Question

Question 1: Daily demand for ground coffee at a Whole Foods store is normally distributed with a mean of 100 pounds (lbs) and a standard deviation of 50 pounds. Store manager continuously monitors the inventory of coffee and currently orders 1,000 lbs of coffee each time the inventory drops to 410 lbs. Whole Foods’s coffee supplier BlackBean takes 4 days to fill an order.

(a): How much safety inventory does the store carry with the current inventory policy?

(b): What service level does the store achieve with the current policy?

(c): On average, how many pounds of ground coffee are there in the store?

(d): On average, how many days does a pound of coffee sit in the store before being sold?

(e): If the store would like to have a 99% service level, what should the reorder point be?

Answer 1

Average daily demand (d) = 100 pounds

Standard deviation of daily demand (d) = 50 pounds

Order quantity (Q) = 1000 pounds

Reorder point (R) = 410 pounds

Lead time (L) = 4 days

a) R = d x L + Safety stock

=> 410 = 100 x 4 + Safety stock

=> 410 = 400 + Safety stock

=> Safety stock = 410-400

=> Safety stock = 10 pounds

b) Safety stock = Z x d x sqrt of L

=> 10 = Z x 50 x sqrt of 4

=> 10 = Z x 50 x 2

=> 10 = Z x 100

=> Z = 10/100

= > Z = 0.10

With a Z value of 0.10 the service level = 0.863 = 86.3%

c) Average inventory = Q/2 = 1000/2 = 500 poinds. So on an average 500 pounds are there in the store

d) Average flow time = Average inventory / d = 500/100 = 5 days

So a pound of coffee sit in the store before being sold for an average of 5 days

e) At 99% service level value of Z = 2.33

Reorder point = d x L + (Z x d x sqrt of L)

= 100 x 4 + (2.33 x 50 x sqrt of 4)

= 400 + (2.33 x 50 x 2)

= 400 + 233

= 633 pounds