APP MTH 2105 - Optimisation and Operations Research II

North Terrace Campus - Semester 2 - 2019

Businesses, governments and not-for-profit organisations are faced with complex decisions, for example, what and where to produce, how to do it cost effectively, and how to schedule resources. In the modern world, factors affecting decisions are complex, and decision-making is often too difficult to do by hand. Operations Research (OR) provides the tools needed to make such decisions rigorously and effectively. This course in OR will present some of the basic methods, concentrating on mathematical modelling and optimisation. But, OR is an interdisciplinary topic drawing from game theory, statistics, computer science and applied mathematics; we will show some of these connections. The course focuses on linear optimisation problems involving both continuous and integer variables, because they are used in a wide range of real-world situations. It will present the theory underlying optimisation, and also demonstrate how to apply optimisation techniques on real problems, for example maximising profit, minimising cost, or minimising risk. Topics covered include: linear programming; simplex method; duality and complementary slackness; sensitivity analysis; primal and dual algorithms; algorithm analysis and complexity; integer linear programming; branch-and-bound; heuristic methods; interior point methods; and network analysis. Examples will be presented from important application areas such as energy, telecommunications, transportation and manufacturing.

  • General Course Information
    Course Details
    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 Businesses, governments and not-for-profit organisations are faced with complex decisions, for example, what and where to produce, how to do it cost effectively, and how to schedule resources. In the modern world, factors affecting decisions are complex, and decision-making is often too difficult to do by hand. Operations Research (OR) provides the tools needed to make such decisions rigorously and effectively. This course in OR will present some of the basic methods, concentrating on mathematical modelling and optimisation. But, OR is an interdisciplinary topic drawing from game theory, statistics, computer science and applied mathematics; we will show some of these connections. The course focuses on linear optimisation problems involving both continuous and integer variables, because they are used in a wide range of real-world situations. It will present the theory underlying optimisation, and also demonstrate how to apply optimisation techniques on real problems, for example maximising profit, minimising cost, or minimising risk. Topics covered include: linear programming; simplex method; duality and complementary slackness; sensitivity analysis; primal and dual algorithms; algorithm analysis and complexity; integer linear programming; branch-and-bound; heuristic methods; interior point methods; and network analysis. Examples will be presented from important application areas such as energy, telecommunications, transportation and manufacturing.
    Course Staff

    Course Coordinator: Dr Andrew Black

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    1. Ability to translate real-world problems, described verbally, into a mathematical formulation.

    2. Understanding of algorithm design and analysis, and computational complexity.

    3. Proficiency in writing computer programs that call solvers to perform optimisations.      

    4. Ability to critically analyse and interpret results and present them in oral and written form.

    5. Ability to work in a team to solve practical problems on time through division of work and effective communication.

    6. Specific knowledge:   
    (a) Formulation of linear programs (LP) in standard form, and use of the simplex method to solve them. 
    (b) MATLAB programming for solving optimisation problems. 
    (c) Use of duality, complementary slackness and sensitivity analysis to examine optimisation problems.
    (d) Algorithm analysis and computational complexity. 
    (d) Formulation of network problems, and methods for solving them.   
    (e) Use of branch-and-bound and heuristic methods to solve integer linear optimisation problems.  
    (f) Better understanding of the application of linear algebra in solving practical problems.

    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
    4,6
  • Learning Resources
    Required Resources
    None.
    Recommended Resources
    1. Taha, H.A. (2011). Operations Research: An Introduction (9th ed.). Prentice Hall, Inc.
    2. Wolsey, L.A. and G.L. Nemhauser (1999). Integer and Combinatorial Optimization. John Wiley & Sons, Inc.
    3. Papadimitriou, C.H and K. Steiglitz (1998). Combinatorial Optimization: Algorithms and Complexity.
    4. Ahuja, R.K., T.L. Magnanti, and J.B. Orlin (1993). Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Inc.
    5. Wright, S.J. (1997). Primal-Dual Interior-Point Methods. Society for Industrial and Applied Mathematics.
    Online Learning
    Course notes will be published on MyUni ahead of delivery of the corresponding lecture. The format is the same as the slides presented in the lecture.

    All assignments, tutorials, practicals and the project will also be published on MyUni progressively.

  • 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 the lectures. Downloading and prereading the course notes will enable the students to more actively engage in the material and interact during lectures.

    Tutorials, practicals and the project supplement the lectures by providing exercises to enhance the understanding obtained through lectures. Written assignments provide 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 23 23
    Practicals 12 24
    Tutorials 6 15
    Assignments 6 30
    Project 1 60
    Total 152
    Learning Activities Summary
    All examinable material for this course is covered in the lecture notes, and practised in assignments, tutorials, practicals and the project.  Lecture topics include: linear programming; simplex method; duality and complementary slackness; sensitivity analysis; primal and dual algorithms; algorithm analysis and complexity; integer linear programming; branch-and-bound; heuristic methods; interior point methods; and network analysis.

    Specific Course Requirements
    Mathematics IA and IB.
    Computer programming skills, in particular Matlab, at an equivalent level to Scientific Computing.

    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
    To pass this course requires an aggregate mark of at least 50%, and at least 40% for the project.
    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
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