Question

Linda L. is in charge of maintaining hospital supplies at General Hospital. During the past year the lead-time when ordering the BX-5 bandage was six weeks. Monthly (four weeks) mean demand was 300 and monthly standard deviation of the demand was 27 units.
Note the additional information: It costs $1.50 to hold such a bandage in stock for a
year. The supplier is offering Linda to shorten the lead-time from 6 weeks to 3
weeks but the unit cost will have to increase from $10 to $15. Follow the
instructions, and show your work in the Answers sheet.

As the lead time here is 6 weeks which is more than a month period of 4 weeks, therefore the mean and standard deviation of demand here are computed as:

Mean ( 6 week demand ) = (6/4)*300 = 450

tandard deviation ( 6 week demand ) = (6/4)*27 = 40.5

Therefore the reorder point now is computed here as:
= Total demand in 6 weeks which is not exceeded with 99% probability.

In EXCEL this is computed as:
= NORMINV(.99, 300*6/4,27*6/4)

1.

a. Calculate lead-time mean demand for the lead times of 6 and 3 weeks.

b. Calculate standard deviation of the lead-time demand for the lead times of 6 and 3 weeks

c. assume the service level is 99%. Determine the two safety stock for the 3 weeks lead time.

Answer 1

Note: In case of any doubt, please mention it in the comment so that I can rectify it for you. Thank you

Solution::

Monthly demand (D) = 300

Number of working weeks = 4

Weekly demand (d) = 300/4

Weekly demand (d) = 75 units

Monthly Standard deviation = 27

Weekly Standard deviation (s) = 27/4

Weekly Standard deviation (s) = 6.75 units

(A)

Mean demand for lead time = Weekly demand × Lead time

Mean demand for lead time of 6 weeks = 75 × 6 = 450 units

Mean demand for lead time of 3 weeks = 75 × 3 = 225 units

(B)

Standard deviation of lead time demand =
S. V LeadTime

Standard deviation of demand for lead time of 6 weeks = (6.75 × 2.44949) = 16.534 units

Standard deviation of demand for lead time of 3 weeks =

(6.75 × 1.73205) = 11.691 units

(C)

Given service level = 99%

Value of Z corresponding to service level of 99% = 2.33

Safety Stock = Z × Standard deviation of demand during lead time

Safety stock for 3 weeks = Z × Standard deviation of demand during lead time of 3 weeks

Safety stock for 3 weeks = 2.33 × 11.691

Safety stock for 3 weeks = 27.2408 units