Problem 13-26 A small copy center uses five 500-sheet boxes of copy paper a week
ID: 450356 • Letter: P
Question
Problem 13-26 A small copy center uses five 500-sheet boxes of copy paper a week. Experience suggests that usage carn be well approximated by a normal distribution with a mean of five boxes per week and a standard deviation of one-half box per week. Two weeks are required to fill an order for letterhead stationery. Ordering cost is $5, and annual holding cost is 35 cents per box. Use Table. Determine the economic order quantity, assuming a 52-week year. (Round your answer to the nearest whole number.) a. EOQ boxes b. If the copy center reorders when the supply on hand is 11 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 seven weeks instead of an ROP is used for reordering, what risk does the copy center incur that it will run out of stationery before this order arrives if it orders 25 boxes when the amount on hand is 23 boxes? (Round "z" value to 2 decimal places and final answer to 4 decimal places.) RiskExplanation / Answer
(a) We know that EOQ = sqrt(2*D*S/H)
D = annual demand = 5*52 = 260
S =$5 ordering cost
H = holding cost =0.35
EOQ = sqrt(2*260*5/0.35) =86.19 units ...............Ans.
(b) LT * = 2 [weeks] * 5 [boxes/week] = 10 [boxes]
= * 0.5 = * 0.5 = (ROP - ) / = (11 – 10)/( * 0.5) = 2.0.
Stockout probability = 1 – Pr (Z < 2.0) = 1 – 0.9772 = 0.0228 = 2.28%
(c) P system: PP = LT + OI = 2 + 7 = 9 [weeks];
OUL = 23 + 25 = 48 [boxes]
= PP * = 9 [weeks] * 5 [boxes/week] = 45 [boxes].
OUL = (48 – 45) / ( * 0.5) = 2
2 to the Z table = .9772
Stock-out probability = 1 – Pr(Z < 2.0) = 1 - 0.9772 = 0.0228