MAT2200 Operations Research 1
|Semester 2, 2019 On-campus Toowoomba|
|Short Description:||Operations Research 1|
|Faculty or Section :||Faculty of Health, Engineering and Sciences|
|School or Department :||School of Agric, Comp and Environ Sciences|
|Student contribution band :||Band 2|
|ASCED code :||010101 - Mathematics|
|Grading basis :||Graded|
Examiner: Trevor Langlands
Pre-requisite: MAT1102 or ENM1600 or equivalent or approval from the examiner.
Enrolment is not permitted in MAT2200 if MAT1200 has been previously completed.
Decision making in fields such as industry, business, marketing, government and environmental management is often difficult because of uncertainty and constraints, and the complex nature of the system under study. Operations research is the scientific approach to solving problems which arise in such complex systems, and hence is an aid to decision making in many areas.
This course focuses on the model development, analytical techniques and the background mathematics necessary for the solution and post-optimal analysis of linear programming, integer programming, transportation, assignment, network, and critical path problems.
On completion of this course students should be able to:
- select and develop appropriate mathematical models for decision making problems
- apply appropriate techniques to solve a range of models of mathematical and real-world problems
- interpret and communicate the results of analyses to expert and non-expert audiences
- analyse the effects of changing model parameters on LP model predictions
- use software to solve and analyse L.P. problems
|1.||Introduction to Linear Programming History of OR, prototype problems, the systems approach to problem solving, methodology of OR. Linear programming will be introduced through a variety of applications, leading to a general definition of an L.P. problem. Graphical solution of problems with 2 decision variables will be shown and the corner point method will be used for solving problems with a 2 or more decision variable. An elementary presentation of sensitivity analysis will be given.||10.00|
|2.||Simplex Method The canonical and standard forms of L.P. problems will be discussed and the concept of slack and surplus variables introduced. Basic and non-basic variables will be introduced via 2-dimensional problems, leading to a discussion of the general case. The simplex method will then be studied and applied to all cases. The cases of infeasible and unbounded problems, and problems with an infinite number of solutions will be examined.||17.00|
|3.||Duality The idea of the dual of an L.P. problem will be introduced, and the relationships between the primal and dual problems studied.||12.00|
|4.||Sensitivity Analysis It will be emphasised that the solution obtained is dependent on the values of the parameters being known precisely, whereas in fact these parameters are only estimates and/or liable to change. The effect on the solution of changing the objective function or constraints will be studied along with the introduction of new constraints and variables.||12.00|
|5.||Transportation and Assignment Problems The special case of L.P. problems which can be formulated as transportation or assignment problems will be studied, using more efficient methods of solving these problems. Transportation problems studied will include those requiring dummy sources and destinations, and a variety of starting procedures will be considered. The Hungarian method will be used in solving assignment problems||20.00|
|6.||Integer Programming Applications of pure and mixed integer programming will be introduced and the branch and bound method will be introduced.||9.00|
|7.||Graphs, Networks, and Trees. Elementary graph theory will be introduced to provide a basis for the use of networks to model a variety of problems. Critical path, shortest route, minimal spanning tree and maximal flow problems will be studied. Eulerian and Hamiltonian graphs will also be studied.||20.00|
Text and materials required to be purchased or accessed
ALL textbooks and materials available to be purchased can be sourced from USQ's Online Bookshop (unless otherwise stated). (https://omnia.usq.edu.au/textbooks/?year=2019&sem=02&subject1=MAT2200)
Please contact us for alternative purchase options from USQ Bookshop. (https://omnia.usq.edu.au/info/contact/)
(Available on the course StudyDesk.).
(Available on the course StudyDesk.).
Student workload expectations
|Description||Marks out of||Wtg (%)||Due Date||Notes|
|Assignment 1||10||4||25 Jul 2019|
|Assignment 2||100||12||22 Aug 2019|
|Assignment 3||100||12||12 Sep 2019|
|Assignment 4||100||12||17 Oct 2019|
|Exam||100||60||End S2||(see note 1)|
- This will be an open exam. The total working time for the examination is 2 hours. The examination date will be available via UConnect when the official examination timetable has been released.
Important assessment information
It is the students' responsibility to participate appropriately in all activities ( scheduled for them, and to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.
Requirements for students to complete each assessment item satisfactorily:
To complete each of the assessment items satisfactorily, students must obtain at least 50% of the marks available for each assessment item
Penalties for late submission of required work:
Students should refer to the Assessment Procedure http://policy.usq.edu.au/documents.php?id=14749PL (point 4.2.4).
Requirements for student to be awarded a passing grade in the course:
To be assured of receiving a passing grade a student must obtain at least 50% of the total weighted marks available for the course (i.e. the Primary Hurdle), and have satisfied the Secondary Hurdle (Supervised), i.e. the end of semester examination by achieving at least 40% of the weighted marks available for that assessment item.
Supplementary assessment may be offered where a student has undertaken all of the required summative assessment items and has passed the Primary Hurdle but failed to satisfy the Secondary Hurdle (Supervised), or has satisfied the Secondary Hurdle (Supervised) but failed to achieve a passing Final Grade by 5% or less of the total weighted Marks.
To be awarded a passing grade for a supplementary assessment item (if applicable), a student must achieve at least 50% of the available marks for the supplementary assessment item as per the Assessment Procedure http://policy.usq.edu.au/documents/14749PL (point 4.4.2).
Method used to combine assessment results to attain final grade:
The final grades for students will be assigned on the basis of the weighted aggregate of the marks obtained for each of the summative assessment items in the course.
An open examination is one in which candidates may have access to any printed or written material and a calculator during the examination.
Examination period when Deferred/Supplementary examinations will be held:
Any Deferred or Supplementary examinations for this course will be held during the next examination period.
University Student Policies:
Students should read the USQ policies: Definitions, Assessment and Student Academic Misconduct to avoid actions which might contravene University policies and practices. These policies can be found at http://policy.usq.edu.au.
Exam paper presentation: All exam papers should be presented in accurate and clear writing by blue or black pen. Pencil writing is not acceptable. Assignments can be presented using any word processor such as Word or Latex, or can be neatly written by blue or black pen (but not by pencil)
Computer, e-mail and Internet access:
Students are required to have access to a personal computer, e-mail capabilities and Internet access to UConnect. Current details of computer requirements can be found at http://www.usq.edu.au/current-students/support/computing/hardware .
Students can expect that questions in assessment items in this course may draw upon knowledge and skills that they can reasonably be expected to have acquired before enrolling in this course. This includes knowledge contained in pre-requisite courses and appropriate communication, information literacy, analytical, critical thinking, problem solving or numeracy skills. Students who do not possess such knowledge and skills should not expect the same grades as those students who do possess them.