QMB 4701
Project Instructions
Description: You will choose a real life problem that can be solved with linear programming. You
can also use the case studies at the end of the chapters. Or you can read a research paper
which formulates a LP problem and the
QMB 4701
HW 3 Solutions
Que1
a) Can you develop a LP model based on the network?
Xij= the amount of bushels to be shipped from node i to node j
X14= amount of bushels to be shipped from Mt. Dora to Ocala
X15= amount of bushels to be shipped from Mt. Dora
Mathematical Programming.
MP is a field of management science that finds the optimal, or most efficient, way
of using limited resources to achieve the objectives of a business.
a.k.a. Optimization
Types of Optimization Problems
Linear programming (LP
Chapter 2 - Introduction to Optimization & Linear Programming : S-1
Chapter 2
Introduction to Optimization & Linear Programming
1.
If an LP model has more than one optimal solution it has an infinite number of alternate optimal
solutions. In Figure 2.8, t
QMB 4701
Exam 1
1. 25 pts (a-10 pts, b-10 pts c-5 pts) If I took off points for the model I will not take off points
again for part c. I just need to see if you know how to interpret them.
a. See attached scanned paper.
Define: x1 = number of HyperLink, x
QMB 4701
Assignment 1
1) Aire-Co produces home dehumidifiers at two different plants in Atlanta and Phoenix. The
per unit cost of production in Atlanta and Phoenix is $400 and $360, respectively. Each
plant can produce a maximum of 300 units per month. In
Introduction
Solving LP problems graphically is only possible when there are two decision
variables.
Few real-world LP have only two decision variables.
Fortunately, we can now use spreadsheets to solve LP problems
Risk Solver Platform
This book com
Integer Programming
ILP problem has integrality condition
Some or all of the variables in the formulation must assume only integer
values.
LP relaxation of original ILP problem
Ignore the integrality conditions and solve the problem as if it were a
s
Management Science
.quantitative approach to solve problems in business.
Management science uses statistical and mathematical tools to make business
decisions.
improve business performance through modeling.
Management Science
sometimes also referred
Solving LP Problems: An Intuitive Approach
Idea: Each Aqua-Spa (X1) generates the highest unit profit ($350), so lets make
as many of them as possible!
How many would that be?
Let X2 = 0
1st constraint: 1X1 <= 200
2nd constraint:9X1 <=1566 or X1 <=1
Aire-Co
X1,j = Number of dehumidifiers made in Atlanta in month j
X2,j = Number of dehumidifiers made in Phoenix in month j
Bj = Beginning inventory in month j
MIN 400 (X11 + X12 + X13 ) +360 (X21 + X22 + X23 ) + 30 ( B1 + B2 + B3 )
ST
B1 + X11 + X21 300
Chapter 1:
Introduction to Managerial
Decision Modeling
Munson
Cliff Young
What is Decision Modeling?
A scientific approach to managerial decision
making
Come up with mathematical solution
ex. Least cost to put items in a warehouse
Qualitative aspects to
Bill Pritchett'
Known Parameters
Selling pric $10.00
Fixed cost
#
Variable cos $5.00
Variables
Number of units, X
Results
Total reven
Fixed cost
Total variab
Total cost
Profit
$0.00
#
$0.00
#
#
Bill Pritchett's Shop
Known Parameters
Selling price per unit
Some Common Physical Networks
Introduction
A number of business problems can be represented graphically as networks.
This chapter focuses on several such problems:
Transshipment Problems
Shortest Path Problems
Generalized Network Flow Problems (practi
Characteristics of Network Flow Problems
Represented as a collection of:
Nodes (Locations)
Arcs (paths, routes or connections b/w locations)
A Transshipment Problem:
The Bavarian Motor Company
Defining the Decision Variables
For each arc in a network fl
Chapter 4
Sensitivity Analysis
Purpose of sensitive analysis
Overcome skepticism of management
Some factors are unknown
Provide a better picture of how the solution will change if different factors in the
model change.
