1. Decision Theory and the Normal Distribution
Module 3
Decision Theory and the Normal Distribution
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
M3-1

2. Learning Objectives Students will be able to
Understand how the normal curve can be used in performing break-even 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

3. 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

4. Normal Distribution for Barclay’s Demand
Break-even
point (Units)
Fixed Cost
Price/Unit - Variable Cost/Unit =
15 Percent Chance
Demand is Less Than 5,000 Games
Demand Exceeds
11,000 Games
Mean of the Distribution, µ
5,000
11,000
µ=8,000
Demand (Games) X
Z =
Demand - µ 
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
M3-4

5. Barclay’s Opportunity Loss Function
In general, the opportunity loss function can be computed by:
Opportunity
loss
K (Break-even point - X)
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

6. Barclay’s Opportunity Loss Function
6,000
Demand
(Games) X
Normal Distribution
Slope = 6
Loss ($)
Opportunity
loss
$6 (6,000 - X)
for X < 6,000 games
$0 for X > 6,000 games =
µ = 8,000
 = 2,885
Break-even point (XB)
Profit
Loss
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
M3-6

7. Expected Value of Perfect Information
EVPI = EOL = K N(D)
µ = mean sales
N(D) = the value for the unit normal loss
integral given in Appendix B, for a
given value of D.
Where
EOL = expected opportunity loss,
K = loss per unit when sales are below
the break-even point
 = standard deviation of the distribution
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
M3-7

8. Expected Value of Perfect Information – cont.
K = $  = 2,885
Therefore
EOL = K N(.69)
= ($6)(2885)(.1453) = $2,515.14
EVPI = $
N(.69) = .1453
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
M3-8