Instructions This homework set has 3 Problems. The total credit for this homewor
ID: 340037 • Letter: I
Question
Instructions This homework set has 3 Problems. The total credit for this homework set is 20. Please write down your name, ID, and section number on the upper-right corner of the paper. Please show your work! Problem 1: (10 Points) A company decides to establish an EOQ for an item. The annual demand is 200,000 units. The ordering costs are $40 per order, and inventory-carrying costs are $2 per unit per year. Calculate the following: (a). The EOQ in units. (b). Number of orders per year (c). Annual ordering cost, annual holding cost, and annual total cost Problem 2: (10 Points) Given this information: Expected demand during lead time 400 units Standard deviation of lead time demand 50 units Assuming that lead time demand is distributed normally. The risk of stockout is 1 percent during lead time. (a) What amount of safety stock is appropriate? (b) Calculate ROPExplanation / Answer
1.
A.
EOQ = (2*annual demand*ordering cost / holding cost)^.5
EOQ = (2*200000*40/2)^.5
EOQ = 2828.43 units or 2828 units
B.
No. of orders per year = Annual demand / EOQ = 200000/2828
No. of orders per year = 70.72 or 71 orders per year
C.
Annual ordering cost = (Annual demand / EOQ)*ordering cost = (200000/2828)*40
Annual ordering cost = $2828.85
Annual Holding cost = (EOQ/2)*holding cost per unit per year
Annual Holding cost = (2828/2)*2 = $2828
Total annual cost = Annual ordering cost + Annual Holding cost = 2828.85 +2828
Total annual cost = $5656.85
2.
A.
The value of Z at 1% stock out risk (99% confidence) = 2.33
SD = 50 units
Then,
Safety stock = Z*SD*L^.5 = 2.33*50*1 = 116.5 units
B.
ROP = Lead time demand + safety stock = 400 + 116.5
ROP = 516.5 or 517 units