presentation of a two stages method to determine the suitable benchmark and return to scale (case study: girls high school of one zone shiraz city)

Document Type: research paper

Author

Department of mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.

Abstract

In this paper, a two stages method to determine suitable benchmark and return scale of the decision making units set is presented. At first, all of the efficient reference set in no radial data envelopment analysis (DEA) based on linear programming is found. first, RAM model is introduced and units is investigated using this model, then, to run the given algorithm below steps is performed. At the first step, the type of reference set is introduced and at the second step, a unique linear programming problem based on primal dual method is proposed to know all of the possible reference sets for a decision making unit. At the third step, return to scale in the no radial DEA method is measured. Ultimately, girls high school of shiraz city one zone efficiency is investigated to show to be applicate of this method and suitable benchmark and return scale is presented for this set of decision making units.

Keywords


Article Title [Persian]

ارائه یک روش دو مرحله ای برای تعیین الگوی مناسب و بازده به مقیاس ( مطاله موردی: دبیرستانهای دخترانه ناحیه یک شهرستان شیراز)

Author [Persian]

  • جواد گرامی
استادیار، گروه ریاضی، دانشکده علوم، واحد شیراز، دانشگاه آزاد اسلامی، شیراز، ایران.
Abstract [Persian]

در این مقاله به ارائه یک روش دو مرحله ای برای تعیین الگوی مناسب و بازده به مقیاس مجموعه ای از واحدهای تصمیم گیرنده می پردازیم. در ابتدا به یافتن همه مجموعه‌های مرجع کارا در تحلیل پوششی داده ها (DEA ) غیر شعاعی بر پایه برنامه‌ریزی خطی می‌پردازیم. ابتدا مدل RAM را معرفی کرده و واحدها را با استفاده از این مدل ارزیابی می‌کنیم. سپس برای اجرای الگوریتم مورد نظر مراحل زیر را انجام می‌دهیم. در گام اول به معرفی سه نوع مجموعه مرجع می‌پردازیم و در گام دوم برای شناسایی همه مجموعه‌های مرجع ممکن برای یک واحد تصمیم گیرنده یک مسئله برنامه‌ریزی خطی منحصر به فرد که بر پایه روش اولیه – دوگانه می‌باشد، پیشنهاد می‌کنیم. در گام سوم بازده به مقیاس را در مدل DEA غیر شعاعی اندازه‌گیری می‌نماییم. در انتها برای نشان دادن کاربردی بودن این روش به ارزیابی و تحلیل کارایی دبیرستانهای دخترانه ناحیه یک شهر شیراز می پردازیم و الگوی مناسب و بازده به مقیاس را برای این مجموعه از واحدهای تصمیم گیرنده ارائه می دهیم.

Keywords [Persian]

  • تحلیل پوششی داده ها
  • الگو یابی
  • بازده به مقیاس
  • مجموعه مرجع کلی

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