the largest symmetric cell to the center of the extreme efficient DMU under evaluation, leading to an efficiency stability radius. In addition, data changes were only applied for the extreme efficient DMU, and the data for the other DMUs were assumed fixed. This stability region was determined by the defining hyperplanes of production possibility set (PPS) of VRS technology and the corresponding half-spaces. The suggested method is illustrated using real-world data.

Keywords

Main Subjects


Article Title [Persian]

تعیین دقیق ناحیه پایداری و شعاع پایداری توسط ابرصفحه های کارا

Authors [Persian]

  • نسیم عرب جزی
  • محسن رستمی مال خلیفه
  • فرهاد حسین زاده لطفی
  • محمد حسن بهزادی
گروه ریاضی، دانشکده علوم پایه، دانشگاه آزاد اسلامی، واحد علوم و تحقیقات، تهران، ایران
Abstract [Persian]

هدف اصلی این تحقیق، تحلیل حساسیتیک واحد تصمیم گیرنده(DMU) کارا با استفاده از فناوری بازده به مقیاس متغیر(VRS) برای توسعه ناحیه پایداری کارایی می باشد. تغییرات در ورودییا خروجی هر DMU می تواند طبقه بندی کارایی آن DMU و دیگرDMU ها را تغییر دهد، یعنییکDMU کارا می تواند ناکارا شود و بالعکس. این مطالعه بزرگترین ناحیه پایداری کارایی را براییکDMU کارای رأسی در نظر می گیرد که داده‌های آن در تمام جهات فضای ورودی/ خروجی تغییر می‌کند: شاملِهر دو جهت بهبود وضعیت و بدتر شدن وضعیت واحد رأسی، به گونه ای که تحت این تغییرات طبقه بندی کارایی همه واحدهای‌های رأسی ثابت خواهد ماند. علاوه بر این، بزرگترین سلول متقارن به مرکز DMU کارای رأسی را ارزیابی خواهیم کرد که منجر به شعاع پایداری کارایی می شود. همچنین، تغییرات داده ها فقط برایDMU رأسی اعمال می شود و داده های دیگر واحدها ثابت است. این ناحیه پایداری با مفهوم ابرصفحه‌های تعریف کننده مجموعه امکان تولید(PPS)با فناوریVRS و نیم فضاهای مربوطه تعیین می شود. روش پیشنهادی با استفاده از داده های دنیای واقعی در صنعت بانکداری نشان داده شده است.

Keywords [Persian]

  • تحلیل پوششی داده ها
  • تحلیل حساسیت
  • ناحیه پایداری
  • شعاع پایداری
  • ابرصفحه های تعریف کننده
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