# pages.stern.nyu.edu~djuran01a.ppt

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```					Session 1a
Overview

• Web Site Tour
• Course Introduction

Decision Models -- Prof. Juran          2
2 Modules
• Module I: Optimization

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What is Decision Modeling?
Decision Modeling Process

Formulation
Real world                                     Decision
System                                         Model

Implementation                                  Deduction

Real World                Interpretation
Model
Conclusions                                     Conclusions

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Seven-step Process
1. Definition
2. Data Collection
3. Formulation
4. Model Verification
5. Selection of an Alternative
6. Presentation of Results
7. Implementation

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Revised Process for This Course
0. Conclusions and Recommendations
1. Managerial Definition
2. Formulation
3. Solution Methodology
4. Discussion? Appendices?

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Software
• Microsoft Excel
–   Data Table
–   Goal Seek
–   Solver
–   Analysis Toolpack
–   Charts and Graphs

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Software
• The Decision Tools Suite
–   @Risk
–   PrecisionTree
–   TopRank
–   BestFit
–   RiskView
–   StatPro

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Software
• Other Software
– Crystal Ball
– Extend
– Sigma

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Descriptive Model
• Approximates how a real system works
(or would work) given certain
assumptions
• Does not give us the “right answer”
• Focus for Module 2

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Prescriptive Model

• Focus of Module 1

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What is Optimization?
• A model with a “best” solution
• Strict mathematical definition of
“optimal”
• Usually unrealistic assumptions
• Useful for managerial intuition

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Elements of an Optimization Model

• Formulation
– Decision Variables
– Objective
– Constraints
• Solution
– Algorithm or Heuristic
• Interpretation

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Optimization Example:
Extreme Downhill Co.

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Optimization Example:
Extreme Downhill Co.

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1. Managerial Problem Definition

Michele Taggart needs to decide how
many sets of skis and how many
snowboards to make this week.

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2. Formulation
a. Define the choices to be made by the manager
(decision variables).
b. Find a mathematical expression for the
manager's goal (objective function).
c. Find expressions for the things that restrict
the manager's range of choices (constraints).

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2a: Decision Variables

Variable Name                   Symbol          Units
Skis                         X      100s of pairs of skis
Snowboards                       Y      100s of snowboards

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2b: Objective Function

Find a mathematical
expression for the
manager's goal (objective
function).

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EDC makes \$40 for every snowboard it
sells, and \$60 for every pair of skis.
Michele wants to make sure she chooses
the right mix of the two products so as to
make the most money for her company.

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What Is the Objective?

Profit  6000X  4000Y

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2c: Constraints

Find expressions for the things
that restrict the manager's range
of choices (constraints).

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Molding Machine Constraint
The molding machine takes three hours to
make 100 pairs of skis, or it can make 100
snowboards in two hours, and the
molding machine is only running 115.5
hours every week.

The total number of hours spent molding
skis and snowboards cannot exceed 115.5.

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Molding Machine Constraint

3X  2Y  115.5

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Cutting Machine Constraint

Michele only gets to use the cutting
machine 51 hours per week. The cutting
machine can process 100 pairs of skis in
an hour, or it can do 100 snowboards in
three hours.

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Cutting Machine Constraint

1X  3Y  51
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Delivery Van Constraint

There isn't any point in making more
products in a week than can fit into the
van The van has a capacity of 48 cubic
meters. 100 snowboards take up one
cubic meter, and 100 sets of skis take up
two cubic meters.

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Delivery Van Constraint

2X  1Y  48

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Demand Constraint

Michele has decided that she will
never make more than 1,600
snowboards per week, because she
won't be able to sell any more than
that.

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Demand Constraint

Y  16
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Non-negativity Constraints

Michele can't make a negative
number of either product.

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Non-negativity Constraints

X0
Y 0
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Solution Methodology
Use algebra to find the best solution.

(Simplex algorithm)

George B. Dantzig
1914 - 2005

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Point X Y
A    0  0
B    0 16
C    3 16
D 18.6 10.8
E 24 0

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Calculating Profits

Point X     Y                  Objective function      Profit
A     0    0                      6000(0)+4000(0) =\$0.00
B    0    16                    6000(0)+4000(16) =\$64,000.00
C     3    16                    6000(3)+4000(16) =\$82,000.00
D    18.6 10.8               6000(18.6)+4000(10.8) =\$154,800.00
E    24   0                     6000(24)+4000(0) =\$144,000.00

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The Optimal Solution

• Make 1,860 sets of skis and 1,080
snowboards.
• Earn \$154,800 profit.

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