INDUSTRIAL MANAGEMENT ENGINEERING SOCIETY
ERGBIO1REVIEWERforQuiz#1
I.
True or False
1. Treatment using vibration has been advocated for improving joint mobility.
2. Hennings smell prism employs five primary odors arranged in the form of a prism.
3. Sound
ABCO Manufacturing
ABCO manufactures 2 products X and Y. ABCO's manager is interested in production and
liquidity planning for the next 2 weeks of operation. The first week has four working days and the
second week has five working days. Each working day
LP
O
I
T
U
SOL
N
SPECIAL CASES
I. NO FEASIBLE SOLUTION
there is no point which will satisfy all
the constraints
Indicators:
The graph produces no feasible region.
The optimal tableau contains R as basic
variable.
Example: Max. Z =
3x1 + 2x2
subject to 2
LP Solution
Methodologies
INOPER1 Notes
Methodologies
Graphical approach
Simplex Method
Big-M Method
Two-Phase Method
Revised Simplex Method
Graphical Approach
This method is most useful for models with only 2 or 3 decision
variables.
This method i
INOPER1
Introduction to Model Building
Operations Research: Applications & Algorithms
4th edition, by Wayne L. Winston
Definition of Operations Research
Operations Research (management
science) is a scientific approach to decision
making that seeks to be
Gokongwei College of Engineering
Department of Industrial Engineering
De La Salle University
Vision Corporation:
Production Planning and Shipping
In partial fulfillment of the requirements for
INOPER1 Term 2 AY 15 - 16
Submitted by:
Brizuela, Jet Niko
Mor
INTRODUCTION TO OPERATIONS RESEARCH I
Problem Set
Sensitivity Analysis
1. A manufacturing firm has discontinued production of certain unprofitable product line. This
created considerable excess production capacity. Management is considering devoting this
INOPER1
study of the effects of the changes in
parameter values on the present basic
optimal solution
Parameters: OFC C
Constraint Coefficients A
RHS b
Present Basic Optimal Solution XB
-refers to the basic variables
themselves, not the values of the BVs
INDUSTRIAL ENGINEERING DEPARTMENT
INTRODUCTION TO OPERATIONS RESEARCH I
Solutions to LP Models
Problem Set II
1.
A comparison shopper is trying to select the cheapest combination of two foods to
meet daily vitamin requirements. The vitamin needs call for
Increasing the demand for RAYco by 50% can be handled by the current system. Labor time for each of
three plants are not fully utilized which means that the unused capacity for the labor time can be used to
handle the increase in demand. Also, the availab
INDUSTRIAL ENGINEERING DEPARTMENT
INTRODUCTION TO OPERATIONS RESEARCH I
Problem Set I
MODEL FORMULATION
1. The Alambre Corporation makes two types of copper wire: Type 1 (rubber-insulated) and Type 2
(vinyl-insulated). Each product is made by processing c
INOPER1
PROBLEM SET
DUALITY
1. For each of the following, formulate the dual.
a.
Min
Z 20 x1 15 x 2
s.t. 2 x1 x 2 5
3x1 2 x 2 3
x1 x 2 3
x1 , x 2 0
b.
Max
Z 15 x1 25 x 2 10 x3
s.t. 6 x 2 3 x3 12
3 x1 12 x 2 6 x3 30
x 1 , x 2 , x 3 0
c.
Min
Z 6 x1 8 x 2 2
LP
O
I
T
U
SOL
N
SPECIAL CASES
I. NO FEASIBLE SOLUTION
there is no point which will satisfy all
the constraints
Indicators:
The graph produces no feasible region.
The optimal tableau contains R as basic
variable.
Example: Max. Z =
3x1 + 2x2
subject to 2
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Section: EB » v i - , 'x. l.‘ -'\
DEPA RTM ENT OF INDUSTRIAL ENGINEERING
OPERATIONS RESEARCH l
Quiz No. 3
luv/rm 'Iinnv'
l
.2 .
llns is a closed notes. closed books: closed formula exam.
All cellular phones
Initiallv draw the network din am for the tr ortation network of the mm anv: Formulate the linear r ammin model for the rolJlem as shown below:
Let:
x3 = Products shippedfrom Plant i to Customer R [Here= i: L2: 3)
Isa = Products shippedfrom Plant i to C
DUALITY THEORY
INOPER1
DUALITY THEORY
LP problems always exist in pairs. The original LP problem
is known as the primal model while its complementary
model is known as the dual.
Symmetric (canonical ) Form of the LP Model :
Max. Z = CX
s.t.
AX < b
X>0
M