Joshs Dilemma
=time to spend on le
A furniture store produces beds and desks. The production process requires assembly and painting.
Each bed requires 9 hours of assembly and 4 hours of painting. Each desk requires 6 hours of assembly
and 8 hours of painting. There are 54 hours of assembly
Members
1 Baoyi Li
2 Jessica Smith
3 Stephanie Wong
Decision Variables:
Objective Function:
Maxmimize revenue
P:
G:
Number of Painting Packets
Number of Glazing Packets
=
5.50P + 4.50G
Constraints:
2.5P + 2.0G
1.8P + 2.0G
P
G
P, G
<=
<=
>=
>=
>=
2160 minu
M
Subject
3T+4
2T+1
C 450
T 1
T,C
Maximizeprofit=$7T+$5C
Subjectto
3T+4C 2,400 (carpentrytime)
2T+1C 1,000 (paintingtime)
C 450 (maximumchairsallowed)
T 100 (minimumtablesallowed)
T,C 0 (nonnegativity)
Flair Fur
Ta Ch
T air
C
ble
s s
Number of units
Prof
Fifth Avenue Industries
S
All silk
P
All poly
B1
B2
Blend-1 Blend-2
Number of units
Selling price
Labor cost
Material cost
Profit
Constraints:
Yards of silk
Yards of polyester
Yards of cotton
Maximum all silk
Maximum all poly
Maximum blend-1
Maximum blend
Minimize
subjectto
5A+10B
4A+3B
0.5A 1.5
A,B 0 (no
Minimizecost=$0.10A+$0.15B
subjectto
5A+10B 45 (proteinrequired)
4A+3B 24 (vitaminrequired)
0.5A 1.5 (ironrequired)
A,B 0 (nonnegativity)
Holiday Meal Turkey Ranch
A
Brand A
B
Brand B
Number of pounds
C
Constra
Constraint:CT75
Flair Furniture - Modified Problem
T
C
Tables Chairs
Number of units
Profit
Constraints:
Carpentry hours
Painting hours
Maximum chairs
Minimum tables
Tables vs Chairs
LHS
Sign RHS
Constraint:C
Constraint:CT75
Flair Furniture - Modi
Best answer
news
Quantity
reach
Cost
non neg
Tv
0
700
500
1
Radio
0
9000
5000
n2
10
4000
2000
tv2
0
500
400
0
7500
4000
1
1
1
1
Reasoning I believe was correct but non linear
News
TV
Radio
Quantity
0.99702273 0.0081977457
3.1227478504
Cost 1
500
5000
2000
Joseph Ginzburg
Revenue
Cost
5.5
1
4.5
1
Printing packet Glazing packet
P
G
Number of units 514.285714286 37.142857143 Obj.
Profit
4.5
3.5 3844.28571
Constraints:
Painting
Collating
Min P
Min G
2.5
1.8
1
2
2
2160 <=
1800 <=
514.285714 >=
1 437.142857 >=
2
X- Coordinate
Y- Coordinate
WareHouse
138.7499997288 116.2499994678 Distance:
Store 1
70
160
Store 2
60
90
Store 3
180
90
Store 4
150
120
Total Distance:
Name
Store 1
Store 1
Store 2
Store 3
Store 4
Wearhouse
Store 2
0
70.71
130.38
89.44
Store 3
70.71
0
1
QMB 4701: Managerial Operations Analysis I
Course Syllabus
Spring 2014, Module 3
Description
This course will provide you some quantitative tools to solve business problems. Excel worksheet
is a commonly used tool in business today. Excel can perform some
QMB 4701
Assignment 2
3)
Microsoft Excel Sensitivity Report (Obtained Using Standard LP/Quadratic
Engine)
Adjustabl
e Cells
Final
Cell
Name
Reduced Objectiv Allowabl Allowabl
e
e
e
Value
Cost
Coefficie Increase Decreas
nt
e
$C$4
Value: X1
12
0
2
1E+30
0
$