Given:

Time Period of 1 week: The lead time for manufacturing and delivery is 8 weeks (L=8); demand is normally distributed with a mean of 50 units and a standard deviation 10 units. Demands across time periods are independent.

Time Period of 2 weeks: The lead time for manufacturing and delivery is 4 biweekly time periods (L=4); demand is normally distributed with a mean of 100 units and standard deviation 14.14 units. Demands across time periods are independent.

Time Period of 4 weeks: The lead time for manufacturing and delivery is 2 four-week time periods (L=2); demand is normally distributed with a mean of 200 units and a standard deviation 20 units. Demands across time periods are independent.

i. For each of the time period alternatives, you are required to determine the optimal order-up-to level(S*) as to achieve:

Order upto level, S is the maximum inventory position or target inventory level or base stock level.

• a Fill rate of 96.5%.

For time period of 1 week

Using the Standard Normal Loss Function Table:

z = 1.20

Convert z into the order-up-to level:

Order-up-to level (S*) =Expected demand over (L+ 1) weeks + z x Standard deviation over (L+ 1) weeks

= 450 + 1.20 x 30

Order-up-to level (S*) =486

HOW DO YOU DERIVE THE Z-SCORE ON THESE PROBLEMS?