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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

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

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