به حداکثر رساندن کارایی کل با تخصیص مجدد منابع در DEA: مطالعه موردی در بورس اوراق بهادار تهران

Subject Areas : International Journal of Industrial Mathematics

عصمت  نوروزی ¹ (گروه ریاضی، واحد تهران شرق، دانشگاه آزاد اسلامی، تهران، ایران.)
الهه  صرفی ² (گروه ریاضی، واحد دامغان، دانشگاه آزاد اسلامی، دامغان، ایران.)

Received: 2018-04-29 Accepted : 2021-12-01 Published : 2022-01-01

Keywords: تخصیص مجدد , , کارایی, به حداکثر رساندن کارایی کلی, تحلیل پوششی داده ها, منابع,

Abstract :

تجزیه و تحلیل پوششی داده ها یک تکنیک مبتنی بر برنامه ریزی ریاضی برای تعیین کارایی واحدهای تصمیم گیری (DMU) است. در برخی موارد ، مدیر قصد ندارد یک منبع جدید اضافه کند ، بلکه یکی از منابع قبلی را مجدداً تخصیص می دهد. تخصیص مجدد منابع ممکن است با اهداف مختلف انجام شود و مزایای متفاوتی داشته باشد. به عنوان مثال ، بدون افزودن منبع جدید و تنها با استفاده از منابع یکسان ، آیا می توان بازده یک واحد را افزایش داد یا حتی کارایی کل سیستم را افزایش داد؟ در این مقاله ، یک مدل ریاضی ارائه شده است که می تواند برای تخصیص مجدد یکی از منابع موجود قبلی بین واحدها به گونه ای استفاده شود که کارایی کل واحدهای تصمیم گیرنده به حداکثر مقدار ممکن برسد. در این مدل ، به منظور جلوگیری از کاهش بیش از حد سهم هر واحد از منبع مورد نظر ، محدودیت هایی در نظر گرفته شده است. در این محدودیت ها ، حد پایینی برای سهم هر واحد مشخص شده است. همچنین ، تخصیص مجدد منابع به احتمال زیاد منجر به تغییراتی در مقادیر خروجی واحدهای تصمیم گیرنده می شود. در مدل ارائه شده ، برخی از محدودیت ها در نظر گرفته می شوند که حد بالایی را برای خروجی های تولید شده توسط واحدها مشخص می کند. محدودیت های دیگری در این مدل وجود دارد. اول این که سهم کل واحدها از منبع مورد نظر نباید از مقدار موجود آن بیشتر باشد و دوم این که کل خروجی تولید شده توسط همه واحدها باید حداقل برابر کل خروجی تولید شده قبل از تخصیص مجدد باشد. مدل ارائه شده در این مقاله ، علاوه بر در نظر گرفتن محدودیت های توصیف شده ، که همه آنها اجتناب ناپذیر هستند ، به یک مدل برنامه ریزی خطی تبدیل شده است که توسط بسیاری از نرم افزارهای موجود قابل حل است.

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