Linear Optimisation Modelling
Credit points
(Generally, 1 credit = 10 hours of classes and independent study.)
Location
Online Real Time
Prerequisites
Co-requisites
(Corequisite units must be studied concurrently with this unit)
Overview
This unit introduces the topic of linear modelling, which is modelling by means of linear inequalities. Such problems arise in every aspect of industry, economics, planning, and management, and the modelling and solution of such problems has become a vital and central part of modern applied mathematics. The emphasis in the unit is on modelling: the creation of a mathematical model to describe a problem. Students are introduced to basic concepts through two- and three-dimensional graphs, as well as to some standard solution methods, such as the well-known Simplex Algorithm. The unit also investigates particular problems which have their own specific methods of modelling and solution, such as the transport and assignment problems. There is also discussion of integer programming – modelling where all the solutions must be integers – and some of the heuristic means of solution.
Learning Outcomes
On successful completion of this unit, students will be able to:
- Analyse optimisation problems and formulate suitable linear programming models for them;
- Implement graphical and other mathematical techniques to solve such problems;
- Reflect on the underlying assumptions, and on the sensitivity of the linear programming models;
- Formulate integer linear programming models and apply heuristic techniques to approximate optimal solutions; and
- Construct computer models for special linear and integer linear programming models and interpret the solutions obtained by the computer system.
Assessment
For Melbourne campuses
Assessment type: Test | Grade: 10%
Quiz 1
Assessment type: Test | Grade: 10%
Quiz 2
Assessment type: Assignment | Grade: 40%
Written Assignment 1 (approximately 6 pages of mathematics)
Assessment type: Assignment | Grade: 40%
Written Assignment 2 (approximately 6 pages of mathematics)
All assessment tasks are individual tasks. Although the two written assignments cover similar learning outcomes, the first assignment is more introductory, and the second will cover the material in more depth. Each of the written Assignments aligns the approximate number of pages to the weighting of the assessment item. This does not include screenshots and computer code.
Required reading
Session notes and other material will be made available to students on the learning management system.
As part of a course
This unit is not compulsory for any specific course. Depending on the course you study, this unit may be taken as an elective.