Transcript Lecture 7

Preparing for Quiz 1
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Review notes, assignments
Take practice quiz
Read Tips on Taking On-line Exams
Get a good night's rest
• Quiz 1 coverage: up to and including
wrap-up of forecasting
Quiz Schedule
Lab
section
Enter lab
Quiz
begins
Quiz
ends
8 am
7:55
8:00
8:40
9 am
8:55
9:00
9:40
11 am
10:55
11:00
11:40
12 pm
11:55
12:00
12:40
All lab sections treated the same
When you come to the lab
• Find your assigned computer
• Logon to the course web
• You may copy materials to the desktop before
the quiz starts
– From USB key, CD, or email
• You may not use a USB key, CD, email, etc.
during the quiz
• Listen carefully to instructions
• Have OneCard ready.
Reminders
• Quiz 3 is now on 30 March
• HW 3 due Wed
• Quiz Review Session, Thu 5 – 6:30 pm,
BUS B-24+28
– Optional
– Q&A session, no new material
MGTSC 352
Lecture 7: Monte Carlo Simulation
Bard Outside example
Bard Outside
• The Bard Outside theatre group puts on plays
by Shakespeare 20 times every summer in a
200-seat outdoor theatre.
• Data:
– Attendance and weather (rain / no rain) for last five
seasons (5 x 20 = 100 shows)
– Revenue = $10 per customer
– Cost = $1,600 per show
• Question: how much would profit increase if the
number of seats were increased?
Profit
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Profit = Revenue – Expenses
Revenue =
Expenses =
What do we need to find out?
How can we do this?
Data Analysis
• What’s the probability of rain?
• What is the mean and standard deviation
of demand when it rains?
• How about when it doesn’t rain?
• How can we simulate demand?
To Excel …
Simulating Profit per show
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Simulate weather
Simulate demand
Make sure 0 ≤ demand ≤ capacity
Calculate revenue
Subtract cost
Replicate!
Remember: freeze tables of simulation
results
Simulating a value from a Normal Distribution:
Breaking the formula down
• ROUND(NORMINV(RAND(),mean,stdev),0)
• Step 1: generate random number
RAND()
• Step 2: convert random number to normal
distribution
NORMINV(RAND(),mean,stdev)
• Step 3: round to whole number
ROUND(NORMINV(RAND(),mean,stdev),0)
Converting random number to a
normal distribution
Cumulative Distribution Function
Probability
1.00
0.80
=RAND()
0.60
0.40
0.20
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=NORMINV(…)
Value = 990.3
500 Simulated 1000
Demand
1500
Final results
Avg. profit / show
$200
$150
$100
$50
$200
210
Seats
220
Comparing Different Capacities
• Want to compare 200 seats
and 210 seats
• Approach 1:
– Simulate demand for 100 days
– Compute profit for each
simulated day, assuming 200
seats
– Simulate demand for another
100 days
– Compute profit for each
simulated day, assuming 210
seats
– Compare average profits
• Approach 2:
– Simulate demand for 100 days
– Compute profit for each
simulated day, assuming 200
seats
– Compute profit for each
simulated day, assuming 210
seats (reuse the 100
simulated demands)
– Compare average profits
• Active learning: which
approach is better?
– 1 min., in pairs
– List as many pros and cons as
you can
Pros and Cons
• Approach 1
(simulate 2  100)
• Approach 2
(simulate 1  100)
Bard Outside Example: A
“Newsvendor Problem”
• Bard Outside:
– Decision: # of seats
– Uncertain future
demand
– Demand > # of seats
 lost revenue
– Demand < # of seats
 empty seats
• A newsvendor:
– Decision: # of
newspapers to get
– Uncertain future
demand
– Demand > # of papers
 lost revenue
– Demand < # of papers
 disposal costs
Active Learning
• In pairs, 1 min.
• Think of three other examples of
newsvendor problems
• Examples:
Bard Outside Revisited
• We estimated the average profit per show
with 200 seats to be about $11 per night
• Bard Outside’s accountant says they’ve
been earning an average of $100 per night
• What’s wrong?
Another look at the No Rain
Attendance Distribution
Attendance
(up to 199)
300
250
200
150
100
50
200 or more: 51% of
the time
What we did: Fit a Normal Distribution
with Mean = 176, Stdev = 39
Attendance of 200 or more: 51%
Demand of 200 or more: 27%
Demand
Can we do better?
300
250
200
150
100
50
Attendance
How about this: Normal Distribution
with Mean = 200, Stdev = 50
Attendance of 200 or more: 51%
Demand of 200 or more: 50%
Demand
300
250
200
150
100
50
Attendance
The attendance distribution is a “censored” version of the demand
distribution. We need to “uncensor” it before using it to simulate.
How Much Difference Does this
Make?
Avg.
profit
($/show)
200
seats
210
seats
220
seats
Extra
profit per
seat
Take 1
$11
$24
$33
$1.10
Take 2
$113
$146
$173
$3.00