این مقاله یک روش جدید بر اساس بردار ورودی ایده آل برای تخمین ورودی ها تحت حفظ اندازه کارایی از یک واحد تصمیم گیرنده وقتی که برخی یا همه خروجی های آن افزایش یافته است، پیشنهاد می دهد. بعبارت دیگر، این مقاله سوال زیر را مطالعه کرده است: تحت حفظ کارایی، به چه میزانی می بایستی ورودی های یک واحد تصمیم گیرنده افزایش یابد در شرایطی که برخی یا همه خروجی های آن افزایش داده شده باشد؟ در روش ارایه شده در این مقاله، برخلاف روش های پیشنهاد شده دیگر، سوال فوق فقط بر پایه مسایل برنامه ریزی خطی تک هدفی پاسخ داده شده است. مساله تخمین ورودی ها بر پایه مدل غیر شعاعی راسل پیشرفته مورد بررسی قرار گرفته است. شرایط لازم و کافی برای تخمین ورودی ها بر پایه برنامه ریزی خطی پیشنهاد گردیده است. بعلاوه، اگر کمبودی در هر یک از مولفه های خروجی واحد تصمیم گیرنده وجود داشته باشد شناسایی می شود. یک مثال با داده های واقعی برای توضیح از روش پیشنهادی ارایه شده است. تفاصيل المقالة

The present study addresses the following question: if among a group of decision making units, the decision maker is required to increase inputs and outputs to a particular unit in which the DMU, with respect to other DMUs, maintains or improves its current efficiencylevel, how much should the inputs and outputs of the DMU increase? This question is considered as a problem of inverse data envelopment analysis, and a method is introduced toanswer this question. Using (weak) pareto solutions of multiple-objective linear programming, necessary and sufficient conditions for inputs and outputs estimation are established.An application of inverse DEA using real data (for choosing a suitable strategy for spreading educational departments in a university) is presented. In addition, two new optimal notions are introduced for multiple-objective programming problems: semi-pareto and semi-weak pareto optimal notions. The aforementioned solutions are used to answer the above question. تفاصيل المقالة

In this paper, we propose a novel method using multiple-objective programming problems to answer the following question: if among a group of decision making units (DMUs), a subset of DMUs are required to merge and form a new DMU with specific input/output levels and a predefined efficiency target, how much should be the outputs/inputs of the merged DMU? This question answered according to the concept of inverse DEA. Sufficient conditions are established for input/output-estimation of the merged DMU using multiple-objective programming problems. A numerical example with real data is presented to illustrate the goals of this paper. تفاصيل المقالة

This paper evaluates the relative performance of open source software projects by evaluating multiple project inputs and multiple project outputs by using data envelopment analysis (DEA) model. The DEA model produces an efficiency score for each project based on project inputs and outputs. One of the important issues in data envelopment analysis is ranking DMUs. In this paper, open source software projects (OSS) are considered as decision making units which consume inputs to generate outputs. In this article, three standard Data Envelopment Analysis (DEA) models are used to evaluate the open source software projects. Also, super-efficiency model are used for ranking. Due to the inability of the models to rank projects, the AP-super efficiency model (the most important and popular method for ranking units) has been used for ranking OSS projects.The result of this research is a practical model that can be used by OSS project developers in order to evaluate the relative performance of their projects and make decision for their sources. Also, OSS projects can now be adequately ranked and evaluated according to project performance. تفاصيل المقالة