Daily demand for a certain product is normally distributed with a mean of 113 an
ID: 435810 • Letter: D
Question
Daily demand for a certain product is normally distributed with a mean of 113 and a standard deviation of 15. The supplier is reliable and maintains a constant lead time of 4 days. The cost of placing an order is $12 and the cost of holding inventory is $0.50 per unit per year. There are no stock-out costs, and unfilled orders are filled as soon as the order arrives. Assume sales occur over 361 days of the year. Your goal here is to find the order quantity and reorder point to satisfy a 75 percent probability of not stocking out during the lead time. a. To manage inventory, the company is using Continuous review system O Periodic review system b. Find the order quantity. (Round your answer to the nearest whole number.) Order quantity books c. Find the reorder point. (Use Excel's NORMSINVO function to find the correct critical value for the given a-level. Do not round intermediate calculations. Round z" value to 2 decimal places and final answer to the nearest whole number.) Reorder pointExplanation / Answer
Ordering cost = Co = $12
Inventory holding cost = Ch = $0.50 per unit per year
Order quantity
= Square root ( 2 x Co x D/ Ch )
= Square root ( 2 x 12 x 40793/0.50)
= 1399.30 ( 1399 rounded to nearest whole number )
ORDER QUANTITY = 1399 UNITS
Z value of instock probability 0.75 = NORMSINV ( 0.75) = 0.6745
Standard deviation of demand during lead time
= Standard deviation of daily demand x Square root ( Lead time )
= 15 x Square root ( 4 )
= 15 x 2
= 30
Required safety stock
= z value x standard deviation of demand during lead time
= 0.6745 x 30
Reorder point
=Average Daily demand x Lead time ( days ) + Safety stock
= 113 x 4 + 20
= 452 + 20
= 472
REORDER POINT = 472
ORDER QUANTITY = 1399 UNITS
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