37242 Introduction to Optimisation
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Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 35101 Introduction to Linear Dynamical Systems OR 33130c Mathematics 1 OR 33290 Statistics and Mathematics for Science OR 37131 Introduction to Linear Dynamical Systems
The lower case 'c' after the subject code indicates that the subject is a corequisite. See definitions for details.
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 35241 Optimisation in Quantitative Management
Description
This subject is intended to introduce optimisation methods and ideas of quantitative management that form an indispensable part of commercial decision support systems in such diverse fields as supply chain management, financial analysis, transportation, production planning and scheduling. It focuses on optimisation techniques for linear models, basic concepts of nonlinear optimisation, and applications of these mathematical methods in management and engineering. The topics covered include linear programming, introduction to nonlinear programming, and introduction to integer programming.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 01. | Apply fundamental principles and concepts of mathematical programming to analyse tractable simplifications of real-world problems in quantitative management and engineering, and demonstrate the understanding of the limitations of the simplified problem formulations; |
|---|---|
| 02. | Choose and implement the most appropriate mathematical programming method to solve a particular optimisation problem |
| 03. | Use industry-standard optimisation software (LINGO and/or Excel) to solve mathematical programming problems |
| 04. | Identify and describe relevant mathematical programming aspects of professional practice in diverse disciplines such as supply chain management, financial analysis, transportation, production planning and scheduling |
| 05. | Present the results of modelling task in a written report providing concise mathematical programming-based analysis and explanation of the methodology used. |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Demonstrate theoretical and technical knowledge of mathematical sciences including calculus, discrete mathematics, linear algebra, probability, statistics and quantitative management. (1.1)
- Evaluate mathematical and statistical approaches to problem solving, analysis, application, and critical thinking to make mathematical arguments, and conduct experiments based on analytical, numerical, statistical, algorithms to solve new problems. (2.1)
- Work autonomously or in teams to demonstrate professional and responsible analysis of real-life problems that require application of mathematics and statistics. (3.1)
- Use succinct and accurate presentation of reasoning and conclusions to communicate mathematical solutions, and their implications, to a variety of audiences, using a variety of approaches. (5.1)
Contribution to the development of graduate attributes
This subject seeks to develop students' abilities to recognise potential quantitative management problems and to provide students with experience in solving quantitative management problems using specialist optimisation solution techniques. This subject contributes to the following graduate attributes:
1. Disciplinary Knowledge
The workshops, tutorials and computer laboratory classes impart knowledge as well as skills, and demonstrate how to apply foundational principles and concepts to solve tractable simplifications of real-world problems.
2. Research, Inquiry and Critical Thinking
The workshops, tutorials, discussions, in-class optimisation tasks, and the modelling assignment provide students with the opportunities to learn and practise the skills in identifying/selecting the most appropriate approach from a set of familiar ones and making links between study designs and approaches to problem solving.
3. Professional, Ethical and Social Responsibility
The use of specialist optimisation software, including LINGO and/or Excel, is assessed in the modelling assignments. The optimisation problem-solving skills in diverse industrial fields, such as supply chain management, financial analysis, transportation, production planning and scheduling, are introduced and discussed in lectures and tutorials. The assessment questions in in-class optimisation tasks, the modelling assignment, and interactive tutorials are based upon practical applications.
5. Communication
Presentation of solutions to problems using appropriate professional language is emphasised in the modelling assignment and interactive tutorials/discussions.
Teaching and learning strategies
The subject is taught using a combination of workshops, tutorials, and interactive discussions according to the topic discussed in that session.
The workshops will involve the presentation, discussion, and exploration of problems, models, and solution techniques in an interactive environment. Students will be encouraged and are expected to contribute actively to the discussions, where significant theoretical and practical insights into real-world models in business and industrial contexts will be explored. Prior to each interactive workshop, students are expected to study and familiarise themselves with material delivered in the previous workshops and preview the topics/problems in workshop notes to be discussed in class. Besides the workshop notes provided via Canvas, online teaching and learning resources including supplementary documents and/or related YouTube clips will be provided.
The tutorials/discussions will provide opportunities for each student to apply mathematical skills including concepts and solution techniques learned from workshops in practice questions. The interactive tutorial activities facilitate effective and efficient collaborative learning in optimisation problem-solving tasks and offer an opportunity to practise communicating solution techniques. Students will be presented with simplified practical optimisation problems which can be solved using the mathematical skills developed in the workshops. Students are expected to attempt tutorial questions provided on Canvas prior to the tutorials and will be encouraged and asked to actively participate in the interactive tutorial classes with numerous opportunities available to receive verbal feedback from the tutors.
