Nonparametric Model of Preferred Efficiency for Interval Scale Data (DEA)
Subject Areas : Data Envelopment Analysis
حسین عباسیان
1
(استادیار دانشکده ریاضی، دانشگاه آزاد اسلامی، واحد علی آباد کتول، علی آباد کتول، ایران)
Keywords: DEA, Preferred Efficiency, Interval Scale, Common Weights, Returns to Scale.,
Abstract :
The obtained benchmarks and preferred efficiency scores are strongly dependent on the selected Most Preferred Solution (MPS) units. The new directional value-based measures are more general than the existing preferred-based measures. We examine the use of interval scale (IS) variables, particularly when the IS variable represents the difference between two variables (such as sales) that serve as inputs and/or outputs. Data Envelopment Analysis models are widely used in commercial firms to assess their technical, cost, and revenue efficiencies. The new models that are introduced in this study are based on inverse DEA, which helps to preserve cost and revenue efficiency. we use a metric called Preferred Efficiency (PE) to measure the efficiency of Decision Making Units (DMUs) that have negative data derived from IS variables. PE is a concept that takes into account the DM's preferences while searching for the Most Preferred combination of DMU inputs and outputs that are efficient in DEA. Moreover, we approximate the indifference contour of the unknown Preferred Function (PF) at the MPS by using a supporting hyper plane on the production possibility set (PPS) at MPS. We propose to assume that it is tangent on the indifference contour of PF. We use radial DEA problems with Variable Returns to Scale (VRS), specifically BCC models, at the combination orientation where both outputs are maximized and inputs are minimized. We also decompose each IS variable into two Ratio Scale (RS) variables. Then, we use a compromise solution approach to generate Common Weights (CW) for the decomposed input/output variables. We will be introducing an MOLP model that uses input and output variables as objective functions. Moreover, the resulting performance evaluation scores and the corresponding methodology can be utilized to address practical issues with the aforementioned models.
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