Ik University Industrial Engineering Department
IE301 Operations Research I Fall 2015
Homework #1
due on Monday, Oct 5th by 4pm at LMF 207A (to Zeynep)
Question 1: You are given the following LP:
Minimize =
1 + 22
. . 21 + 2 2
1 + 22 7
1 3
1 , 2 0
(a) Sol
Discrete Event System
Simulation
IE-303- 2015, LECTURE 1
BY
DR. MUSTAFA HEKMOLU
IE-303, Fall 2015, Instructor: Dr. M. Hekimoglu
9/7/2015
References
Reference #1:
Discrete-Event System Simulation, 2005, Banks,
Carson ,Nelson, Nicol, 5th Ed.
Reference #2:
S
Fundamentals of Operations Research
Prof. G. Srinivasan
Department of Management Studies
Indian Institute of Technology, Madras
Lecture No. # 1
Linear Programming Formulations
This course is titled in Fundamentals of Operations Research. In this course, y
EXECUTIVE GUIDE TO OPERATIONS RESEARCH
SEAT-OF-THE
PANTS-LESS
THE WORLDS MOST SUCCESSFUL EXECUTIVES ARE MAKING BOLDER DECISIONS
AND RUNNING EVERYDAY OPERATIONS WITH LESS RISK AND BETTER OUTCOMES.
THEIR SECRET? OPERATIONS RESEARCH: THE SCIENCE OF BETTER
I
Wrocaw University of Technology
Business Information Systems
Micha Kulej
OPERATIONS RESEARCH
Developing Engine Technology
Wrocaw 2011
Copyright by Wrocaw University of Technology
Wrocaw 2011
Reviewer: Jacek Mercik
ISBN 978-83-62098-83-5
Published by PRINT
06IP/IM74 OPERATIONS RESEARCH
PART B, UNIT - 7: Replacement Analysis
(By Dr.NVR Naidu, Prof & HOD (IE&M), MSRIT, Bangalore )
High repairs and expenses
Point of major
overhauling
Maintenance
Cost or
Running
Cost or
Operating
Cost
Old Equipment
New Equipmen
Computing in Operations Research using Julia
Miles Lubin, Iain Dunning
MIT Operations Research Center, 77 Massachusetts Avenue, Cambridge, MA USA
mlubin@mit.edu, idunning@mit.edu
arXiv:1312.1431v1 [math.OC] 5 Dec 2013
The state of numerical computing is c
Operational Research Study of the
UNICEF GEP3 Female Teacher Trainee
Scholarship Scheme
(EDOREN OR2 Study)
12 December 2014
OR2 Study of FTTSS
OR2 team members
Research consultants
Moses Dauda
Jiddere Kaibo
Swadchet Sankey
UNICEF
Saratu Yunusa
Bauchi Team
IJRRAS 3 (2) May 2010
Agarwal & al. Operations Research-Contemporary Role in Managerial Decision Making
OPERATIONS RESEARCH - CONTEMPORARY ROLE IN
MANAGERIAL DECISION MAKING
Sangeeta Agrawal1, KR Subramanian2 & S.Kapoor3
1&2
Omkarananda Institute of Manag
Operations Research
Sensitivity Analysis
Dr. zgr Kabak
Reduced Cost
The reduced cost for any nonbasic variable:
the amount by which the nonbasic variable's objective
function coefficient must be improved
before that variable will become a basic variable i
Ik University Industrial Engineering Department
IE301 Operations Research I Fall 2015
Homework #1 - Solution
Question 1: You are given the following LP:
Minimize = 1 + 22
. . 21 + 2 2
1 + 22 7
1 3
1 , 2 0
(a)
A
C
B
Optimal solution occurs at the intersect
Ik University Industrial Engineering Department
IE301 Operations Research I Fall 2015
Homework #2 - SOLUTIONS
Question 1:
Let
ct = cash on hand at end of month t.
xt = corn purchased at beginning of month t (in tons).
yt = corn sold at end of month t (in
Ik University Industrial Engineering Department
IE301 Operations Research I Fall 2015
Homework #3 - SOLUTION
Question 1:
Variables are already defined in problem as G, LTR, HTR, and C. Lets first write each goal with a constraint:
Goal1 1.5 + 25 + 15 (100
Ik University Industrial Engineering Department
IE301 Operations Research I Fall 2015
Homework #4 - SOLUTIONS
Question 1: Primal problem is given in the question as:
a) Dual problem:
Min
w = 3y1 + 2y2 + y3
s. t.
