Question

A small copy center uses five 500-sheet boxes of copy paper a week. Experience suggests that...

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. Five 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.


a.

Determine the economic order quantity, assuming a 52-week year. (Round your answer to the nearest whole number.)


EOQ_______83_______________ boxes


b.

If the copy center reorders when the supply on hand is 28 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 is used for ordering instead of an ROP, how many boxes should be ordered if there are currently 24 boxes on hand, and an acceptable stockout risk for the order cycle is .0104? (Round "z" value to 2 decimal places and final answer to the nearest whole number.)


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Homework Answers

Answer #1

a. EOQ = [ 2x5x52x4 /0.3]1/2  = 83.26 =83

b. Reorder point = demand during lead time + safety stock

28 = 5x5+ z x SDLT

28 = 25 + z x 0.5 ( 5)1/2

z = 28-25 / 1.118 = 2.68

Corresponding service level = 99.632 %

chances of stockout = 1-0.99632 =0.368%

c.

SD of demand during protection period ( 5+7 =12 weeks)

SDP+L= 0.5 x ( 12)1/2 = 1.73

z value for Service level of ( 1-0.0104) =98.96% = 2.31

Safety stock = z x SDP+L = 2.31 x 1.73 = 3.99 =4

T = demand x ( P+L) + Safety stock

= 5x 12 +4 = 64

As there are already 24 units on hand, 40 units need to be ordered.

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