Assessing the value efficiency of each unit in relation to the tangent hyper plane in DEA (units including negative data with interval scale)
محورهای موضوعی : Operation Research
Hossein Abbasiyan
1
,
Seyyed Ali Kazemipour
2
1 - Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran
2 - Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran
کلید واژه: Relative Efficiency, Radial Models in Data Envelopment Analysis, Interval Scale data, Most Preference Solution,
چکیده مقاله :
In data envelopment analysis, value efficiency is an efficiency concept that uses the decision maker's priorities to calculate it. In this article, data with interval scale is the difference of two different data of inputs and outputs with a ratio scale, and one of the innovations of this research is that it calculates the value efficiency of units that include negative data with an interval scale. In real value efficiency, the indifference curve of the value function is used, which is unknown, and another innovation of this research is that we approximate this curve with the tangent hyper plane at the point with most preferences and with the proposal of the decision maker, we consider one of the technical efficiency units as the point with the most preferences. To find this tangent hyper plane, we use the dual problem of radial models, which have returns to variable scale. Finally, the distance of each decision-making unit to the tangent hyper plane shows the value efficiency of that unit. In the presented numerical example, the obtained results are very close to the results of Halme and his colleagues’ models, and this method can provide a suitable approximation for value efficiency.
In data envelopment analysis, value efficiency is an efficiency concept that uses the decision maker's priorities to calculate it. In this article, data with interval scale is the difference of two different data of inputs and outputs with a ratio scale, and one of the innovations of this research is that it calculates the value efficiency of units that include negative data with an interval scale. In real value efficiency, the indifference curve of the value function is used, which is unknown, and another innovation of this research is that we approximate this curve with the tangent hyper plane at the point with most preferences and with the proposal of the decision maker, we consider one of the technical efficiency units as the point with the most preferences. To find this tangent hyper plane, we use the dual problem of radial models, which have returns to variable scale. Finally, the distance of each decision-making unit to the tangent hyper plane shows the value efficiency of that unit. In the presented numerical example, the obtained results are very close to the results of Halme and his colleagues’ models, and this method can provide a suitable approximation for value efficiency.
