اندازه‌گیری کارایی سود کلی استوار با در نظر گرفتن عدم قطعیت در بردارهای قیمت ورودی و خروجی
محورهای موضوعی : آمار
محمدعلی رعایت پناه
1
(گروه علوم ریاضی و کامپیوتر، دانشگاه خوارزمی، تهران، ایران)
نازیلا آقایی
2
(گروه ریاضی، واحد اردبیل، دانشگاه آزاد اسلامی، اردبیل، ایران)
کلید واژه: Data Envelopment Analysis, robust optimization, overall profit efficiency, uncertain data,
چکیده مقاله :
مدل کارایی سود کلی کلاسیک نیاز به اطلاعات دقیق از ورودی‌ها، خروجی‌ها و بردارهای قیمت ورودی و خروجی دارد. در حالی‌که در دنیای واقعی همه داده‌ها بطور دقیق در دسترس نمی‌باشد. در این حالت می‌توان از روش‌های تصادفی یا فازی برای محاسبه کارایی سود کلی استفاده نمود. در محاسبه کارایی سود کلی با این روش‌ها نیاز به اطلاعات بیشتری از داده‌ها از جمله تابع توزیع احتمال یا تابع عضویت داده‌ها می‌باشد، که در بعضی حالت‌ها ممکن است اطلاعات کافی برای تخمین این توابع وجود نداشته باشد و تنها دانش مربوط به پارامترها، تغییر آنها در یک فضای محدب بسته و کراندار است. لذا، در این مقاله با توجه به مدل عدم قطعیت بودجه‌ای در بهینه‌سازی استوار که قابل اعمال به مسایل بهینه‌سازی می‌باشد و نیز آنکه قابلیت تنظیم درجه محافظه کاری را دارد، مدل معادل استوار مساله محاسبه کارایی سود کلی با عدم قطعیت پارامتر بردار قیمت مطرح می‌گردد و سپس همتای استوار مدل برنامه‌ریزی خطی ارائه می‌شود. نتایج عددی نشان می­دهند مقدار کارایی سود کلی واحدهای تصمیم گیرنده توسط مدل پیشنهادی در مقایسه با حالت خوش‌بینانه بیشتر است.
The classic overall profit needs precise information of inputs, outputs, inputs and outputs price vectors. In real word, all data are not certain. Therefore, in this case, stochastic and fuzzy methods use for measuring overall profit efficiency. These methods require more information about the data such as probability distribution function or data membership function, which in some cases may not have sufficient information to estimate them, and only we have knowledge about the parameters so that they change in a convex space that is closed and bounded. Therefore, in this paper, we consider a budget uncertainty model in the robust optimization problem that able to adjust the conservative degree. The robust model by the input and output price vectors is proposed to compute overall profit efficiency measure. To illustrate the application of the proposed method, a numerical example is presented and the results show that the robust overall efficiency of the decision making units is higher than the optimistic model.
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