تخصیص هزینه های ثابت با استفاده از کارایی متقاطع و نظریه بازی
محورهای موضوعی : آمارمصطفی داوطلب علیائی 1 , فاطمه قندی 2 , فریده داوطلب علیائی 3
1 - گروه ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه کاشان، کاشان، ایران
2 - گروه ریاضی کاربردی، دانشکده علوم پایه، دانشگاه تربیت دبیر شهید رجایی، تهران، ایران
3 - گروه ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه کاشان، کاشان، ایران
کلید واژه: Data Envelopment Analysis, Game theory, Cross-efficiency evaluation, Fixed costs allocation,
چکیده مقاله :
در بسیاری از کاربردها هزینه‌هایی ثابت برای ایجاد زیر ساخت‌های مشترک برای واحدهای یک سازمان وجود دارند که می‌بایستی میان واحدهای تصمیم گیرنده تقسیم شود. نحوه تخصیص هزینه‌ها میان واحدها که در رقابت با یکدیگر هستند از اهمیت زیادی برخوردار است. تحلیل پوششی داده‌ها ابزاری مناسب برای ارزیابی عملکرد واحدها با چندین ورودی و چندین خروجی است که بطور موفقی در مساله تخصیص هزینه‌های ثابت بکار گرفته شده است. دو روش عمده‌ای که برای تخصیص هزینه‌های ثابت مورد استفاده قرار می‌گیرند بر اساس بهبود و یا تغییر ناپذیری کارایی نسبی واحدها پس از تخصیص هستند. اما در تخصیص هزینه‌ها در میان واحدها بایستی هم جنبه رقابتی و هم جنبه همکاری میان واحدها در نظر گرفته شود. به همین منظور استفاده از تکنیکی که بر اساس ارزیابی همتا، کارایی واحدها را مورد بررسی قرار دهد بیشتر معقولانه به نظر می‌رسد. برای این منظور ما از روش ارزیابی کارایی متقاطع در تحلیل پوششی داده‌ها برای انجام تخصیص هزینه‌های ثابت استفاده می‌کنیم. در این مقاله با استفاده از روش ارزیابی کارایی متقاطع و مفاهیمی از نظریه‌ی بازی، یک روش تخصیص هزینه ثابت جدید، به گونه‌ای ارائه می‌دهیم که بردار امتیازهای کارایی متقاطع واحدها پس از تخصیص پاراتو باشد. در نهایت به کمک یک مثال کاربردی به بیان بهتر روش پیشنهادی و مقایسه آن با برخی از روش-های موجود می‌پردازیم.
In many applications, there are some fixed costs for constructing the common platform of an organization which must be shared by all decision making units (DMUs). It is important how one should allocate such costs among all competing DMUs. Data envelopment analysis (DEA), which is a useful tool to evaluate the relative efficiency of DMUs, has been successfully used in allocating fixed costs among DMUs. Two main approaches have been proposed to allocate fixed costs that are based on maintaining or improving the relative efficiency of DMUs. In fixed costs allocation, one however needs to take into account both competitive and cooperative aspects among all DMUs. Therefore, it seems more reasonable to apply a peer-evaluation method in evaluating the efficiency of DMUs. To this end, we use cross-efficiency evaluation in DEA to allocate fixed costs between DMUs. Using cross-efficiency method and some concepts of game theory, we propose a new fixed costs allocation approach to share costs between DMUs such that the vector of cross-efficiency scores of DMUs after allocation is Pareto. We use a real application to more illustrate the proposed method and compare it with some of the existing methods.
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