MAT1200 Operations Research 1
|Semester 2, 2012 On-campus Toowoomba|
|Faculty or Section :||Faculty of Sciences|
|School or Department :||Maths and Computing|
|Version produced :||30 December 2013|
Examiner: Trevor Langlands
Moderator: Ron Addie
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:
- formulate various problems that occur in decision making as mathematical models;
- understand the techniques used to investigate these models;
- apply these techniques to various problems;
- 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.||Networks 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||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://bookshop.usq.edu.au/bookweb/subject.cgi?year=2012&sem=02&subject1=MAT1200)
Please contact us for alternative purchase options from USQ Bookshop. (https://bookshop.usq.edu.au/contact/)
Introductory Book 2012, Course MAT1200 Operations Research I, USQ Distance and e-Learning Centre, Toowoomba.
Study Book 2012, Course MAT1200 Operations Research I, USQ Distance and e-Learning Centre, Toowoomba.
Winston, WL 2004, Operations research: applications and algorithms, 4th edn, Thomson Brooks/Cole, Australia.
Hillier, F & Lieberman, G 2005, Introduction to operations research, 8th edn, McGraw-Hill, Boston.
Kolman, B & Beck, R 1995, Elementary linear programming with applications, 2nd edn, Academic Press, San Diego.
Taha, HA 2006, Operations research: an introduction, 8th edn, Prentice-Hall, Upper Saddle River, NJ.
Student workload requirements
|Description||Marks out of||Wtg (%)||Due Date||Notes|
|ASSIGNMENT 1||100||4||27 Jul 2012|
|ASSIGNMENT 2||100||12||24 Aug 2012|
|ASSIGNMENT 3||100||12||14 Sep 2012|
|ASSIGNMENT 4||100||12||19 Oct 2012|
|2 HR OPEN EXAMINATION||100||60||End S2||(see note 1)|
- Examination dates will be available during the Semester. Please refer to Examination timetable when published.
Important assessment information
It is the students' responsibility to attend and participate appropriately in all activities (such as lectures, tutorials, laboratories and practical work) 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:
If students submit assignments after the due date without (prior) approval of the examiner then a penalty of 5% of the total marks gained by the student for the assignment may apply for each working day late up to ten working days at which time a mark of zero may be recorded. No assignments will be accepted after model answers have been posted.
Requirements for student to be awarded a passing grade in the course:
To be assured of receiving a passing grade a student must achieve at least 50% of the total weighted marks available for the course.
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.
The due date for an assignment is the date by which a student must despatch the assignment to the USQ. The onus is on the student to provide proof of the despatch date, if requested by the Examiner.
If requested, students will be required to provide a copy of assignments submitted for assessment purposes. Such copies should be despatched to USQ within 24 hours of receipt of a request being made.
The Faculty will NOT accept submission of assignments by facsimile.
Students who, for medical, family/personal, or employment-related reasons, are unable to complete an assignment or to sit for an examination at the scheduled time may apply to defer an assessment in a course. Such a request must be accompanied by appropriate supporting documentation. One of the following temporary grades may be awarded IDS (Incomplete - Deferred Examination; IDM (Incomplete Deferred Make-up); IDB (Incomplete - Both Deferred Examination and Deferred Make-up).