Transcript Practice Exam #1

Risk Pooling
John H. Vande Vate
Spring, 2006
1
1
Safety Stock Basics
• n customers
• Each with lead time demand N(m, s)
• Individual safety stock levels
– Choose z from N(0,1) to get correct
probability that lead time demand exceeds z,
– Safety stock for each customer is zs
– Total safety stock is nzs
2
2
Safety Stock Basics
• Collective Lead time demand N(nm, ns)
• This is true if their demands and lead times are
independent!
• Collective safety stock is nzs
• Typically demands are negatively or positively
correlated
• What happens to the collective safety stock if
demands are
– positively correlated?
– Negatively correlated?
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3
Risk Pooling Case 3.3 p 64
Historical Data for Product A
Massachusetts
New Jersey
Pooled
Massachusetts
New Jersey
Pooled
Week
1
33
46
79
Average
39.25
38.63
77.88
2
45
35
80
Std Dev
13.18
12.05
20.71
3
37
41
78
4
38
40
78
Avg. Lead
time
Coeff of
Var
Demand
0.34
39.25
0.31
38.63
0.27
77.88
Historical Data for Product B
Massachusetts
New Jersey
Pooled
Massachusetts
New Jersey
Pooled
5
55
26
81
Safety
Stock
24.78
22.66
38.95
Week
1
0
2
2
Average
1.13
1.25
2.38
2
2
4
6
3
3
0
3
Std Dev
1.36
1.58
1.92
Coeff of
Var
1.21
1.26
0.81
4
0
0
0
Avg. Lead
time
Demand
1.13
1.25
2.38
5
0
3
3
Safety
Stock
2.55
2.97
3.62
Inventory Comparison
Product A
Product B
Total
Massachusetts New Jersey
91
88
14
15
105
103
Total
179
28
207
Pooled
132
20
152
Reduction
26%
30%
27%
The6 impact7 is less 8than
30
18
58
48the sqrt
18 of 2 law
55
78
36
113
It predicts that if 2 DCs
need 47 units
then aAvg.
Reorder
Order Up
Point
To Level
single EOQ
DC will
needInventory
33
64
61
117
132
131
186
196
192
303
91
88
132
The impact is greater
than
the 7sqrt of 28 law
6
It 11predicts30 that if 002 DCs
2
0
need
5.53 units then
a
single DC will need 4
Reorder
Point
EOQ
4
4
6
22
24
32
Order Up
Avg.
To Level Inventory
26
14
28
15
38
20
Pooling Inventory can
reduce safety 4stock
4
Inventory (Risk) Pooling
• Centralizing inventory can reduce
safety stock
• Best results with high variability and
uncorrelated or negatively correlated
demands
• Postponement ~ risk pooling across
products
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5
Examples
• Describe techniques for pooling risk
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