NAMEPRACTICAL/TUTORIAL GROUP
Unit Course book
Operation Research
Course code:Mth 403 OR
Unit Coordinator
Hawkar Qasim Birdawod
2012/2013
Soran University
Faculty of Science
Department of Mathematics
Stage 4
University of Soran
College of sciences
Mathematical Department
Course Book
Course Title: Operation research
Academic Year: 2012-2013
Level of study: Fourth year
Course Lecturer: Hawkar Qasim Birdawod
Email: hawkarqasim@gmail.com or hawkar.birdawod@mhe-krg.org
Course Coordinator: Farhad Ganaty
Course Description:
Through this Year the students will study the Solution of the problems by using the Mathematical methods to get the best models and the best solution types.
Objectives of the Course
1. This course is intended to provide students with a knowledge that can make them appreciate the use of various research operations tools in decision making in organizations.
2. Making decisions as well as being able to formulate organizational problems into OR models for seeking optimal solutions.
3. Grasp the methodology of OR problem solving.
4. Understand and differentiate deterministic/probabilistic/stochastic static/ dynamic problem solving situations. Develop formulation skills in building be able to understand and interpret solutions and sensitivity/ parametric analyses.
5. Skills in the use of Mathematical Programming software.
Course Content
DateSubject1st weekChapter one: basics of operations research
Introduction, Art of modeling, types of operation research model, the structure of mathematical models.2nd
weekChapter one: basics of operations research
Mathematical models in operation research, phases of operation research study, scientific method in operation research.3rd weekChapter two: Linear programs and Integer programming
Mathematical program, linear programs, Integer programs, Quadratic programs.4th and 5th weeksChapter two: Linear programs and Integer programming
Problem formulation6th and 7th weeksChapter three: Methods for solving Linear programming model
Graphical method, Special case of graphical solution (multiple optimal, infeasible solution)8th and 9th weeks Chapter three: Methods for solving Linear programming model
Special case of graphical solution (Unbound solution, Degeneracy solution), examples, Redundant constraint, slack variable.10th weekChapter three: Methods for solving Linear programming model
Simplex method, the steps of the simplex algorithm.11th and 12th weeksChapter three: Methods for solving Linear programming model
Requirements for standard form, examples for simplex method13th and 14th weeksChapter three: Methods for solving Linear programming model
Artificial variables techniques: (The big M-method), example. 15th weekChapter three: Methods for solving Linear programming model
Artificial variables techniques: (the two phase method), example.16th week Chapter Four: Duality in linear programming
Duality, type of duality, example.17th weekChapter Four: Duality in linear programming
Solving the Dual theorems, example.18th weekChapter Four: Duality in linear programming
Dual simplex model, example19th and 20th weeksChapter Five: Transportation problem
Transportation problem, definition of the model, the transportation technique, starting Basic solution.21st week Chapter Five: Transportation problem
How to find the Basic solution: (Northwest corner method), examples.22nd weekChapter Five: Transportation problem
How to find the Basic solution: (Least- cost method), examples.23rd weekChapter Five: Transportation problem
How to find the Basic solution: (Vogel method), examples.24th and 25th weeksChapter six: game theory
Definition game theory, saddle point, solution by graphical.26th and 27th weeksChapter six: game theory
Linear Programming method, example
Assessment: Written Exam
Samples of the expected questions and their answers
The questions will be objective. Exercises similar to those in the class will be included, where recognition and analysis are required on the part of the examinees. Some useful hints will be provided to the students when they are required to produce some samples.
Q / A company produces two types of cowboy hats, each hat of the first type requires twice as much labor time as the second type. If all hats are of the second type only, the company can produce a total of 500 hats a day the market limits daily sales of the first and second types to 150 and 250 hats. Assume the profits per hat are 8$ for type (1) and 5$ for type (2), determine the number of hats to be produced of each type in order to maximize profit.
Answer
.
Q/ Compare between Slack variables and artificial variables.
Answer
SubjectsSlack variablesArtificial variables?-S+R?+S---=---+R
Q/ / Find the optimal solution from the following mathematical method:
Answer
Above there was a tie for least non-negative ratio:
either row 1 or row 2 could have become the pivot row, and either choice leads to the final tableau after one additional pivoting. At the right is the result of the final 3 row operations.
Q/ Find the stepping stone to find the solution of the North West corner method, compare the computations.
5104a1=1007523a2= 5061090a3= 502416a4= 25b1=20b2100b3=30b4=100Answer:
5104a1=1002080X13X147523a2= 50X212030X2461090a3= 50X31X320502416a4= 25X41X42X43250000a5=25X51X52X5325b1=20b2100b3=30b4=100250
References:
1- Hamdy A. Taha, "Operations research an introduction", second edition, (1982).
2- S. C. Sharma, "Introductory operation research", (2006).
3- P. K Gupta, "operation research an introduction"
4- Phillips, D., "operation research principle and practice"
5- Shuma's servies, "operation research".
6- James K. Strayer, Linear Programming and Applications, (1989) Springer-Verlag