NAMEPRACTICAL/TUTORIAL GROUP
Unit Course book
Linear Programming
Course code:MthA 304 LP
Unit Coordinator
Nowzad A Ahmed
2012/2013
Soran University
Faculty of Science
Department of Mathematics
Stage 3
Education Aims:
To provide the for the students to get familiar with the history of linear programming and its
origin. He should learn that whatever he studies is a miniature of what is happening in the computer. One should understand that any operation taking place in his living environment is possible to be done in a better way and very likely in the best way. He should fully learn the masterpiece of George B Dantzig, that is, simplex method and the great role it has played in saving billions of dollars in the large incorporations around the world. The impact of computer on the progress of the field of operations research should be appreciated. They should learn how to work with a number of software available to solve the linear programming problems, including Matlab. The students should be acquainted with the real life applications of the operations research such as Transportation problem, game theory, network problems and how to solve them.
Learning Outcomes:
An appreciation of the way in which ordinary differential equation relates to other aspects of mathematics and the natural sciences
* An appreciation of modeling techniques to model practical and real life problems into linear programming so that to be solved by common software.
* Understand geometrical and algebraic bases of the simplex method.
* Appreciation of advanced simplices such as, revised, dual, bounded, and prima dual simplex.
* Being able to work out problems on their own at home
* Undertake practical experiments with Matlab or Maple
* Getting familiar with special applications of linear programming such as Transportation, Game Theory, Network optimization.
Communications with Academic Staff
The email rules
* Write your email in acceptable English.
* In your emails you must include: full name, stage, department and the unit title.
* We only respond to queries from students using genuine/Soran University email accounts.
* Appointments can be arranged through the email system, if you wish.
* We respond to genuine problems and queries as soon as possible, normally within 7 days.
* We will not respond to emails which do not have a subject line.
Staff associated with the unit:
Staff
Room Number
Email
Farhad Djannaty
Head of Mathematics Dep. Room
fdjanaty@soranu.com
Soran University
Department of Mathematics
Unit: Linear Programming
Credit 3
Method of Assessment:
1 x 3 h lectures
Examination and grading
Theory (100% of total course marks)
* The average of 4 written examinations/assessments will stand for 35% of the total course marks.
* Written home works stands for 5% of the total marks
* A Final examination will stand for the remaining 60% of total course marks.
Marking System
The grades for each piece of assessed work are as follows:
* 90-100 % is excellent
* 80-89% is very good
* 70-79% is good
* 60-69% is a moderate pass
* 50-59% is a pass
* <49% is a fail
Unit Timetable/Content
Academic
week
Lecture title and content1st weekThe Origins of Operations Research, The Nature of Operations Research, The Impact of Operations Research, Algorithms and OR Courseware2nd weekDefining the Problem and Gathering Data, Formulating a Mathematical Model
Deriving Solutions from the Model, Testing the Model, Preparing to Apply the
Model.3rd weekModel Implementation, Prototype Example, The Linear Programming Model , Assumptions of Linear Programming4th weekProblem solving sessions5th weekSome Case Studies, Displaying and Solving Linear Programming Models using Matlab, Additional Examples, Formulating Very Large Linear Programming Models6th week Answering questions about the first exam.
First examination7th weekCase study 1 Auto Assembly
Case study 2 Cutting Cafeteria Costs
Case study 3 Staffing a Call Center8th weekProblem solving sessions9th weekFoundations of the Simplex Method, The Revised Simplex Method, A Fundamental Insight , Conclusions 10th weekThe Essence of Duality Theory, Economic Interpretation of Duality, Primal-Dual Relationships, Adapting to Other Primal Forms11th weekAnswering questions about the second exam
Second examination12th week The Role of Duality Theory in Sensitivity Analysis, The Essence of Sensitivity Analysis, Applying Sensitivity Analysis 13th weekCase study 1 Controlling Air Pollution,
Case study 2 Farm Management
Case study 3 Assigning Students to Schools14th weekThe Dual Simplex Method, Parametric Linear Programming 15th week The Upper Bound Technique, The Upper Bound Technique 16th weekProblem solving sessions17th weekAnswering questions about the third exam.
Third examination18th weekAn Interior-Point Algorithm 19th weekProblem solving sessions20th weekThe Transportation Problem, North west method, Russell Method, Vogel Method21st week A Streamlined Simplex Method for the Transportation Problem22nd weekAnswering questions about the forth exam
Forth examination 23rd weekA Streamlined Simplex Method for the Transportation Problem
The Assignment Problem 24th weekHungarian method, Shipping
Case study 1 Wood to Market
Case study 2 Project Pickings25th weekNetwork Optimization Models, Prototype Example, The Terminology of Networks, The Shortest-Path Problem 26th weekThe Minimum Spanning Tree Problem, The Maximum Flow Problem,
The Minimum Cost Flow Problem, The Network Simplex Method 27th weekProblem solving
Fifth examination
References:
1. Hillier, S.H. and Lieberman, G. J. "Introduction to Operations Research", Mc Graw Hill, 2007
2. Bazaraa, M.S., Jarvis, J.J., "Linear Programming and Network Flows", Johan Wiley, 2005
3. Taha H.. "Operations research: An Introduction 9th Edition", Printice Hall, 2010
4. Bronson R., Naadimuthu, G "Schaum's Outline of Operations Research" Mc-Graw Hill 1997