| Semester 2, 2023 Online | |
| Units : | 1 |
| School or Department : | School of Mathematics, Physics & Computing |
| Grading basis : | Graded |
| Course fee schedule : | /current-students/administration/fees/fee-schedules |
Staffing
Course Coordinator:
Requisites
Pre-requisite: MAT1102 or ENM1600 or equivalent or approval from the examiner.
Enrolment is not permitted in MAT2200 if MAT1200 has been previously completed.
Overview
Decision making in fields such as industry, business, marketing, government and environmental management is often difficult because of uncertainty and constraints, and the complex nature of the system under study. Operations research is the scientific approach to solving problems which arise in such complex systems, and hence is an aid to decision making in many areas.
This course focuses on the model development, analytical techniques and the background mathematics necessary for the solution and post-optimal analysis of linear programming, integer programming, transportation, assignment, network, and critical path problems.
Course learning outcomes
On completion of this course students should be able to:
- select and develop appropriate mathematical models for decision making problems
- apply appropriate techniques to solve a range of models of mathematical and real-world problems
- interpret and communicate the results of analyses to expert and non-expert audiences
- analyse the effects of changing model parameters on LP model predictions
- use software to solve and analyse L.P. problems
Topics
| Description | Weighting(%) | |
|---|---|---|
| 1. | Introduction to Linear Programming History of OR, prototype problems, the systems approach to problem solving, methodology of OR. Linear programming will be introduced through a variety of applications, leading to a general definition of an L.P. problem. Graphical solution of problems with 2 decision variables will be shown and the corner point method will be used for solving problems with a 2 or more-decision variable. An elementary presentation of sensitivity analysis will be given. | 10.00 |
| 2. | Simplex Method The canonical and standard forms of L.P. problems will be discussed, and the concept of slack and surplus variables introduced. Basic and non-basic variables will be introduced via 2-dimensional problems, leading to a discussion of the general case. The simplex method will then be studied and applied to all cases. The cases of infeasible and unbounded problems, and problems with an infinite number of solutions will be examined. | 17.00 |
| 3. | Duality The idea of the dual of an L.P. problem will be introduced, and the relationships between the primal and dual problems studied. | 12.00 |
| 4. | Sensitivity Analysis It will be emphasised that the solution obtained is dependent on the values of the parameters being known precisely, whereas in fact these parameters are only estimates and/or liable to change. The effect on the solution of changing the objective function or constraints will be studied along with the introduction of new constraints and variables. | 12.00 |
| 5. | Transportation and Assignment Problems The special case of L.P. problems which can be formulated as transportation or assignment problems will be studied, using more efficient methods of solving these problems. Transportation problems studied will include those requiring dummy sources and destinations, and a variety of starting procedures will be considered. The Hungarian method will be used in solving assignment problems | 20.00 |
| 6. | Integer Programming Applications of pure and mixed integer programming will be introduced, and the branch and bound method will be introduced. | 9.00 |
| 7. | Graphs, Networks, and Trees. Elementary graph theory will be introduced to provide a basis for the use of networks to model a variety of problems. Critical path, shortest route, minimal spanning tree and maximal flow problems will be studied. Eulerian and Hamiltonian graphs will also be studied. | 20.00 |
Text and materials required to be purchased or accessed
(Available on the course StudyDesk.).
(Available on the course StudyDesk.).
Student workload expectations
To do well in this subject, students are expected to commit approximately 10 hours per week including class contact hours, independent study, and all assessment tasks. If you are undertaking additional activities, which may include placements and residential schools, the weekly workload hours may vary.
Assessment details
| Description | Group Assessment |
Weighting (%) | Course learning outcomes |
|---|---|---|---|
| Quiz | No | 10 | 1,2,3 |
| Problem Solving 1 | No | 30 | 1,2,3,5 |
| Problem Solving 2 | No | 30 | 1,2,3,4 |
| Problem Solving 3 | No | 30 | 1,2,3,5 |