Chapter2
Introduction to Optimization
and Linear Programming
1
Introduction
We all face decision about how to use
limited resources such as:
Oil in the earth
Land for dumps
Time
Money
Workers
2
Mathematical Programming.
MP is a field of management
Chapter6
Integer Linear Programming
1
Introduction
When one or more variables in an LP problem
must assume an integer value we have an
Integer Linear Programming (ILP) problem.
ILPs occur frequently
Scheduling workers
Manufacturing airplanes
Integer
QMDS300
Quantitative Decision
Analysis
1
Chapter1(Ragsdale)
Introduction to Modeling
and Decision Analysis
2
Introduction
We face numerous decisions in life &
business.
We can use computers to analyze the
potential outcomes of decision
alternatives.
Sprea
The Shortest Path Problem (Sec. 5.2)
Many decision problems boil down to
determining the shortest (or least costly) route
or path through a network.
Ex. Emergency Vehicle Routing
This is a special case of a transshipment
problem where:
There is one su
Managerial Decision
Modeling
6th edition
Cliff T. Ragsdale
Chapter7
Goal Programming and
Multiple Objective
Optimization
Introduction
Most of the optimization problems considered to
this point have had a single objective.
Often, more than one objective
The Maximal Flow Problem
In some network problems, the objective is to
determine the maximum amount of flow that can
occur through a network.
The arcs in these problems have upper and
lower flow limits.
Examples
How much water can flow through a netwo
Chapter 5
Network Modeling (I)
Introduction
A number of business problems can be
represented graphically as networks.
This chapter focuses on several such problems:
Transshipment Problems
Shortest Path Problems
Maximal Flow Problems
Transportation/Assig
A Contract Award Problem
B&G Construction has 4 building projects and
can purchase cement from 3 companies for the
following costs:
Co.1
Co.2
Co.3
Needs
(tons)
Max.
CostperDeliveredTonofCement
Project1 Project2 Project3 Project4 Supply
$120
$115
$130
$12
Sensitivity Analysis (III) and
the Simplex Method
1
The Simplex Method
To use the simplex method, we first convert all
inequalities to equalities by adding slack
variables to <= constraints and subtracting
slack variables from >= constraints.
For example
Chapter3,Part3
More Examples on Modeling
and Solving LP Problems in a
Spreadsheet
1
Benchmarking schools
Outputs
n
1
2
3
4
School
A
B
C
D
1
86
82
81
81
2
75
72
79
73
I nputs
3
71
67
80
69
1
0.06
0.05
0.08
0.06
2
260
320
340
460
3
11.3
10.5
12
13.1
2
Steak
Chapter3,Part1
Modeling and Solving LP
Problems in a Spreadsheet
Introduction
Solving LP problems graphically is only
possible when there are no more than two
decision variables
Few real-world LP have fewer than two
decision variables
We can now use sp
Chapter3,Part2
More Examples on Modeling
and Solving LP Problems in a
Spreadsheet
1
A Blending Problem:
The Agri-Pro Company (Sec.3.12)
Agri-Pro has received an order for 8,000 pounds of
chicken feed to be mixed from the following feeds.
Percent of Nutri
Sensitivity Analysis (II)
1
Sensitivity Report
Report Created: 2012/2/24 ? ? 12:45:04
Engine: Standard LP/Quadratic
Objective Cell (Max)
Cell
Name
$D$6 Unit Profits Total Profit
Final Value
66100
Decision Variable Cells
Final
Cell
Name
Value
$B$5 Number t
Chapter4
Sensitivity Analysis (I)
1
Introduction
When solving an LP problem we assume
that values of all model coefficients are
known with certainty.
Such certainty rarely exists.
Sensitivity analysis helps answer
questions about how sensitive the opti