A small copy center uses 4 450-sheet boxes of copy paper a week. Experience sugg
ID: 328225 • Letter: A
Question
A small copy center uses 4 450-sheet boxes of copy paper a week. Experience suggests that usage can be well approximated by a normal distribution with a mean of 4 boxes per week and a standard deviation of .60 boxes per week. 3 weeks are required to fill an order for letterhead stationery. Ordering cost is $6, and annual holding cost is 33 cents per box.
Use Table.
a. Determine the economic order quantity, assuming a 52-week year. (Round your answer to the nearest whole number.)
EOQ boxes
b. If the copy center reorders when the supply on hand is 13 boxes, compute the risk of a stockout. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
Risk
c. If a fixed interval of 5 weeks is used for ordering instead of an ROP, how many boxes should be ordered if there are currently 27 boxes on hand, and an acceptable stockout risk for the order cycle is .0228? (Round "z" value to 2 decimal places and final answer to the nearest whole number.)
Q0
Explanation / Answer
Annual Demand = 4*52 = 208 boxes
Ordering Cost S = 6 $
Annual Holding Cost H = 0.33 $
a) EOQ = SQRT(2*D*S/H) = SQRT(2*208*6/0.33) = 87 boxes
b) ROP = 13 boxes = d*L+SS = d*L+z*?d *d*?L
4*3+z*0.6*4*?3 = 13 => z*2.4*?3 = 1 => z = 0.24 => Service level = 0.5948 => 59.48%
Risk of stockout = 1-0.5948 = 0.4052
c) Fixed interval t = 5 weeks
Current boxes
Total time period t+L = 5+3 = 8 weeks
Demand during the period = 8*4 = 32 boxes
Stockout risk = 0.0228 => Service level = 0.9772 => z = 2
z = (X - D)/? => 2 = (X-32)/0.6 => X = 33.2 boxes