y1 + y3 2
y1 + y2 1
y1 + y2 + y3 1
y1 0, y2
Ik University Industrial Engineering Department
IE301 Operations Research I Fall 2015
Homework #5 SOLUTIONS
Question 1
(a)
The profit earned from shipping a barrel is as follows:
From Field 1 to England: 6 - 3 - 1 = $2
From Field 1 to Japan: 6.5 - 3 - 2 =
Ik University Industrial Engineering Department
IE301 Operations Research I Fall 2015
Homework #4 - SOLUTIONS
Question 1: Primal problem is given in the question as:
a) Dual problem:
Min
w = 3y1 + 2y2 + y3
s. t.
y1 + y3 2
y1 + y2 1
y1 + y2 + y3 1
y1 0, y2
LP (2003) 1
OPERATIONS RESEARCH: 343
1. LINEAR PROGRAMMING
2. INTEGER PROGRAMMING
3. GAMES
Books:
3 Intro to OR F.Hillier & J. Lieberman;
33 OR H. Taha;
333 Intro to Mathematical Prog F.Hillier & J. Lieberman;
3@ Intro to OR J.Eckert & M. Kupferschmid
LP
Ik University Industrial Engineering Department
IE301 Operations Research I 2014 Spring
Homework #1
due on Tuesday, March 11th by 4pm at LMF 207 (to Pinar)
Question 1: Alden Enterprises produces two products. Each product can be produced on either machine
Ik University Industrial Engineering Department
IE301 Operations Research I 2014 Spring
Homework #2
due on Monday, Mar 31th by 2 pm at LMF 207 (to Pinar)
Question 1
Consider the following matrix:
[
]
a) Find
for the matrix using Gauss-Jordan method.
b) Us
Ik University Industrial Engineering Department
IE301 Operations Research I 2014 Spring
Homework #1 - SOLUTIONS
Question 1:
Let xijkm = units of product i produced on machine j during month k for sale in month m
max z = 55(x1111 + x1211) + 12(x1112 + x121
Ik University Industrial Engineering Department
IE301 Operations Research I 2014 Spring
Homework #4
due on Friday, May 16th by 4pm at LMF 207 (to Pinar)
Question 1: Consider the following LP:
(First constraint)
(Second constraint)
(Third constraint)
, and
Ik University Industrial Engineering Department
IE301 Operations Research I 2014 Spring
Homework #3
due on Monday, April 28th by 2pm at LMF 207 (to Pinar)
Question 1
Use simplex algorithm to solve the following problem.
HINT: You need to use Big M Method,
Ik University Industrial Engineering Department
IE301 Operations Research I 2014 Spring
Homework #5 SOLUTIONS
Question 1:
(a)
= 1 if is matched with ; 0 otherwise
cfw_ ( ) ( ) ( ) (
where
)
cfw_ (
) (
) (
) (
)
max z 7 x11 5 x12 8 x13 2 x14 7 x 21 8 x 22
Ik University Industrial Engineering Department
IE301 Operations Research I 2014 Spring
Homework #4 - SOLUTION
Question 1:
a) Lets first write the standard form of the LP:
Since x1, s2, s3 are non-basic variables, their values should be zero. After replac
Ik University Industrial Engineering Department
IE301 Operations Research I 2014 Spring
Homework #5
due on Wednesday, May 28th by 4pm at LMF 207 (to Pinar)
Question 1:
Tom Cruise, Brad Pitt, Ben Affleck, and Matt Damon are marooned (tr: mahsur kalmak) on
IE301 Operations Research I 2014 Spring
Homework #3 SOLUTIONS
Question 1
According to the big-M method, the problem turns into the following form after adding slack, excess, and
artificial variables:
Initial Tablue
max
z
x1
Row 0
1
-2
Row 1
0
1
Row 2
0
2
Ik University Industrial Engineering Department
IE301 Operations Research I Fall 2015
Project # 1
due on Tuesday, November 10th by Midnight (11:59 pm) Course online submission required
A farm family owns 640 acres of land. Its members can produce a total
Syllabus for IE301 - Operations Research I
Fall 2015
Class Hours: Sec01:T678 Sec02:W678 Lab Hours: Sec01:F34
Prerequisites: MATH 200 - Linear Algebra
Sec02:F67
Instructor: Assist. Prof. Burak Cavdaroglu (AMF-328)
Office Hours: W5, F8
Teaching Assistant: Z