## MAS3090 Operations Research (NJTech)

 Semester 1, 2019/20 10 Credits Lecturer: Dr Yi Li Reading List Aims Outcomes Teaching Methods Assessment Full Syllabus

Mathematical Programming is the title given to a collection of optimisation algorithms that deal with constrained optimisation problems. Here the problems considered will all involve constraints which are linear, and for which the objective function to be maximised or minimised is also linear. These problems are not continuously differentiable; special algorithms have to be developed. The module considers not only the solution of such problems but also the important area of post-optimality analysis; i.e. given the solution can one answer questions about the effect of small changes in the parameters of the problem (such as values of the cost coefficients)?

There are no prerequisites for this module.
No other modules have this module as a prerequisite.

## Outline syllabus

• Graphical techniques
• The Simplex Method
• Artificial variables, the M-Method and the two-phase Method
• The dual simplex Method
• Integer Programming and piece-wise linear programming
• Duality
• Elementary post-optimality analysis

## Aims

• To develop the mathematical skills that will provide you with the appropriate foundations for further mathematical studies in Operations Research.
• To enable you to analyse OR problems that may arise in your future employment.

## Learning outcomes

By the end of the module you should
• be able to use the Simplex Method and its variants, to solve Linear Programming Problems
• have an understanding of duality and its relevance in sensitivity analysis
• be familiar with the techniques of sensitivity analysis
• have an understanding of logical integer programming
• be familiar with running AMPL with common solvers

## Teaching methods

Lectures, problem solving, and computer lab sessions

32 lectures, 22 tutorials, 10 practicals

## Assessment

One formal 2 hour written examination (75% of final marks). Format: 4 compulsory questions.

Computer project (25% final marks)

## Full syllabus

• Graphical techniques: Converting a "word" problem into a mathematical. Graphical solutions for two-dimensional problems.
• The Simplex Method: A heuristic development of the Simplex Algorithm
• Artificial variables, the M-Method, the Two-Phase Simplex Method, and the Dual Simplex method.
• Integer Programming and piece-wise linear programming problems.
• The matrix formulation of the simplex algorithm.
• The dual problem and its relation to the Primal problem; construction of the Dual problem; properties of the primal-dual pair.
• Elementary post-optimality analysis: Adding and removing variables and constraints; changing cost coefficients and resources.