M451 Supply Chain Management- Tutorial 3

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M451 Supply Chain Management- Tutorial 3 Solution
Dr Banafsheh Khosravi
Discrete and Continuous News Vendor models
1)
pp =1800         sp = 2500        s = 1700
Cu = 2500-1800 = 700            Cv = 1800-1700 = 100
P (D = 130) = 0.09
P (D ≤ 140) = 0.02 + 0.05 + 0.08 + 0.09 + 0.11 = 0.35
P (D > 140) = 1 – 0.35 = 0.65
P (D ≥ 140) = 1 – 0.35 + 0.11 = 0.76
2)
Profit = 5-3 = £2          Loss = 3-0.5 = £2.5
Order quantity
Demand
Expected profit
10
20
30
40
50
60
10
2
2
6
6
2
2
20
20
-0.5
4
12
12
4
4
35.5
30
-3
1.5
18
18
6
6
46.5
40
-5.5
-1
10.5
24
8
8
44
50
-8
-3.5
3
16.5
10
10
28
60
-10.5
-6
-4.5
9
7.5
12
7.5
P(x)
0.10
0.10
0.30
0.30
0.10
0.10

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3)
Note: Find the closest probability values to 0.5883 in the standard normal distribution Table and do the interpolation which results in z’= 0.2231. Therefore, z = – 0.2231 as the complement probability was looked up in the table.
4)
Note: Find the closest probability values to 0.6 in the standard normal distribution Table and do the interpolation which results in z= 0.2533.
Note: Find the closest z values to 0.477 in the standard normal distribution Table and do the interpolation which results in P(Z ≤ 0.477) = 0.6833