The computer laboratory classes are provided to give students a brief introduction to mathematical programming software packages, and it is expected that students can use them for solving tutorial/assignment questions.
In order to achieve effective and successful teaching and learning, it is expected that students attend all workshops, tutorials, discussions as well as computer laboratory classes, submit all assessment tasks, and actively participate in all teaching and learning activities. The recommended reading and references are provided as an aid to students’ learning. Canvas is used as the main medium for communication and learning support.
Relevant information will be announced on Canvas or sent to the students by email. A student can use only the UTS email account which is registered for this subject. It is the student's responsibility to have the email account in working condition and to check it regularly.
Content (topics)
The major topics covered in this subject are listed below.
1. Linear Programming: Concepts and Techniques
- Revision of Linear Algebra
- Simplex Method in Tabular Form
- Simplex Method in Algebraic Form
- Big-M method and Two-phase Simplex Method
- Revised Simplex Method
- Sensitivity Analysis
- Duality Theory and Dual Simplex Method
2. Introduction to Nonlinear Programming
- Unconstrained Nonlinear Programming: Steepest Descent Method and Newton's Method
- Constrained Nonlinear Programming: Lagrangian Relaxation Method
3. Introduction to Integer Programming
- Branch-and-Bound Method
- Cutting Plane Method
Assessment
Assessment task 1: Modelling written report
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge 2. research, inquiry and critical thinking 3. professional, ethical, and social responsibility 5. communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 01, 02, 03, 04 and 05 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1, 3.1 and 5.1 |
| Type: | Report |
| Groupwork: | Group, group assessed |
| Weight: | 20% |
| Length: | 4 weeks |
| Criteria: | 1. Correct application of fundamental principles and concepts of mathematical programming in optimisation analysis 2. Correct choice and implementation of mathematical programming solution procedures in optimisation problem solving 3. Effectiveness and efficiency of solution procedure implementation using standard software 4. Correct identification and description of relevant mathematical programming models in diverse disciplines of operations research 5. Quality of the problem solving results and analysis presented in the written report |
Assessment task 2: Class Tests
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge 2. research, inquiry and critical thinking |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 01 and 02 This assessment task contributes to the development of course intended learning outcome(s): 1.1 and 2.1 |
| Type: | Quiz/test |
| Groupwork: | Individual |
| Weight: | 40% |
| Length: | Class Test 1 - 45 min Class Test 2 - 75 min |
| Criteria: | 1. Correct application of fundamental principles and concepts of mathematical programming in optimisation analysis 2. Correct choice and implementation of mathematical programming solution procedures in optimisation problem solving |
Assessment task 3: Final Exam
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge 2. research, inquiry and critical thinking 5. communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 01, 02 and 05 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1 and 5.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 40% |
| Length: | 2 hours. Additional time will be allocated for the upload. |
| Criteria: | 1. Correct application of fundamental principles and concepts of mathematical programming in optimisation analysis 2. Correct choice and implementation of mathematical programming solution procedures in optimisation problem solving 3. Clarity of communication |
Minimum requirements
The final mark is a combination of all the marks gained in the components of assessment. In order to pass this subject, a student must get a final mark of at least 50.
Recommended texts
- W.L. Winston, Operations Research: Applications and Algorithms, 4th edition, Thomson, 2004.
References
- I. Griva, S.G. Nash and A. Sofer, Linear and Nonlinear Optimization. SIAM, 2009.
- S.G. Nash and A. Sofer, Linear and Nonlinear Programming. McGraw-Hill, 1996.
- R.L. Rardin, Optimization in Operations Research, Prentice-Hall, 1998.
- S.I. Gass, Linear Programming: Methods and Applications, McGraw-Hill, 1985.
- R.J. Vanderbei, Linear programming: Foundations and Extensions, Springer US, 2014.
- D.G. Luenberger and Y. Ye, Linear and Nonlinear Programming, Springer US, 2008.
- M.S. Bazaraa, J.J. Jarvis and H.D.Sherali, Linear Programming and Network Flows, Wiley, 2010.
- M.S. Bazaraa, H.D. Sherali and C.M. Shetty, Nonlinear Programming: Theory and Algorithms, Wiley, 2006.
- L. Schrage, Optimization Modelling with LINGO, Lindo Systems Inc., 2006.