Question

In: Operations Management

A small copy center uses 5 500-sheet boxes of copy paper a week. Experience suggests that...

A small copy center uses 5 500-sheet boxes of copy paper a week. Experience suggests that usage can be well approximated by a normal distribution with a mean of 5 boxes per week and a standard deviation of .50 boxes per week. 2 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. a. Determine the economic order quantity, assuming a 52-week year. (Round your answer to the nearest whole number.) EOQ 86 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 7 weeks is used for ordering instead of an ROP, how many boxes should be ordered if there are currently 25 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

Expert Solution

a) Economic order quantity Q

Annual demand D = 5 per week * 52 weeks = 260 boxes

Ordering cost S =$5

Annual holding cost H= $0.35

= 86.19 = 86 units

b) Given ROP = 11 boxes

Weekly demand d = 5 boxes

Lead time L =2 weeks

Standard deviation = 1/2 box

dL = 5*2 = 10

z= 1.41

Service probability at z=1.41 is 0.9207 ( we can calculate by normsdist(1.41) in excel)

Risk = 1- probability = 1- 0.9207 = 0.0793 = 7.93%%

c)

Service Level =1-acceptable stockout risk = 1- 0.0228 = 0.9772

Z value at 0.9772 = 2

Time between orders OI = 7 weeks

Lead time LT = 2 weeks

weekly demand d =5 boxes

= 1/2 boxes

On-hand inventory A = 25

Amount to order Q

= 23 boxes

keosha answered 1 year ago

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