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Humboldt Oysters case consider the
following common questions.
What
• is the marginal upside profit for a unit?
• is the marginal downside cost of a unit?
• things can you control?
• things can’t you control?
• concepts/elements of the course are applicable?
Theme: Coping with Uncertain Demand

Anglesea Cabins   Humboldt Oysters

Upside

Downside

Control

Uncontrolled

technique
Theme: Coping with Uncertain Demand
Topics Covered Today

• Anglesea Cabins Case
• Normal distribution AWZ 6.2
• Humboldt Oysters Case
Anglesea Cabins

The problem.

Cnx
They call up
I decide

Uncertain profit of \$200 times x.
Anglesea Cabins

Current policy.
• If C≤11 take n=C bookings
• If C>11, take n=11 bookings
• What is the chance of a “show”?
• X is binomial n=11, p=0.8

Uncertain profit of \$200 times x.
Anglesea Cabins
When they take 11 bookings:
Profit =200  X
X has mean value np=110.8=8.8
Mean Profit =200  8.8 = \$1760
1760        20% loss         2200

What does the payoff table look like?
Anglesea Cabins
When they take 11 bookings:
TAKE n=11 BOOKINGS
Shows(x)       Prob          Profit
0                          \$0
1                         \$200
2                         \$400
3                         \$600
4                         \$800
5                         \$1,000
6                         \$1,200
7                         \$1,400
8                         \$1,600
9                         \$1,800   Bino(11,0.8)
10                        \$2,000
11                        \$2,200
Anglesea Cabins
When they take 11 bookings:
TAKE n=11 BOOKINGS
Shows(x)       Prob          Profit
0          0.0000          \$0
1          0.0000         \$200
2          0.0000         \$400
3          0.0002         \$600
4          0.0017         \$800
5          0.0097         \$1,000
6          0.0388         \$1,200
7          0.1107         \$1,400
8          0.2215         \$1,600
9          0.2953         \$1,800
10         0.2362         \$2,000
11         0.0859         \$2,200
SIMULATE CASE

Anglesea Cabins
When they take 12 bookings:
• What is the payoff table?
• What is the mean profit? How does this
compare to the previous profit?
• What is the chance of being under/over?
Have you gone far enough?
31%

1760           1899                  2200
20% loss

anglesea_inclass.xls
Anglesea Cabins
Why did I fix the number of calls C?
What if demand increases?
What if Regal is full?
Other issues?
Normal Distribution
The normal distribution
• is used in market research, quality control
(also in testing theory eg: GMAT)
• describes error in many industrial processes
• describes distribution of human features
• is the basis of inferential statements based on
regression output
• is a continuous distribution

What is the probability of being 180cm tall?
Normal Distribution
Continuous distributions described by a curve.
Areas under curve represent probabilities.
Normal Distribution
The normal distribution defined by its
mean μ – centre of the distribution
standard deviation σ – spread of distribution
Bell like shape

 calculus
 tables
 computer/XL
Normal Distribution
Any normal variable is within
1 σ of μ 68%      of time
2 σ’s of μ 95%    of time
3 σ’s of μ 99.75% of time

 calculus
 tables
 computer/XL
Standard Normal Distribution
The standard normal distribution is the normal
distribution with mean 0 and std. deviation 1
Non-standard normal variable can be made
standard normal variable by

X 
Z

Z measures how many std.dev’s above or below
the mean you are.
Standard Normal Distribution
The standard normal distribution is the normal
distribution with mean 0 and std. deviation 1

NORMSDIST(z)

z
Normal Distribution
Computing Probabilities
Step 1: Convert question about variable X into a
question about standard normal variable Z.
Step 2: Draw a diagram* of the area you require
and express it in terms of areas to the left of z.

Step 3: Use NORMSDIST to obtain these areas.

Java Demo

* The curve is symmetric about 0 and total area is 1.
Normal Distribution
Graduate students sitting GMAT have scores that
are normally distributed with mean 570 and
standard deviation 60.
What is the chance someone scores over 700?

Let X be the GMAT score.
Normal (570,60)
Z = (X-570)/60 is standard normal.

X  700  Z  700  570  / 60  2.1666
Normal Distribution
Graduate students sitting GMAT have scores that
are normally distributed with mean 570 and
standard deviation 60.
What is the chance someone scores over 700?

Let X be the GMAT score.
Normal (570,60)
Z = (X-570)/60 is standard normal.

Pr( X  700)  Pr( Z >2.166)
Normal Distribution
Graduate students sitting GMAT have scores that
are normally distributed with mean 570 and
standard deviation 60.
What is the chance someone scores over 700?

Let X be the GMAT score.
Normal (570,60)
Z = (X-570)/60 is standard normal.
Normal Distribution
Graduate students sitting GMAT have scores that
are normally distributed with mean 570 and
standard deviation 60.
What is the chance someone scores over 700?

Let X be the GMAT score.
Normal (570,60)
Z = (X-570)/60 is standard normal.
Pr Z  2.166  1  NORMSDIST 2.166
 1  0.9849
 0.0151
Normal Distribution
Graduate students sitting GMAT have scores that
are normally distributed with mean 570 and
standard deviation 60. What is the probability that
someone scores between 500 and 700?

X  500  Z  500  570  / 60  1.1666

Pr(500  X  700)  Pr(1.167  Z  2.167)
Normal Distribution

Pr(500  X  700)  Pr(1.167  Z  2.167)
 Pr(Z  2.167)  Pr(Z  1.167)
Normal Distribution
Graduate students sitting GMAT have scores that
are normally distributed with mean 570 and
standard deviation 60. What is the probability that
someone scores between 500 and 700?

Pr  1.167  Z  2.167   Pr Z  2.167   Pr Z  1.167 
 NORMSDIST 2.167   NORMSDIST  1.167 
 0.9849  0.1216  0.8633.
Humboldt Oysters
• What is the distribution of unknown demand D?
What does it mean in simple language?
-\$5.35     \$2.45
Humboldt Oysters
• What is the distribution of unknown demand D?
What if I set n=12150 production?
-\$5.35     \$2.45
Humboldt Oysters
• What is the distribution of unknown demand D?
What if I set n=12150 production?
• What is probability that I sell it and make \$2.45?
Use Excel and link so that you can change the
12150 policy.
• Calculate the mean profit on the last item.

Outcome        Chance        Profit
Sell                      \$2.45
Don’t sell                  -\$5.35
Class exercise
Normal Distribution
Graduate students sitting GMAT have scores that
are normally distributed with mean 570 and
standard deviation 60. The top 1% of students
score over what GMAT score?

Use 2.33 for 1% percentiles.
Use 1.65 for 5% percentiles.
Use 1.28 for 10% percentiles.
Use 0.68 for 25% percentiles (quartiles).
Class exercise
Normal Distribution
Graduate students sitting GMAT have scores that
are normally distributed with mean 570 and
standard deviation 60. The top 1% of students
score over what GMAT score?

Normal variable is 2.33 std.dev’s above mean
with probability 1%.
For GMAT, 2.33 std.dev’s above mean is
570+2.32660=709.6.
Humboldt Oysters
Demand will exceed what value with probability
99%. What production level should I set to be
90% sure of selling everything?
KEY TAKE AWAYS FROM CLASS
•In judging the level of production, two key quantities
are the profit of selling the last unit and the loss
incurred in not selling it.
•The normal distribution is a continuous distribution.
• Problems can always be translated to one involving
standard normal probabilities.
• Excel:
   NORMSDIST(x) – prob less than x
   NORMSDIST(z) – for standard normal

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