Problem 13-26 A small copy center uses five 500-sheet boxes of copy paper a week
ID: 446500 • Letter: P
Question
Problem 13-26
A small copy center uses five 500-sheet boxes of copy paper a week. Experience suggests that usage can 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. Three weeks are required to fill an order for letterhead stationery. Ordering cost is $4, and annual holding cost is 30 cents per box.
Determine the economic order quantity, assuming a 52-week year. (Round your answer to the nearest whole number.)
If the copy center reorders when the supply on hand is 16 boxes, compute the risk of a stockout.(Round "z" value to 2 decimal places and final answer to 4 decimal places.)
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 28 boxes when the amount on hand is 23 boxes? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
A small copy center uses five 500-sheet boxes of copy paper a week. Experience suggests that usage can 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. Three weeks are required to fill an order for letterhead stationery. Ordering cost is $4, and annual holding cost is 30 cents per box.
Use Table.Explanation / Answer
Annual Demand (5 boxes/week * 52 weeks ) 260 Ordering Cost $ 4.00 Holding Cost $ 0.30 a. EOQ = 2AO / H where A = Annual Demand O = Ordering Cost per order H = Holding Cost per unit per annum EOQ = 2AO / h = (2 * 260 * 4) / 0.30 = 83.26664 units or, 83 units b. ROP = Lead Time Demand + Safety Stock or, 16 = 3*5 + Std Dev * Z Value or, 16 = 3*5 + Std Dev * Z Value or, 16 = 15 + 1.5 * Z value or, Z Value = 1/1.5 = 0.67 Risk of Stock out from Z tables = 0.2514 c. Units on hand = 23 Lead Time =3 weeks Order Interval = 7 week Order Units = 28 28 = 7 weeks * 5 units + z value * 1.5 * 10^0.5 or, -22 = 4.47434 * Z value or, Z Value =-7 / 4.47434 or, Z Value = -1.48 Risk of Stock out from Z tables = 0.9306