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 (whole numbers) - and some of the heuristic means of solution.  (Integer programming is, in general, much more difficult than standard linear programming).

Unit details

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Learning Outcomes

On successful completion of this unit, students will be able to:
  1. Analyse optimisation problems and formulate suitable linear programming models for them;  
  2. Implement graphical and other mathematical techniques to solve such problems;  
  3. Reflect on the underlying assumptions, and on the sensitivity of the linear programming models;  
  4. Formulate integer linear programming models and apply heuristic techniques to approximate optimal solutions; and  
  5. Construct computer models for special linear and integer linear programming models and interpret the solutions obtained by the computer system.  


Assessment type Description Grade
Other Quiz 10%
Other Written Reflection 10%
Assignment Written Assignment 1 (approximately 6 pages of mathematics) 40%
Assignment Written Assignment 2 (approximately 6 pages of mathematics) 40%
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 amount of pages to the weighting of the assessment item. This does not include screenshots and computer code.

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