Transcript Lecture 16

Exam
• Covers everything not covered by the last exam.
Starts with simulation
• If you cant’ get the optimal solution – get a pretty
good one.
• You may run out of time. Don’t spend time
looking for an answer you don’t know until you
have finished what you DO know.
• SAVE AND SUBMIT OFTEN
• The Exams will begin at 5 minutes after the hour.
Everyone will be let into the labs on the hour.
Please do not attempt to enter earlier.
What if you see an unfamiliar
solver message
• Ask a TA / manager
• Possible answers:
– I’ll fix it for you
– We have discussed the meaning of this
message in lecture / labs / assignments
– There is a problem with your model
• Always better to ask than not ask
MGTSC 352
Lecture 16:
Forecast Errors and Aggregate Planning
Air Alberta revisited:
using safety staffing to hedge
against uncertain turnover
Mountain Wear revisited:
using safety stock to hedge
against uncertain demand
Material under
development: not in
course pack
Forecast errors and
aggregate planning
• Forecasts provide input to aggregate
planning
• So far, we have only used point forecasts
• What about forecast errors?
• How do they impact aggregate plans?
Back to Air Alberta
•
•
•
•
“Normal attrition … is 10% per month.”
p = 10% is a point forecast
Suppose we have n = 100 employees
Actual attrition is a random variable:
binomial distribution with n = 100, p = .10.
• Expected value: n  p = 100  0.1 = 10
• Standard deviation:
n  p  (1  p)  100  0.1 0.9  9  3
What’s a Binomial Distribution?
• Toss a die 5 times
• X = number of tosses with a 1 or a 2
• X has a binomial distribution with n = 5, p = 2/6
Probability
40%
32.9%
32.9%
30%
20%
10%
16.5%
13.2%
4.1%
0.4%
0%
0
1
2
3
4
Number of tosses with a 1 or a 2
5
Active Learning
• In pairs, 1 min.
• Think of 3 other situations that can be
described by a binomial distribution
Our goal
Air Alberta
Flight Attendant Staffing Plan
Random values
generated
by the computer March
April
May
June
July
Attendant Hrs. needed
8000
7000
8000
10000
9000
Trained Attendants
60
58
64
74
76
Trainees Hired
2
13
15
7
16
Attrition: mean
6.00
5.80
6.40
7.40
7.60
Attrition: stdev
2.32
2.28
2.40
2.58
2.62
Attrition: actual
4
7
5
5
7
Attendant Hrs. Available
8800
7400
8100
10400
9800
Monthly Staffing Cost $ 91,400.00 $ 96,100.00 $ 106,500.00 $ 115,900.00 $ 125,200.00 $
Surplus
800
400
100
400
800
Shortage
0
0
0
0
0
Turnover rate:
Attendant cost
Trainee cost:
Attendant availability:
Trainee availability:
10% /month
$1,500 /person/month
$700 /person/month
150 hrs/person/month
-100 hrs/person/month
Total Staffing Cost: $
Formula in B9: =ROUND(NORMINV(RAND(),B7,B8),0)
August
12000
85
0
8.50
2.77
14
12750
127,500.00
750
0
662,600.00
Back to Air Alberta
• Actual attrition:
– n = # of trained attendants, p = 0.10
– Binomial distribution with mean = 0.1*n,
standard deviation SQRT(0.09*n)
– We’ll approximate this with a normal
distribution with the same mean and standard
deviation
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)
Q: What’s the impact of random
attrition?
• A: Attendant hour shortages (and surplus)
• What we’ll do:
– Come up with a hiring plan
– Evaluate the hiring plan by simulating attrition
– Compute shortages
– Replication: simulate n future scenarios
– Summarize results of the future scenarios
Active Learning
• Pairs, 1 min.
• How can we modify a hiring plan to hedge
against uncertain attrition?
• (Hedge = protect / insure)
Safety capacity vs.
staffing cost tradeoff
• Higher safety capacity  higher staffing cost 
less shortage
• Set safety capacity = X% of required hours
• Try X = 0, 2.5, 5
• Generate a hiring plan for each X
• Use simulation to evaluate each hiring plan
Let’s do it …