Question

The amount of denim used daily by the Southwest Apparel Company in its manufacturing process to make jeans is normally distributed with an average of 4000 yards of denim and a standard deviation of 600 yards. The lead time required to receive an order of denim from the textile mill is a constant 7 days. Determine the: a. safety stock b. reorder point if the company wants to limit the probability of a stockout and work stoppage to 5% and c. what level of service would a safety stock of 2000 yards provide?

Answer 1

a) safety stock is 2611 yards

b) Reorder point is 30611 yards

c) Z = 0.8962 or 89.62%

Step-by-step explanation:

Given that;

jeans is normally distributed with an average of 4000 yards.

standard deviation is 600 yards

the company wants to limit the probability of a stock out and work stoppage to 5%

so ∝ = 1 - 5% = ( 1 - 5/100) = 0.95

from table; z value = 1.645

lead time = 7 days

now;

a) safety stock

safety stock is determined using the following;

⇒ Z-score × standard × √lead time

so we substitute

safety stock = 1.645 × 600 × √7

= 2611.3565 ≈ 2611 yards

b) reorder point

reorder point is determined using the following;

⇒ demand × lead time + safety stock

we substitute

reorder point = (4000 × 7) + 2611

reorder point = 30611 yards

c) level of service would a safety stock of 2000 yards provide

safety stock = Z√lead time × standard deviation

we substitute

2000 = Z × √7 × 600

Z = 2000 / ( 600 × √7 )

Z = 1.25988 ≈ 1.26

FROM table; Z = 0.8962 or 89.62%