Stability region of returns to scale using inverse Data Envelopment Analysis
Subject Areas : International Journal of Data Envelopment Analysis
Haleh moradi
1
,
Farhad Hosseinzadeh Lotfi
2
*
,
Mohsen Rostamy
3
1 - Department of Mathematics, science and research Branch, Islamic Azad University, Tehran, Iran
2 - Islamic Azad University, Science and Research Branch
3 - Department of Mathematics, science and research Branch, Islamic Azad University, Tehran, Iran
Keywords: Inverse Data Envelopment Analysis (IDEA), Maximum Productivity Size Scale (MPSS), Output/Input Estimation, Returns to Scale (RTS), Resource Constraints.,
Abstract :
The returns to scale (RTS) is an economic issue that would play a crucial role in the expansion or limitation of the decision-making unit (DMU) under-evaluation in data envelopment analysis (DEA). In this paper, we study an inverse DEA problem in which besides finding the appropriate amount of increase in output, preserving the primary classification of returns to scale for the DMU under-evaluation is considered. This research discusses two cases: when the DMU operates under constant returns to scale (CRS), and the other case considers DMUs with increasing returns to scale (IRS). Respectively for DMUs with CRS the upper bound obtained from the sensitivity analysis method is applied to determine the maximum amount of authorized output increase to preserve the primary classification of RTS. Then, we present two methods for the case of DMUs operating under the IRS. In the first one, we use an upper limit of the authorized amount of output's increase for modeling the problem in such a way that the IRS has remained unchanged. Then, the second method provides a model based on the closest most productivity scale size (MPSS) to the projection of the DMU under evaluation to solve the output estimation problem with maintaining the IRS. Finally, we give a numerical example to examine the application of the presented models.
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