Linear Optimisation Methods and Applications

Singapore University of Social Sciences

Linear Optimisation Methods and Applications (MTH310)

Synopsis

The formulation of optimization models is considered, together with applications, and the various solution techniques widely used to solve the underlying linear objective function under a constrained systems of linear equations. The computer software accompanying this course is used as a powerful tool to solve various linear optmimization models.

Level: 3
Credit Units: 5
Presentation Pattern: Every January
E-Learning: BLENDED - Learning is done MAINLY online using interactive study materials in Canvas. Students receive guidance and support from online instructors via discussion forums and emails. This is supplemented with SOME face-to-face sessions. If the course has an exam component, this will be administered on-campus.

Topics

Systems of linear equations.
Solution space.
Formulation of linear programming models.
Matrix formulation of simplex method.
Principles of the simplex solution method.
One-phase and two-phase simplex method.
Integer programming models.
Solution methods.
Applications of linear programming.
Integer programming.
Optimization problem-solving.
Case studies of industrial and applied problems.

Learning Outcome

Apply LU decomposition and examine conditions for convergence of solutions of linear systems.
Formulate linear programming models. Apply the graphical method to find the optimum solution of two-variables linear programming models.
Use the standard one-phase simplex method to solve linear optimisation models.
Analyse linear optimisation problems with the two-phase simplex solution technique.
Employ the branch and bound method to solve integer programming and 0-1 variable models.
Compute the optimum solution of a large linear programming model with the modern interior point method.
Construct a range of mathematical techniques to solve a variety of quantitative problems.
Formulate solutions to problems individually and/or as part of a group.
Analyze and solve a number of problem sets within strict deadlines.
Verify solutions related to linear optimisation using Mathcad.