3OR Website

MATH3321 3OR: Operations Research
Lecturer: Prof. Song Wang, MATH:Room 2.29, Phone: 6488 3350

Introduction

This is a 3rd year unit on Operations Research/Optimisation. It covers project mangement, linear/integer programming, dynamic programming and nonlinear programming etc. Operations Research (OR) is the mathematical theory of organization, planning and decision making. For example, how should Telstra plans a fibre-optic network? How should a house builder arrange the ordering of the various tasks, some of which can be done in parallel? How can a bank represent and optimize its currency trading? These and other questions such as airline staff rostering, optimal feed planning by farmers, many aspects of cluster analysis in statistics and image processing, time tabling, and vast numbers of others, come within the scope of operations research and are solvable by the methods we'll learn in this course.

Unit information

A list of the topics to be covered in this course is given in the Unit information sheet.

Tuition Pattern & Class Times

The course contains approximately 33 lectures and 6 tutorials.

Lectures/Tutorials

Monday 9am - 9:45am, MLR3.
Tuesday 1pm - 1:45pm and 2pm - 2:45pm, MLR2.

Assessment

The final assessment will be based on 3 marked assignments worth 30% and the final examination worth 70%. The assignments will be given to students in due course.

Lecture Notes

Notes on scheduling, project mangement, and integer and dynamic programming.
Notes on nonlinear programming.
If you have forgoten the 2nd year level OR, you may wish to read my notes on network optimisation and linear programming from my old MATH2224 website to refresh your mind.

References

Hillier F.S., Lieberman, G.J., Introduction to Operations Research, 7th Ed., McGraw-Hill, 2001.
Luenberger, D.G., Linear and Nonlinear Programming. Addison-Wesley, 1984.
Winston, W.L., Operations Research: Applications and Algorithms, 4th Ed.2004.

Exercise Problems & Assignments

Problem Sheet 1 (containing 2 Assignment 1 problems). Solutions to some problems.
Problem Sheet 2 (containing 3 Assignment 1 problems). Solutions to some problems.
Problem Sheet 3 (containing 4 Assignment 2 problems). Solutions to some problems.
Problem Sheet 4 (containing 4 Assignment 3 problems). Solutions to some problems.
Problem Sheet 5 (containing 3 Assignment 3 problems). Solutions to some problems.

Matlab Codes

In this course we will use MATLAB programs and the on-line lp_solve . The main MATLAB routine used in this course is Matlab linprog help page.

A Matlab code example: Matlab code for solving the LP problem
min (-50x1 - 60x2 - 80x3)
subject to
2x1 + 5x2 + 8x3 <= 300
6x1 + 4x2 + 5x3 <= 350
8x1 + 4x2 + 5x3 <= 480
x1,x2,x3 >= 0.

A Matlab code for the example on project critical paths.

Matlab code for solving Q9 of exercise sheet 2: drive programme; Subroutine for soving MIPs written by Sherif A. Tawfik of Cairo University.

Matlab code for solving the 2D Dynamic Programming problem: Question 9 of Practice Sheet 3.

Matlab code for solving the 1D minimisation problem by Newton's method:

Matlab codes for solving min f(x) = x_1^2 + x_1^2x_2^2 + 3 x_2^4 in Problem by

Newton method: newton2d.
Steepest descent method: SDM.m and SDMfunc.m.
Quasi-Newton method with Rank-1 correction: Rank1Correction.m and SDMfunc.m.

Matlab codes fo solving Q.2 of Problem Sheet 5: newton3d.m.

Matlab codes fo solving Q.4(a) of Problem Sheet 5: cg2d.m and CGfunc.m.

Faculty's policies

You should be familiar with the faculty's policies on assessment, plagiarism, appeal, calculators etc.