1. The total variance of demand during lead time is given by:
This result comes directly from law of total variance and therefore, holds for any distribution of lead
times. Now, this variance has two components, which behave quite differently from each other. For
example, for the distribution for Germany in Problem 2c, the variances will behave as follows with
changing the probability of lead time being 4 weeks:
Lead Time l
(in Weeks)
8
4
P(L
=l)
0.25
0.75
Mean Weekly
Demand
4000
4000
Standard
Deviaiton
2200
2200
E(DDLT|L=l) = l*mean
weekly demand
32000
16000
Var(DDLT | L=l)
= l*(SD^2)
38720000
19360000
Behaviour of Variances
100
Millions
80
60
Var [ Exp ]
40
Exp [ Var ]
Total Variance
20
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Effect on Safety Stock
18000.00
16000.00
14000.00
12000.00
10000.00
Sigma (DDLT)
8000.00
Safety Stock
6000.00
4000.00
2000.00
0.00
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1