APP MTH 2105 - Optimisation and Operations Research II
North Terrace Campus - Semester 2 - 2016
General Course Information
Course Code APP MTH 2105 Course Optimisation and Operations Research II Coordinating Unit School of Mathematical Sciences Term Semester 2 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 3.5 hours per week Available for Study Abroad and Exchange Y Prerequisites MATHS 1012 Assumed Knowledge Basic computer programming skills such as would be obtained from COMP SCI 1012, 1101, MECH ENG 1100, 1102, 1103, 1104, 1105, C&ENG ENG 1012 Course Description Every business in the world needs to make complex decisions. These decisions -- what to make, how to do it cheaply, how to schedule production, whether to outsource, how to get their goods to market, and so on -- dramatically affect their profitability. However, in the modern world, the factors affecting choices are too complex to manage by hand. Operations Research (OR) provide the tools needed to make these decisions rigorously and effectively.
This first course in OR will present some of the basic tools, concentrating on mathematical modelling and optimisation. But OR is an interdisciplinary topic drawing from game theory, statistics, and computer science as well as applied mathematics, and we will show some of these connections.
The course focuses on linear optimisation problems involving both continuous and integer variable, because these are used in a vast range of real situations. It will present techniques for optimisation and the theory behind them, but will also show how to use these techniques on real problems, for example minimising cost, maximising production capacity, or minimising risk.
Topics covered are: formulating a linear program; the Simplex Method; duality and complementary slackness; sensitivity analysis; primal-dual approaches; brand-and-bound; and heuristics such as the greedy method and simulated annealing. Examples will be presented from important application areas, such as the emergency services, telecommunications, transportation, and manufacturing.
Course Coordinator: Professor Matthew Roughan
Name Role Location Prof. Matthew Roughan Lecturer Inkgarni Wardli, 6.17 email@example.com
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes1. Understand how to translate a real-world problem, given in words, into a mathematical formulation.
2. Better understand design and analysis of algorithms: specifically through complexity analysis.
3. Write and apply computer code to problems, including
(a) mathematical optimisation techniques;
(b) using existing optimisation toolkits;
(c) writing computer programs to implement algorithms, and solve problem; and
(c) methods to deal with ingesting data.
4. Critically analyse and interpret results and present this in both oral and written form.
5. Specific knowledge:
(a) Formulate a Linear Program (LP) or translate into standard form, and use the Simplex Method to solve.
(b) Matlab programming for solving optimisation problems;
(c) Use duality and complementary slackness to analyse problems, for instance in applying sensitivity analysis to a LP.
(d) Formulation and solution of network problems using graph optimisation algorithms.
(e) Use branch-and-bound, and heuristic methods to solve general integer problems.
(f) Better understand the topic of linear algebra and its use in practical problems.
6. Ability to work in a team: specifically to solve larger problems, communicate technical knowledge, partition a problem into smaller tasks, and complete tasks on time.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
1,2,3,4,5,6 Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
1,2,3,4,5,6 Teamwork and communication skills
- developed from, with, and via the SGDE
- honed through assessment and practice throughout the program of studies
- encouraged and valued in all aspects of learning
6 Career and leadership readiness
- technology savvy
- professional and, where relevant, fully accredited
- forward thinking and well informed
- tested and validated by work based experiences
1,3,4,5 Self-awareness and emotional intelligence
- a capacity for self-reflection and a willingness to engage in self-appraisal
- open to objective and constructive feedback from supervisors and peers
- able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
Recommended Resources1. Taha. An introduction to operations research. Prentice Hall, 2007.
2. Nemhauser and Wolsey. Integer and combinatorial optimisation. Wiley, 1988.
3. Papadimitriou and Steiglitz. Combinatorial optimization -- Algorithms and complexity. Prentice Hall, 1982.
4. Ahuja, Magnanti and Orlin. Network flows: theory, algorithms, and applications. Prentice Hall, 1993.
5. Wright. Primal-dual interior point methods. SIAM, 1997.
Online LearningA version of the course notes will available online for those who wish to download and print prior to attending lectures. The format (either as two or one slide per page) is the same as the presentation slides used in the lectures, with room for you to annotate during lectures.
All assignments, tutorials, handouts and solutions where appropriate will also be available online progressively as the course ensues.
Learning & Teaching Activities
Learning & Teaching ModesThis course relies on lectures as the primary delivery mechanism for the material. The lecturer will guide the students through the material presented in this course in a total of 24 lectures. Downloading and prereading the online notes will enable the students to more actively engage the material and interact during lectures.
Practicals and tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload hours Lectures 24 24 Practicals 12 24 Tutorials 6 18 Assignments 5 30 Project 1 60 Total 156
Learning Activities SummaryLecture Outline
Lectures 1-2: Intro and revision
Lectures 3-7: Linear programming and the Simplex method
Lectures 8: Complexity of algorithms, and big-0 notation
Lectures 9-10: Duality, complementary slackness, and sensitivity analysis
Lectures 11: Integer programming intro
Lectures 12-13: Complexity analysis
Lectures 14: Matlab and AMPL
Lectures 15-16: Branch and Bound
Lectures 17-20: Solutions to integer programs
Lectures 21-22: Interior Point Algorithms
Lectures 23-24: Sensitivity analysis revised
Specific Course RequirementsMathematics IA and IB.
Computer programming skills, in particular Matlab, at an equivalent level to Scientific Computing.
Small Group Discovery ExperienceStudents will undertake a group project based on a real OR problem.
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Component Weighting Learning Outcomes Assessed Assignments 10% All Exam 70% All Project 20% All
Assessment Related RequirementsAn aggregate score of at least 50% is required to pass the course. A mark of at least 40% for the project is also required to pass the course.
Assessment DetailTo be announced later.
All written assignments are to be submitted to the designated hand-in boxes within the School of Mathematical Sciences with a signed cover sheet attached.
Late assignments will not be accepted, but students may be excused from an assignment for medical or compassionate reasons. In such cases, documentation is required and the lecturer must be notified as soon as possible before the fact.
The final written project report must be submitted on time with an appropriate signed assessment cover sheet attached to the report itself. Late project reports will not be accepted. Project reports will be retained by the lecturer but will be assessed prior to the beginning of the examination period and may be viewed by arrangement with the lecturer.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending
Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
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