Efficiency Evaluation Using Data Envelopment Analysis by Modelling the Sum of Linear Ratios

Loading...
Thumbnail Image
File version
Primary Supervisor

Tatham, Peter

Other Supervisors

Saen, Reza Farzipoor

Wu, Yong

Editor(s)
Date
2016
Size
File type(s)
Location
License
Abstract

This dissertation explores a special class of the performance measurement problem where the overall performance is defined as the sum or arithmetic mean of two or more ratios (fractions). The problem is investigated with its links to the sum of linear ratios (SLR) problem in optimization theory, and a solution procedure based on linear goal programming (GP) is developed. The developed GP model is applied in three main areas of (i) the joint measurement of efficiency and effectiveness, (ii) the joint measurement of the technical efficiency and ecological efficiency, and (iii) the joint measurement of the efficiencies of the stages 1 and 2 of a two-stage process or activity. These three problems require simultaneous optimization of two linear ratios and can be defined as the maximization of the sum of two ratios. Unlike the traditional data envelopment analysis (DEA) models with only one efficiency ratio in the objective function, the problems investigated in this thesis do not belong to the class of quasiconvex optimization problems, and they also cannot be converted into linear models using the Charnes–Cooper transformation approach. Furthermore, optimizing the sum of linear ratios is a challenging problem, since several local optima might exist and obtaining a global optimal solution is not always guaranteed.

Journal Title
Conference Title
Book Title
Edition
Volume
Issue
Thesis Type

Thesis (PhD Doctorate)

Degree Program

Doctor of Philosophy (PhD)

School

Griffith Business School

Publisher link
Patent number
Funder(s)
Grant identifier(s)
Rights Statement
Rights Statement

The author owns the copyright in this thesis, unless stated otherwise.

Item Access Status
Note
Access the data
Related item(s)
Subject

Performance measurement

Sum of linear ratios problem

Data envelopment analysis

Charnes–Cooper transformation approach

Persistent link to this record
Citation