b. What should R be? c. An inventory withdrawal of 10 bags was just made. Is it
ID: 353256 • Letter: B
Question
b. What should R be? c. An inventory withdrawal of 10 bags was just made. Is it time to reorder? It is time to reorder. d. The store currently uses a lot size of 480 bags (i.e., Q 480). What is the annual holding cost of this policy? The annual holding costis s 660. (Enter your response rounded to two decimal places.) What is the annual ordering cost? The annual ordering cost is S 566.04. (Enter your response rounded to two decimal places.) Without calculating the EOQ, how can you conclude from these two calculations that the current lot size is too large? A. When Q 480, the annual holding cost is larger than the ordering cost, therefore Q is too large. 0 B. There is not enough information to determine this. ° C. When Q-480, the annual holding cost is less then the ordering cost, therefore Q s too small. D. Both quantities are appropriate. e. What would be the annual cost saved by shifting from the 480-bag lot size to the EOQ? The annual holding cost with the EOQ is 611.88. (Enter your response rounded to two decimal places.) The annual ordering cost with the EOQ is Enter your response rounded to two decimal places.)Explanation / Answer
Given are following data :
Annual demand = D =95 bags/ week x 52 weeks = 4940 bags
Order cost = Co = $55/ order
Annual unit holding cost = Ch = 25% of $11= $2.75
The optimal order quantity ( EOQ )
= Square root ( 2 x 55 x 4940 / 2.75 )
= 444.52 ( 445 rounded to nearest whole number )
SAM’S OPTIMAL ORDER QUANTITY = 445 BAGS
Average time between orders
= EOQ/Annual demandx 52 weeks
= 445 /4940x 52
= 4.68 ( 4.7 rounded to 1 decimal point )
AVERAGE TIME BETWEEN ORDERS = 4.7 WEEKS
Standard deviation of weekly demand = 18 bags
Lead time = 4 weeks
Therefore , standard deviation of demand during lead time = 18 x Square root ( 4 ) = 18 x 2 = 36
Cycle service level = 0.90 ( i.e 90 %)
Corresponding Z value = NORMSINV ( 0.90 ) = 1.2815
Safety stock
= Z value x standard deviation of demand during lead time
= 1.2815 x 36
Reorder point ( ROP )
= 95 bags / week x 4 weeks + Safety stock
= 95 x 4 + 46.13
= 380 + 46.13
= 426.13 ( 426 rounded to nearest whole number )
Initial on hand inventory = 350 bags
Withdrawal made = 10 bags
Therefore , current on hand inventory after withdrawal = 350 – 10 = 340 bags
Since 340 bags < Reorder point of 426, it is time to REORDER
IT IS TIME TO REORDER
Revised lot size = 480 bags
Annual holding cost = Annual unit holding cost x Revised lot size/ 2 = 2.75 x 480/2 = 2.75 x 240 = $660
The annual ordering cost
= Cost per order ( Co) x Number of orders
= Co x Annual demand / Order size
= 55 x 4940 / 480
= $566.04
THE ANNUAL HOLDING COST = $660
THE ANNUAL ORDERING COST = $566.04
At Q = 480, annual holding cost > annual ordering cost
At EOQ , annual holding cost = annual ordering cost
Since , Order quantity appears at the numerator for calculation of annual holding cost and denominator for calculation of annual ordering cost, We can assume that order quantity is greater than the EOQ which has resulted in Annual holding cost > Annual ordering cost .
Therefore Q > EOQ
WHEN Q = 480 , THE ANNUAL HOLDING COST IS LARGER THAN THE ORDERING COST , THEREFORE Q IS TOO LARGE
Annual cost saving by shifting from 480 bag lot size to EOQ :
Annual holding cost with EOQ = Ch x EOQ / 2 =$ 2.75 X 445/ 2 =$611.87
Annual ordering cost with EOQ = Co x D/EOQ =55 X 4940/445 = $610.56
Total inventory cost under EOQ = Annual ordering cost + Annual Holding cost = $611.87 + $610.56 = $1222.43
Total inventory cost under Q = 480 = Annual ordering cost + Annual holding cost = $660 + $566.04 = $1226.04
The savings = $1226.04 - $1222..43 = $3.61
SAM’S OPTIMAL ORDER QUANTITY = 445 BAGS
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