Module 3
Decision Theory and
the Normal
Distribution
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
M3-1
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Learning Objectives
Students will be able to
• Understand how the normal curve
can be used in performing breakeven analysis.
• Compute the expected value of
perfect information (EVPI) using
the normal curve.
• Perform marginal analysis where
products have a constant marginal
profit and loss.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
M3-2
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Module Outline
M3.1 Introduction
M3.2 Break-Even Analysis and
the Normal Distribution
M3.3 EVPI and the Normal
Distribution
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
M3-3
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Normal Distribution
for Barclay’s Demand
Break-even
Fixed Cost
point (Units) = Price/Unit - Variable Cost/Unit
Mean of the Distribution, µ
15 Percent Chance
Demand Exceeds
11,000 Games
15 Percent
Chance
Demand is
Less Than
5,000 Games
X
5,000
11,000 Demand (Games)
µ=8,000
Z=
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
Demand - µ

M3-4
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Barclay’s
Opportunity Loss
Function
In general, the opportunity loss function
can be computed by:
Opportunity K (Break-even point - X)
loss =
for X < Break-even
$0 for X > Break-even
where
K = the loss per unit when sales are below the
break-even point
X = sales in units.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
M3-5
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Barclay’s
Opportunity Loss
Function
Opportunity $6 (6,000 - X)
loss =
for X < 6,000 games
$0 for X > 6,000 games
Loss Profit
Loss ($)
µ = 8,000
 = 2,885
Slope = 6
Breakeven
point (XB)
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
Normal
Distribution
µ
6,000
M3-6
X
Demand
(Games)
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Value of
Perfect Information
EVPI = EOL = K N(D)
Where
EOL = expected opportunity loss,
K = loss per unit when sales are below
the break-even point
 = standard deviation of the
distribution
  breakeven
D

µ = mean sales
N(D) = the value for the unit normal loss
integral given in Appendix B, for a
given value of D.
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
M3-7
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Expected Value of
Perfect Information –
cont.
 = 2,885
K = $6
8,000  6,000
D
 0.69  0.60  0.09
2,885
N(.69) = .1453
Therefore
EOL = K N(.69)
= ($6)(2885)(.1453) = $2,515.14
EVPI = $2515.14
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
M3-8
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458