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?

a) safety stock is 2611 yards

b) Reorder point is 30611 yards

c) Z = 0.8962 or 89.62%

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%

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