Maximizing total efficiency by resource reallocation in DEA: A case study on Tehran Stock Exchange
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
1 - Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran.
2 - Department of Mathematics, Damghan Branch, Islamic Azad University, Damghan, Iran
کلید واژه: Efficiency, DEA, DMU, Reallocation, Data Envelopment Analysis,
چکیده مقاله :
Data Envelopment Analysis is a technique based on mathematical planning for specifying the efficiency of decision making units (DMUs). In some cases, manager is not going to add a new resource but to reallocate one of the previous resources. Reallocating a resource may be done for different purposes and has different benefits. For example, without adding a new resource and only using the same resources, is it possible to increase the efficiency of one unit or even increase the efficiency of the whole system? In this paper, a mathematical model is presented that can be used to reallocate one of the previous available resources between units in such a way that the total efficiency of decision-making units reaches the maximum possible value. In this model, in order to prevent excessive reduction of the share of each unit of the desired source, restrictions have been considered. In these constraints, a lower bound for the share of each unit is specified. Also, reallocating a resource is likely to lead some changes in output values of decision-making units. In the presented model, some constraints are considered that specify an upper bound for outputs produced by the units. There are other restrictions in this model. The first is that the total share of units from the desired resource should not exceed the amount available of it and the second is that the total output produced by all units should be at least equal to the total output produced before reallocation. The model presented in this article, in addition to considering the restrictions described, all of which are unavoidable, has been transformed into a linear programming model that can be solved by many existing software.
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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