APP MTH 7105 - Optimisation & Operations Research
North Terrace Campus - Semester 2 - 2014
General Course Information
Course Code APP MTH 7105 Course Optimisation & Operations Research Coordinating Unit Applied Mathematics Term Semester 2 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3.5 hours per week Prerequisites MATHS 1012 Course Description Operations Research (OR) is the application of mathematical techniques and analysis to problem solving in business and industry, in particular to carrying out more efficiently tasks such as scheduling, or optimising the provision of services. OR is an interdisciplinary topic drawing from mathematical modelling, optimisation theory, game theory, decision analysis, statistics, and simulation to help make decisions in complex situations. This first course in OR concentrates on mathematical modelling and optimisation: for example maximising production capacity, or minimising risk. It focuses on linear optimisation problems involving both continuous, and integer variables. The course covers a variety of mathematical techniques for linear optimisation, and the theory behind them. It will also explore the role of heuristics in such problems. Examples will be presented from important application areas, such as the emergency services, telecommunications, transportation, and manufacturing. Students will undertake a team project based on an actual Adelaide problem.
Topics covered are: formulating a linear program; the Simplex Method; duality and Complementary slackness; sensitivity analysis; an interior point method; alternative means to solve some linear and integer programs, such as primal-dual approaches methods from a complete solution (such as Greedy Methods, and Simulated Annealing), methods from a partial solution (such as Dijkstra's shortest path algorithm, and branch-and-bound).
Course Coordinator: Professor Matthew Roughan
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes
1. Formulate a Linear Program and use the Simplex Method to solve Linear Programs and perform a sensitivity analysis on parameters in a Linear Program. 2. Use interior point methods and other alternative methods to solve Linear Programs, such as greedy methods, simulated annealing and branch-and-bound. 3. Construct a Dual Linear Program and use knowledge based on the theory of duality to determine optimality. 4. Write computer code for algorithms and heuristics and critically analyse and interpret results and present this analysis and interpretation of results in both oral and written form. 5. Understand the theoretical background of algorithms, and hence be able to adapt methods for related problems, being aware of the complexity issues that arise in optimisation algorithms.
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) Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. 1,2,3,4,5 The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 3,4 An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 1,2,3,4,5 Skills of a high order in interpersonal understanding, teamwork and communication. 4 A proficiency in the appropriate use of contemporary technologies. 1,4,5 A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 1,2,3,4,5 A commitment to the highest standards of professional endeavour and the ability to take a leadership role in the community. 4 An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. 4
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. PrenticeHall, 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 30 lectures. Downloading and prereading the online notes will enable the students to more actively engage the material and interact during lectures.
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 30 75 Tutorials 6 15 Assignments 5 30 Project 1 36 Total 156
Learning Activities SummaryLecture Outline
1. Introduction (1 lecture)
2. Linear Programming (17 lectures), including:
3. introduction to linear programming (1 lecture)
4. simplex phase II (3 lectures)5. simplex phase I (2 lectures)
6. duality and complementary slackness (2 lectures)
7. matrix algebra of linear programming (1 lecture)
8. sensitivity analysis (2 lectures)
9. primal/dual simplex methods (1 lecture)
10. complexity (2 lectures)
11. interior point methods (3 lectures)
12. Integer Programming (9 lectures), including:
13. introduction (1 lecture)
14. naïve approaches (1 lecture)
15. network problems (1 lecture)
16. greedy heuristics (2 lectures)
17. branch-and-bound and Dakin's methods (2 lectures)
18. random search methods (2 lectures)19. Revision (2 lectures)
1. Introduction to linear programming
2. Simplex method
3. Sensitivity analysis
4. Interior point methods
5. Networks and greedy heuristics
6. Random search methods
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.
SubmissionAll 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.
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