Two Methods to Obtain Preferred Efficiency for Negative Data (IS)

Subject Areas : International Journal of Mathematical Modelling & Computations

Hossein Abbasiyan ^{1 *} , Mohammad Jafar Doostideilami 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.

Received: 2022-02-28 Accepted : 2022-10-06 Published : 2023-03-01

Keywords: Common weights, interval scale, preferred efficiency, supporting hyper plane,

Abstract :

The original DEA models were applicable only to technologies characterized by positive inputs/outputs. We consider the interval scale (IS) variables especially when the IS variable is a difference of two different variables (like sales etc.) have been used as inputs and/or outputs. We measure Preferred Efficiency (PE) in Data Envelopment Analysis (DEA) with negative data when these data derived from IS variables. The PE is an efficiency concept that takes into account the decision maker’s (DM) preferences. We search the Most Preferred combination of inputs and outputs of Decision Making Units (DMUs) which are efficient in DEA. Also, we approximate indifference contour of the unknown Preferred Function (PF) at Most Preference Solution (MPS) with supporting hyperplane on PPS at MPS. We propose a way to obtain this the supporting hyperplane and also assume this the hyperplane is tangent on the indifference contour of PF. We use from the radial DEA problems with Variable Returns to Scale (VRS) (BCC models) at the combination orientation (both outputs are maximized and inputs are minimized). Also, We decompose each IS variable into two Ratio Scale (RS) variables and then utilizing from a compromise solution approach generate Common Weights (CW) for the decomposed input/output variables. In other to, we will introduce an MOLP model which its objective functions are input/output variables subject to the defining constraints of production possibility set (PPS) of DEA models. Lastly, the procedure and the resulting PE scores are applicable to solving practical problems by the mentioned models.

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