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MTH309Sciences3 Unitsintermediate

Optimisation Theory

This course introduces students to the fundamental concepts and techniques of optimization theory. It covers linear programming, including problem formulation, graphical and algebraic solutions, and the simplex algorithm. Topics include duality, sensitivity analysis, transportation problems, integer programming, and unconstrained and constrained optimization in R^n. Students will learn to apply these methods to solve real-world problems in various fields.

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156h
Study Time
13
Weeks
12h
Per Week
intermediate
Math Level
Course Keywords
OptimizationLinear ProgrammingSimplex AlgorithmDualityInteger Programming

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
📊
Math Level
Moderate Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Linear Programming Formulation

2

Graphical Solution of LPP

3

Algebraic Solution of LPP

4

Simplex Algorithm

5

Duality in Linear Programming

6

Transportation Problem

7

Integer Programming

8

Unconstrained Optimization

9

Constrained Optimization

Total Topics9 topics

Ready to Start

No specific requirements needed

This course is designed to be accessible to all students. You can start immediately without any prior knowledge or specific preparation.

Assessment Methods

How your progress will be evaluated (3 methods)

Assignments

Comprehensive evaluation of course material understanding

Written Assessment

Tutor-Marked Assessments

Comprehensive evaluation of course material understanding

Written Assessment

Final Examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Operations Research Analyst

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Management Scientist

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Logistics Coordinator

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Supply Chain Manager

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Data Analyst

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Industry Applications

Real-world sectors where you can apply your knowledge

ManufacturingLogisticsSupply Chain ManagementFinanceOperations Management

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Linear Programming

3h

Unit 1: Linear Programming

3 study hours
  • •Read the introduction to Linear Programming.
  • •Define decision variables, objective functions, and constraints.
  • •Formulate LP problems from word problems.
Week
2

Module 1: Linear Programming

3h

Unit 1: Linear Programming

3 study hours
  • •Understand the general form and matrix form of LPP.
  • •Perform sensitivity analysis on LP problems.
  • •Interpret economic implications of sensitivity analysis.
Week
3

Module II: Methods of Solutions to Linear Programming Problems

3h

Unit 2: Graphical and Algebraic Methods

3 study hours
  • •Learn graphical methods for solving LPP.
  • •Understand the procedure for solving LPP by graphical method.
  • •Analyze different cases in graphical solutions.
Week
4

Module II: Methods of Solutions to Linear Programming Problems

3h

Unit 2: Graphical and Algebraic Methods

3 study hours
  • •Apply algebraic methods to solve LPP.
  • •Understand the relationship between graphical and algebraic methods.
  • •Solve TMAs related to graphical and algebraic methods.
Week
5

Module II: Methods of Solutions to Linear Programming Problems

4h

Unit 3: Simplex Algorithm (Algebraic and Tabular forms)

4 study hours
  • •Study the algebraic simplex method.
  • •Apply the simplex algorithm to solve LPP.
  • •Understand the tabular form of the simplex method.
Week
6

Module II: Methods of Solutions to Linear Programming Problems

4h

Unit 3: Simplex Algorithm (Algebraic and Tabular forms)

4 study hours
  • •Learn pivoting in the simplex method.
  • •Apply simplex algorithm to solve maximization problems.
  • •Apply simplex algorithm to solve minimization problems.
Week
7

Module II: Methods of Solutions to Linear Programming Problems

4h

Unit 4: Artificial Variables Technique

4 study hours
  • •Understand the artificial variables technique.
  • •Learn the Charne's Big M method.
  • •Apply the Big M method to solve LPP.
Week
8

Module II: Methods of Solutions to Linear Programming Problems

4h

Unit 4: Artificial Variables Technique

4 study hours
  • •Study the Two-Phase Simplex Method.
  • •Apply the Two-Phase Simplex Method to solve LPP.
  • •Compare Big M and Two-Phase Simplex Methods.
Week
9

Module II: Methods of Solutions to Linear Programming Problems

4h

Unit 5: Simplex Algorithm- Initialization and Iteration

4 study hours
  • •Understand initialization in the simplex algorithm.
  • •Learn about degeneracy and methods to resolve it.
  • •Study termination conditions in the simplex algorithm.
Week
10

Module III

4h

Unit 6: Duality in Linear Programming

4 study hours
  • •Study duality in linear programming.
  • •Formulate dual problems from primal problems.
  • •Understand important results in duality.
Week
11

Module III

4h

Unit 6: Duality in Linear Programming

4 study hours
  • •Apply the dual simplex method.
  • •Perform sensitivity analysis in linear programming.
  • •Solve TMAs related to duality and sensitivity analysis.
Week
12

Module IV

4h

Unit 7: Transportation Problem

4 study hours
  • •Study the transportation problem.
  • •Understand mathematical formulation of the transportation problem.
  • •Learn definitions related to transportation problems.
Week
13

Module IV

4h

Unit 7: Transportation Problem

4 study hours
  • •Apply North-West Corner Rule, Least Cost Method, and Vogel's Approximation Method.
  • •Perform optimality test using the MODI method.
  • •Resolve degeneracy in transportation problems.

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Review all key definitions and theorems related to linear programming.

2

Practice formulating LP problems from various scenarios.

3

Master the steps of the simplex algorithm and its variations.

4

Understand the relationship between primal and dual problems.

5

Practice solving transportation and integer programming problems.

6

Focus on understanding the assumptions and limitations of each method.

7

Create concept maps linking modules and units

8

Review all TMAs and assignments

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