Question

Imagine you are doing an inventory review for your new employer. One of the first items you look at is a cookware set. Demand is normally distributed with a mean of 17 units/day. The standard deviation for demand during lead time is 34.6. The company currently purchases the cookware set when the inventory level falls to 400. Supply lead time is 21 days.
Required:
a. How much safety stock is currently being held?
b. What Cycle Service Level is currently being supported?
c. If a 95% CSL is desired, what reorder point should be used?
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?

Answer 1

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