# Singapore University of Social Sciences

## Linear Optimisation Methods and Applications (MTH310)

Applications Open: To be confirmed

Applications Close: To be confirmed

Next Available Intake: To be confirmed

Language: English

Duration: 6 months

Fees: To be confirmed

Area of Interest: Science & Technology

Schemes: Lifelong Learning Credit (L2C)

Funding: To be confirmed

### 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.