Question

The manager at the local store of a national home improvement chain is studying their inventory system. He has chosen one high volume product as the first product to examine. The historical supply and demand data for this item has indicated a constant lead time of 16 days. Demand per day (d) is normally distributed with a mean demand of 2000 per day and standard deviation of 240 per day. He plans to set the in-stock probability (or service level) for this item at 95% during lead time. The ordering cost for this item is $500 per order. The product cost is $10 per unit. The annual inventory carrying cost is 30% of the item cost per year. The store operates 300 days a year. The manager decides to use the fixed quantity system (reorder point and economic order quantity). Based on the information provided, answer the following questions. 1. What is the safety stock level for this item? Round your answer to the nearest integer. Your answer is [x]. (1 point) Note: use “NORMSINV” function in Excel to find the accurate z value. 2. What is reorder point? Round your answer to the nearest integer. Your answer is [y]. (1 point) 3. What is the economic order quantity? Round your answer to the nearest integer. Your answer is [z]. (1 point) 4. How many orders will be placed per year under the policy you find? Round your answer to the nearest integer. Your answer is [k]. (1 point) 5. Using your answers of safety stock in question 1 and EOQ in question 3, what is the average inventory level under the order policy you find (including cycle inventory and safety inventory)? Round your answer to the nearest integer. Your answer is [l]. (1 point) 6. What is the annual ordering cost? Note: use your answer from question 4. Round your answer to the nearest integer. Your answer is [m]. (1 point) 7. Using your answer from question 5, what is the annual inventory carrying cost including both cycle inventory and safety inventory? Round your answer to the nearest integer. Your answer is [n]. (1 point) 8. Based on your answers to question 6 and 7, what is the total annual inventory cost? Round your answer to the nearest integer. Your answer is [o]. (1 point) ( Some of my answers listed below were wrong )

Specified Answer for: x 1579 Specified Answer for: y 33579 Specified Answer for: z 14142 Specified Answer for: k 42 Specified Answer for: l 8650 Specified Answer for: m 21213 Specified Answer for: n 25951 Specified Answer for: o 47164

Answer 1

1.

Safety stock = z*standard deviation of demand during lead time = normsinv(0.95)*240*sqrt(16) = 1579.059482 = 1579 (Rounded to nearest integer)

2.

reorder point = daily demand*lead time + safety stock = 2000*16+1579 = 33579

3.

Annual demand = 300*2000 = 600000 = D
EOQ = Square root ((2*D*S)/h) S = ordering cost per order = $500 and h = holding cost = 30% of $10 =>$3
EOQ = Sqrt((2*600000*500)/3) = 14142.13562 = 14142(Rounded to nearest integer)

4.

No of orders = Annual demand/EOQ = 600000/14142 = 42.42681375 = 42 (Rounded to nearest integer)

5.

Average inventory level = cycle inventory + safety inventory

= (14142/2)+1579 = 8650

6.

Annual ordering cost = no of orders*ordering cost = 42*500 = 21000

7.

annual inventory carrying cost including both cycle inventory and safety inventory = 8650*3 = 25950

8.

total annual inventory cost = Annual ordering cost +
annual inventory carrying cost including both cycle inventory and safety inventory = 21000+25950 = 46950