APP MTH 2105 - Optimisation and Operations Research II

North Terrace Campus - Semester 2 - 2015

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).

  • General Course Information
    Course Details
    Course Code APP MTH 2105
    Course Optimisation and Operations Research II
    Coordinating Unit Applied Mathematics
    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
    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 Staff

    Course Coordinator: Professor Matthew Roughan

    Name Role Location Email
    Prof. Matthew Roughan Lecturer Inkgarni Wardli, 6.17 matthew.roughan@adelaide.edu.au
    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes
    1. 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 programming techniques;  
    (b) using existing optimisation toolkits; 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) Use duality and complementary slackness to analyse problems, for instance in applying sensitivity analysis to a LP.  
    (c) Formulation and solution of network problems using graph optimisation algorithms.   
    (d) Use branch-and-bound, and heuristic methods to solve general integer problems.  
    (e) 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)
    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. 1,3,4,5
    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. 1,4
    A proficiency in the appropriate use of contemporary technologies. 3
    A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 1,2,3,4,5,6
    A commitment to the highest standards of professional endeavour and the ability to take a leadership role in the community. 1,2,3,4,5,6
  • Learning Resources
    Required Resources
    None.
    Recommended Resources
    1. 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 Learning
    A 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 Modes
    This 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.

    Workload

    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 Summary
    Lecture Outline

    Lectures 1-2:   Intro and revision
    Lectures 3-4:   Linear programming and the Simplex method
    Lectures 5-6:   Complexity of algorithms
    Lectures 7-8:   Duality
    Lectures 9-10: Transportation algorithm
    Lectures 11-12: Integer programming intro
    Lectures 13-14: First heuristics: implicit, greedy
    Lectures 15-16: Branch and Bound
    Lectures 17-20: Random Search: SA and Genetic Algorithms
    Lectures 21-22: extra topics: Interior Point Algorithms
    Lectures 23-24: project

    Specific Course Requirements
    Mathematics IA and IB.
    Some computer programming skills.

    Small Group Discovery Experience
    Students will undertake a group project based on a real OR problem.
  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    Component Weighting Learning Outcomes Assessed
    Assignments 10% All
    Exam 70% All
    Project 20% All
    Assessment Related Requirements
    An 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 Detail
    To be announced later.
    Submission

    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.

    Course Grading

    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.

  • Student Feedback

    The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

    SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

  • Student Support
  • Policies & Guidelines
  • Fraud Awareness

    Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student’s disciplinary procedures.

The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.