Optimisation Theory
- Sciences
- 300 level
- 3 credit units
- 288 pages
- 12 units
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.
About this course
- Difficulty
- Intermediate
- Study hours
- 156 hours
- Maths
- Intermediate
- Content
- Theoretical, problem solving, case study
- Practical work
- No
- Assignments
- Tutor Marked Assessments
- Final Examination
What you'll read
The real module and unit structure of MTH309, taken from the course material NOUN publishes.
- UNIT 1: LINEAR PROGRAMMINGPage 8
- UNIT 2. GRAPHICAL AND ALGEBRAIC METHODS.Page 28
- UNIT 3: SIMPLEX ALGORITHM (ALGEBRAIC AND TABULAR FORMS)Page 45
- UNIT 4: ARTIFICIAL VARIABLES TECHNIQUEPage 81
- UNIT 5 SIMPLEX ALGORITHM- INITIALIZATION AND ITERATIONPage 95
- UNIT 6: DUALITY IN LINEAR PROGRAMMINGPage 123
- UNIT 7: TRANSPORTATION PROBLEMPage 157
- UNIT 8: INTEGER PROGRAMMINGPage 179
- UNIT 9: BASIC CONCEPTS OF RNPage 205
- UNIT 10: OPTIMIZATION IN RNPage 229
- UNIT 11: UNCONSTRAINED OPTIMIZATIONPage 241
- UNIT 12: CONSTRAINED OPTIMIZATIONPage 264
One paragraph, so you can see how it reads
MTH309 · UNIT 1: LINEAR PROGRAMMING
The Simplex method which is the most popualar and powerful tool for solving linear pro- gramming, to be studied in full later in this course, was published by Dantzig in 1949.
What you should be able to do
- Formulate linear programming problems from real-world scenarios.
- Solve linear programming problems using graphical and algebraic methods.
- Apply the simplex algorithm to solve optimization problems.
- Understand and apply duality theory in linear programming.
- Solve transportation problems using various methods.
- Apply integer programming techniques to solve discrete optimization problems.
- Analyze and solve unconstrained and constrained optimization problems.
What it prepares you for
- Operations Research Analyst
- Management Scientist
- Logistics Coordinator
- Supply Chain Manager
- Data Analyst
- Manufacturing
- Logistics
- Supply Chain Management
- Finance
- Operations Management
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module II: Methods of Solutions to Linear Programming Problems
Unit 3: Simplex Algorithm (Algebraic and Tabular forms)
The algebraic simplex method requires a strong understanding of linear algebra and matrix operations, making it challenging for students with weaker mathematical backgrounds.
- Module II: Methods of Solutions to Linear Programming Problems
Unit 4: Artificial Variables Technique
The Charne's Big M method involves introducing a large penalty (M), which can be conceptually difficult and lead to computational errors if not handled carefully.
- Module III
Unit 6: Duality in Linear Programming
The dual simplex method requires understanding the relationship between primal and dual problems, and the logic behind selecting entering and leaving variables is counterintuitive compared to the regular simplex method.
A suggested way through it
13 weeks, about 48 hours in total. Yours will differ.
- Week 1Module 1: Linear Programming
Unit 1: Linear Programming · 3 hours
Read the introduction to Linear Programming.. Define decision variables, objective functions, and constraints.. Formulate LP problems from word problems..
- Week 2Module 1: Linear Programming
Unit 1: Linear Programming · 3 hours
Understand the general form and matrix form of LPP.. Perform sensitivity analysis on LP problems.. Interpret economic implications of sensitivity analysis..
- Week 3Module II: Methods of Solutions to Linear Programming Problems
Unit 2: Graphical and Algebraic Methods · 3 hours
Learn graphical methods for solving LPP.. Understand the procedure for solving LPP by graphical method.. Analyze different cases in graphical solutions..
- Week 4Module II: Methods of Solutions to Linear Programming Problems
Unit 2: Graphical and Algebraic Methods · 3 hours
Apply algebraic methods to solve LPP.. Understand the relationship between graphical and algebraic methods.. Solve TMAs related to graphical and algebraic methods..
- Week 5Module II: Methods of Solutions to Linear Programming Problems
Unit 3: Simplex Algorithm (Algebraic and Tabular forms) · 4 hours
Study the algebraic simplex method.. Apply the simplex algorithm to solve LPP.. Understand the tabular form of the simplex method..
- Week 6Module II: Methods of Solutions to Linear Programming Problems
Unit 3: Simplex Algorithm (Algebraic and Tabular forms) · 4 hours
Learn pivoting in the simplex method.. Apply simplex algorithm to solve maximization problems.. Apply simplex algorithm to solve minimization problems..
- Week 7Module II: Methods of Solutions to Linear Programming Problems
Unit 4: Artificial Variables Technique · 4 hours
Understand the artificial variables technique.. Learn the Charne's Big M method.. Apply the Big M method to solve LPP..
- Week 8Module II: Methods of Solutions to Linear Programming Problems
Unit 4: Artificial Variables Technique · 4 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 9Module II: Methods of Solutions to Linear Programming Problems
Unit 5: Simplex Algorithm- Initialization and Iteration · 4 hours
Understand initialization in the simplex algorithm.. Learn about degeneracy and methods to resolve it.. Study termination conditions in the simplex algorithm..
- Week 10Module III
Unit 6: Duality in Linear Programming · 4 hours
Study duality in linear programming.. Formulate dual problems from primal problems.. Understand important results in duality..
- Week 11Module III
Unit 6: Duality in Linear Programming · 4 hours
Apply the dual simplex method.. Perform sensitivity analysis in linear programming.. Solve TMAs related to duality and sensitivity analysis..
- Week 12Module IV
Unit 7: Transportation Problem · 4 hours
Study the transportation problem.. Understand mathematical formulation of the transportation problem.. Learn definitions related to transportation problems..
- Week 13Module IV
Unit 7: Transportation Problem · 4 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..
Preparing for the exam
- Review all key definitions and theorems related to linear programming.
- Practice formulating LP problems from various scenarios.
- Master the steps of the simplex algorithm and its variations.
- Understand the relationship between primal and dual problems.
- Practice solving transportation and integer programming problems.
- Focus on understanding the assumptions and limitations of each method.
- Create concept maps linking modules and units
- Review all TMAs and assignments
Questions students ask about this course
What is MTH309 about?
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.
How many units does MTH309 have?
MTH309, Optimisation Theory, has 12 units across 1 module, over 288 pages of course material. You can read it one unit at a time.
How many credit units is MTH309?
MTH309 carries 3 credit units, at 300 level in Sciences.
Is MTH309 hard?
MTH309 is rated intermediate level, with intermediate mathematical content. It is mostly theoretical, problem solving and case study work.
How long does MTH309 take to study?
About 156 hours of study, spread across its 12 units.
How is MTH309 assessed?
MTH309 is assessed by Assignments, Tutor Marked Assessments and Final Examination.
What can I do with MTH309?
Operations Research Analyst, Management Scientist, Logistics Coordinator, Supply Chain Manager and Data Analyst.