Mixed input and output orientations of Data Envelopment Analysis with Linear Fractional Programming and Least Distance Measures

Qaiser Farooq Dar,Arif Muhammad Tali,Tirupathi Rao Padi

doi:10.19139/soic.v4i4.225

Qaiser Farooq Dar, Arif Muhammad Tali + Show 1 more

Open Access

https://doi.org/10.19139/soic.v4i4.225

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Abstract

Data Envelopment Analysis (DEA) is an optimization technique to evaluate the efficiency of Decision- Making Units (DMU’s) together with multiple inputs and multiple outputs on the strength of weighted input and output ratios, where as Linear fractional programming is used to obtain DEA frontier. The efficiency scores of DMU obtained through either input orientation or output orientation DEA model will provide only local optimum solution. However, the mixed orientation of input and output variables will provide the global optimal solution for getting the efficient DMUs in DEA. This study has proposed the relationships of a mixed orientation of input and output variables using fractional linear programming along with Least-Distance Measure (LDM). Both constant returns to scale (CRS) and variable returns to scale (VRS) are considered for the comparative study.

Highlights

The objective function involving the ratio of two programming problems is the fractional programming
Data Envelopment Analysis (DEA) is a most powerful optimization technique to take the challenges of efficiencies like Technical efficiency, scale efficiency, allocate efficiency, economic efficiency as well as scope and super efficiency
Cooper, and Rhodes [8] introduced a non-parametric optimization technique for evaluates the efficiency of DMU known as DEA which is a special case of fractional programming problems (FPP)

Summary

Introduction

The objective function involving the ratio of two programming problems is the fractional programming. Many profit and non-profit organizations make use of DEA optimization technique for evaluating and benchmarking the relative efficiencies of different DMUs in the organization. Cooper, and Rhodes [8] introduced a non-parametric optimization technique for evaluates the efficiency of DMU known as DEA which is a special case of FPP. The attempt has been made to explore the concept of input-oriented and outputoriented models for assessing the productive efficiency by mixed-orientation of inputs and outputs in DEA and find the global optimal solution by using LDM. Section second explains the development of DEA for evaluation of technical efficiencies of organization which is characterized by constant and variable returns to scales with different orientations.

Linear Fractional Programming

BCC Data Envelopment Analysis Model with mixed-orientation

Mathematical formulation of BCC-model with mixed-orientation

Empirical illustration