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# Another Look at Educational League Tables

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## Topic Description

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Summary
This project describes how the current university rank works and considers examining the effects of the weights on the performance of the universities. The uncertainty about the weights is solved by block modeling and the integer programming approach has been employed in helping construct the block model. A MP program has been written to analyze the test data and results were obtained. The project will discuss the results and evaluate those approaches for solving the problem.
Further improvement and modifications for the model are discussed. The main purpose is to produce a model which can solve such block modeling problem in any size. The MP model produced in this project is working particular well for solving block modeling problems in practice; further evaluation is included in the report.

Chapter 1 – An Introduction to the university ranking system
1.1 Introduction …………………………………………………………………………………1
1.2 The Existing Ranking System of the Universities………………………………………… .1
1.3 Reasons for Considering Alternative Models of Calculating the Rank …………………….2
Chapter 2 – Objectives and Project Management
2.1 Project Aim…………………………………………………………………………………4
2.2 Project Objectives………………………………………………………………………………4
2.3 Minimum Requirements ……………………………………………………………………4
2.4 Possible Extensions……………………………………………………………….. ……….4
2.5 Project Schedule ……………………………………………………………………………4
2.5.1 The Original Schedule ………………………………………………………………5
2.5.2 The Revised Schedule ……………………………………………………………….6
Chapter 3 – Background
3.1 Introduction …………………………………………………………………………………8
3.3 Block model in Math Form …………………………………………………………………..9
3.4 Herfindahl-Hirschman Index………………………………………………………………..10
3.5 Integer Programming Models……………………………………………………………….11
Chapter 4 – Building the Maths Models for Block Modeling
4.1 Introduction ……………………………………………………………………….. .13
4.2 Transfer Into Integer Linear Programming Model………………………………………… .13
Chapter 5 – The MP Model
5.1 Introduction …………………………………………………………………………………17
5.2 The Choice of IP Modeling Software ………………………………………………………17
5.3 The XPRESS-MP IP Model …………………………………………………………………..17
5.4 Decision Variables……………………………………………………………………………19
5.5 Building the Constraint……………………………………………………………………….20
5.6 Testing the Model…………………………………………………………………………….21
Chapter 6 –Data Transformation
6.1 Introduction ………………………………………………………………………….23
6.2 Re Produce the League Table…………………………………………………………..23
6.3 Produce the Test Data………………………………………………………………….24
Chapter 7 – Evolution and Evaluation of the Models
7.1 Introduction …………………………………………………………………………………..27
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7.2 Producing Random Test Data ………………………………………………………………..27
7.3 Testing the MP Model ………………………………………………………………………….28
7.4. Initial Test Results …………………………………………………………………………..29
7.5 Revised Test Results …………………………………………………………………………30
7.6 Evaluate Performance of the MP Model ………………………………………………………31
7.7 Compare with Published Data ……………………………………………………………….33
Chapter 8 – Conclusion
8.1 General Conclusions ……………………………………………………………………….37
8.2 Future Enhancements ………………………………………………………………………37
References………………………………………………………………………………………39
Appendices
Appendix A: Personal Reflection ……………………………………………………………40
Appendix B: Two example university tables ………………………………………………41
Appendix C: Transformation of Raw Data ………………………………………………………45
Appendix D: MP Model Results ………………………………………………………………..50
Appendix E: Final Test Results