تعیین الگوی ایده آل واحدها با بررسی هم زمان کمترین هزینه، بیشترین درآمد و کوتاه‌ترین فاصله

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری، گروه ریاضی، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران

2 استاد، گروه ریاضی، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران

3 استاد، گروه ریاضی، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران

4 استادیار، گروه مدیریت، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران

چکیده

تحلیل پوششی داده‎ها، تکنیکی برای محاسبه کارایی نسبی مجموعه ای از واحدهای تصمیم گیری (DMUs) است. در این تکنیک ناکارآیی واحدهای تصمیم‎گیری را می‎توان با افزایش سطح خروجی‎ها ویا کاهش سطح ورودی‎ها بهبود بخشید. برای هر واحد ناکارآ نقطه تصویری روی مرز کارآ به عنوان الگو تعیین می شود. در این مقاله روشی ارائه می‎شود که درآن برای هر واحد ناکارآ الگوی ایده‌آلی به‎دست می‎آید که به صورت ترکیب محدب نقاط تصویر کارآیی هزینه، درآمد و کوتاه ترین فاصله می‌باشد. نکتهء قابل ذکر این است که اگرچه تضمینی وجود ندارد که الگوی به دست آمده روی مرز کارآ قرار گیرد ولی کارآیی آن به مراتب بیشتر از کارآیی واحد تحت ارزیابی‎اش خواهد بود و به‎طور همزمان سه هدف کمترین هزینه، بیشترین درآمد و کوتاه ترین فاصله را تا حد ممکن برآورده می‎کند. همچنین تضمین می‌شود هزینه ایده آل هر واحد کمتر یا مساوی هزینه مشاهده شدهء آن واحد و درآمد ایده آل هر واحد نیز بیشتر یا مساوی درآمد مشاهده شدهء آن واحد است. بنابراین پیدا کردن چنین الگوی ایده‌آلی برای هر واحد ناکارآ می‎تواند از اهمیت بالایی برخوردار باشد. در انتها، مدل پیشنهادی روی یک مثال ساده پیاده‌سازی خواهد شد.

کلیدواژه‌ها


عنوان مقاله [English]

Determining the ideal pattern of units by simultaneously examining the lowest cost, highest revenue and closest distance

نویسندگان [English]

  • Seyedeh Fatemeh Bagheri 1
  • Alireza Amirteimoori 2
  • Sohrab Kordrostami 3
  • Mansour Soufi 4
1 PhD Student, Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
2 Professor, Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
3 Professor, Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
4 Assistant Professor, Department of Management, Rasht Branch, Islamic Azad University, Rasht, Iran
چکیده [English]

Data envelopment analysis (DEA ) is a technique to evaluate the relative performance of a set of decision - making units ( DMUs ) . Corresponding to each inefficient DMU , an efficient benchmark on efficient frontier is determined and inefficient DMUs are projected to this benchmark by increasing their outputs and decreasing inputs . In this paper , a DEA - based procedure is proposed to determine an ideal benchmark to each inefficient unit . Our proposed benchmark dominates the unit under evaluation and it is a convex combination of projection points obtained from different aspects : cost, revenue efficiencies and the closest distance . A n important point is that although the obtained benchmark is not necessarily an efficient point, however , it dominates the unit under consideration . At the end of the paper , the proposed model would be implemented on a simple numerical example .

کلیدواژه‌ها [English]

  • Data Envelopment Analysis
  • Ideal pattern
  • Cost Efficiency
  • Revenue efficiency
  • Closest distance
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