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Evaluation of Primary Schools Using DEA

10,000 3,000

Topic Description

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Summary
The purpose of this project was to use Data Envelopment Analysis (DEA) as a method of
performance measurement to derive the relative efficiencies of primary schools. To my current
knowledge this is the first application of DEA to the primary school education system in the United
Kingdom.
The objectives of this project were:
• To study Data Envelopment Analysis and its application to measure the efficiency of primary
schools.
• To implement the DEA models using suitable optimisation software packages.
• To determine efficient and inefficient primary schools.
These objectives were achieved by considering the work of Thanasoullis [1, 3] and Charnes [2] in the
field of Data Envelopment Analysis. By investigating suitable measures for performance evaluation, I
was able to construct a basic DEA model that when implemented in the form of a linear program
generated valid solutions. These solutions determined which primary schools were underachieving
and those which could be deemed efficient.
The following was achieved in this project:
• Research into the field of DEA, demonstrating its derivation, current applications, strengths
and weaknesses.
• The determination of a set of primary schools that would undergo performance evaluation.
• Investigation of suitable measures for which primary school performance assessment could
be based on.
• Mathematical design and construction of a DEA model implemented using an optimisation
software package. Construction of automaton programs using Perl to enhance the
performance of applying DEA to the data.
• Validation and analysis of the relative efficiencies derived from DEA.
• Derivation of targets for inefficient primary schools to improve performance.
All project milestones and deliverables have been completed. The implementation of the DEA
models, the data used for performance measurement and the automaton programs are on the CD that
accompanies this project report.

Contents
CHAPTER 1: PERFORMANCE MEASUREMENT AND DEA……………………………………………………………..1
1.1: THE IMPORTANCE OF PERFORMANCE MEASUREMENT…………………………………………………………………………1
1.2: PERFORMANCE MEASUREMENT METHODS OUTLINE …………………………………………………………………………..1
1.3: DEA – A BRIEF INTRODUCTION ……………………………………………………………………………………………………….2
1.4: PROJECT AIMS AND MINIMUM REQUIREMENTS…………………………………………………………………………………..3
1.5: DELIVERABLES ………………………………………………………………………………………………………………………………..4
1.6: PROJECT SCHEDULE …………………………………………………………………………………………………………………………4
1.7: RELEVANCE TO DEGREE PROGRAM……………………………………………………………………………………………………6
1.8: METHODOLOGY ……………………………………………………………………………………………………………………………….6
CHAPTER 2: THE CONCEPTS OF DEA……………………………………………………………………………………………….8
2.1: INTRODUCTION TO LINEAR PROGRAMMING………………………………………………………………………………………..8
2.2: CHARNES ET AL’S BASIC DEA MODEL (1978) ……………………………………………………………………………………8
2.3: THANASOULLIS AND DUNSTAN’S DEA MODEL ………………………………………………………………………………..11
2.4: BREAKDOWN OF THANASOULLIS AND DUNSTAN’S DEA MODEL……………………………………………………….12
2.5: PREVIOUS APPLICATIONS………………………………………………………………………………………………………………..13
2.5.1: Police Services……………………………………………………………………………………………………………………….13
2.5.2: Financial Services ………………………………………………………………………………………………………………….14
2.6: STRENGTHS AND WEAKNESSES OF DEA…………………………………………………………………………………………..14
CHAPTER 3: DETERMINING THE DATA SET………………………………………………………………………………….16
3.1: PRIMARY SCHOOLS TO BE EVALUATED ……………………………………………………………………………………………16
3.2: LIMITATIONS OF GATHERING DATA …………………………………………………………………………………………………18
CHAPTER 4: DETERMINING THE INPUT AND OUTPUT MEASURES………………………………………….19
4.1: INPUT AND OUTPUT MEASURES……………………………………………………………………………………………………….19
4.2: THE RETURNS TO SCALE CONCEPT ………………………………………………………………………………………………….24
CHAPTER 5: DESIGN AND IMPLEMENTATION OF THE DEA MODEL……………………………………….27
5.1: BASIC DEA MODEL (M1) FOR PRIMARY SCHOOL EVALUATION ………………………………………………………..27
5.2: TOOLS, APPLICATIONS AND SOFTWARE……………………………………………………………………………………………28
5.2.1: The Operating System Environment…………………………………………………………………………………………28
5.2.2: The Problem Solving Process ………………………………………………………………………………………………….29
5.3: VALIDATING THE MODEL SOLUTIONS………………………………………………………………………………………………31
5.3.1: Problems with Input Weights…………………………………………………………………………………………………..31
5.3.2: Problems with Output Weights ………………………………………………………………………………………………..32
5.4: MODEL IMPROVEMENTS AND WEIGHT RESTRICTIONS ………………………………………………………………………33
5.4.1: Input Weight Restrictions………………………………………………………………………………………………………..33
5.3.2: Output Weight Restrictions ……………………………………………………………………………………………………..34
CHAPTER 6: ANALYSING THE RESULTS OF DEA………………………………………………………………………….37
6.1: ANALYSIS OF RESULTS……………………………………………………………………………………………………………………37
CHAPTER 7: SETTING TARGETS FOR INEFFICIENT PRIMARY SCHOOLS ………………………………40
7.1: THE DUAL MODEL………………………………………………………………………………………………………………………….40
7.2: DERIVATION OF FEASIBLE TARGETS ………………………………………………………………………………………………..41
7.3: TARGETS FOR INEFFICIENT PRIMARY SCHOOLS…………………………………………………………………………………43
CHAPTER 8: PROJECT EVALUATION AND CONCLUSIONS…………………………………………………………45
8.1: EVALUATION AGAINST MINIMUM REQUIREMENTS ……………………………………………………………………………45
8.2: EVALUATION OF EXTENSIONS………………………………………………………………………………………………………….46
8.3: SUGGESTIONS FOR FURTHER WORK…………………………………………………………………………………………………47
REFERENCES ………………………………………………………………………………………………………………………………………..48
APPENDIX 1: PERSONAL EXPERIENCE……………………………………………………………………………………………

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