Answer: a. 43units
b. 89.5%
c. 414 units
d. $68.30
Explanation:
The information given are written below:
Demand, d = 17 units per day
Standard Deviation during lead time, SD = 34.6
Reorder point R = 400
Lead Time, L = 21 days
Since Reorder point = (d×L) + (Z×SD)
400 = (17 × 21) + (34.6 × Z)
400 = 357 + 34.6Z
34.6Z = 400 - 357
34.6Z = 43
Z = 43/34.6
Z = 1.24
a. How much safety stock is currently being held?
= 1.243 × 34.6
= 43 units
b. What Cycle Service Level is currently being supported?
Since the value of Z = 1.243, then, the service level from the service table will be: = 89.5%
c. If a 95% CSL is desired, what reorder point should be used?
This will be:
=(17 × 21) + (1.645 × 34.6)
= 357 + 56.917
= 413.917
= 414 units
d. If the annual holding cost is 20% of item cost and the item costs $12/unit, what is the cost of safety stock inventory based on a 95% CSL?
First, we need to know the average inventory for the 95% service level which will be:
= Safety stock / 2
= (1.645 × 34.6) / 2
= 28.46 units
The cost of safety stock inventory will be:
= Average inventory × Item cost × Holding cost
= 28.46 × 12 × 20%
= $68.30
