Answer:
Reorder point necessary to provide 98% service probability is 1569 units
If the production manager is asked to reduce the safety stock of the item by 50%, the new service probability will be 84.7%
Explanation:
Data:
Weekly demand (d)= 300 units
Lead time (L)= 4 weeks
Standard Deviation (SD) = 90units
(A) To find reorder point.
-standard deviation (SDw) with lead time of 4 weeks = [tex]\sqrt{4}[/tex] x (90) = 180units
-98% probability is needed, use the formular NORMSINV (0.98) in Excel Spread sheet and get value of "z" to be 2.05
R = d*L + z*(SDw)
R = 300 x (4) + (2.05) x (180)
R = 1,569 units
Note; determining the safety cost "SS"
SS = z * SDw = 2.05 x 180 = 369 units
for a 50% reduction, 369 x 0.50 = 184.5 ≅ 185 units
(B) now calculate "z" when safety stock is 185 units
SS = z * SDw
185 = z (180)
z = 1.02
In table, the corresponding probability value of 1.02 is 84.7%
If the production manager wants to have a 50% reduction in the safety stock, then the service probability is 84.7%
The first thing to do is to calculate the standard deviation with a lead time of 4 weeks. This will be:
= ✓Lead time × Standard deviation
= ✓4 × 90
= 2 × 90.
= 180
Since there's a 98% service probability, the value of z will be 2.05. Then, the new order will be:
= 300 × 4 + (2.05 × 180)
= 1569 units.
Then, the safety stock will be:
= (0.50) × (2.05 × 180)
= 185 units
Finally, we'll calculate the value of z when the safety stock is 185 units. This will be;
185 = z × 180
185 = 180z
z = 185/180.
z = 1.02.
Then, the z value will be checked in the table and thus will be 84.7%.
Read related link on:
https://brainly.com/question/16968150
