Question 1 (35 pts): Weekly demand for Barilla pasta at a Hy-Vee store is normal

Question

Question 1 (35 pts): Weekly demand for Barilla pasta at a Hy-Vee store is normally distributed, with a mean of 250 boxes and a standard deviation of 150 boxes. The store manager continuously monitors inventory and currently orders 1,000 boxes of pasta each time the inventory drops to 600 boxes. Barilla currently takes two weeks to fill an order. (a) (7 pts) How much safety inventory does the store carry given the current policy? (b) (7 pts) What service level does store achieve for Barilla pasta with the current policy? (c) (7 pts) On average, how many boxes of Barilla pasta are there in the store? (d) (7 pts) On average, how many weeks does a box of Barilla pasta sit in the inventory before being sold? (e) (7 pts) If the Hy-Vee store would like to have a 99% service level, what should the reorder point be?

Explanation / Answer

Answer to question a and b:

Standard deviation of weekly demand = 150 boxes

Lead time to fill an order = 2 weeks

Hence, Standard deviation of demand during lead time

= Standard deviation of weekly demand x Square root ( Lead time )

= 150 x Square root ( 2 )

= 150 x 1.414

= 212.1

Let Z value corresponding to the service level = Z1

Since inventory is always maintained at 600 boxes, safety stock = 600

Since,

Safety stock = Z value x Standard deviation of demand during lead time

Or, 600 = Z1 x 212.1

Or, Z1 = 600/212.1 = 2.828 ( 2.83 rounded to 2 decimal places )

Corresponding value of probability for Z= 2.83 as derived from standard normal distribution table = 0.99767 ( 0.9977 rounded to 4 decimal places)

Thus , service level = 0.9977 x 100 = 99.77%

SAFETY STOCK = 600

SERVICE LEVEL = 99.77%

Answer to question c :

Number of boxes of Barilla Pasta in the store = Order quantity /2 + Safety stock = 1000/2 + 600 = 500 + 600 = 1100

Answer to question d :

When 1000 boxes ae ordered , first box gets sold immediately and the last box gets sold in = 1000/ 250 = 4 weeks ( since average weekly demand is 250). Therefore, on average a Box of Barilla Pasta sits for = 4/ 2= 2 weeks

ON AVERAGE A BOX OF BARILLA PASTA SITS 2 WEEKS BEFORE IT GETS SOLD

Answer to question e :

Z value corresponding to 99% service level = NORMSINV ( 0.99) = 2.326

Hence safety stock = z value x standard deviation of demand during lead time = 2.326 x 212.1 = 493.34 ( 494 rounded to next higher whole number )

Reorder point = Average weekly demand x Lead time ( weeks ) + safety stock = 250 x 2 + 494 = 994 boxes

REORDER POINT = 994 BOXES

SAFETY STOCK = 600

SERVICE LEVEL = 99.77%

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