Question

In: Operations Management

A small copy center uses 4 400-sheet boxes of copy paper a week. Experience suggests that...

A small copy center uses 4 400-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 .40 boxes per week. 2 weeks are required to fill an order for letterhead stationery. Ordering cost is $4, 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 =?

b. If the copy center reorders when the supply on hand is 9 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 22 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

Demand = 4 boxes per week

Order Cost = $4

Holding Cost = $0.33 (33 cents per box)

Standard Deviation = 0.4 boxes per week

Lead Time = 2 weeks

Mean Demand = 4 boxes per week

a. EOQ = 2*Annual Demand*Ordering Cost/ Holding Cost = 2*4*52*4/0.33 = 71 boxes

b. Copy center orders when supply on hand is 9. This means, Reorder Point = 9

ROP = Demand During Lead Time + z vaue * Standard Deviaition During Lead Time

Demand During Lead time = Weekly Demand * Lead time

Standard Deviation during Lead Time = weekly standard deviation * lead time

Hence , 9 = 4*2+z*0.4*2

or z = (9-8) / (0.4*1.414) = 1.76

Confidence interval using z table at z = 1.76 is 0.96 or 96% service level.

96% of the time there will be no stockout if reordered when stock on hand is 9 units or there will be 4% of the time there will be stock out.

The risk is 4%.

c. Fixed Interval = 5 weeks

Risk = 0.0228

Service Level = 1-0.0228 = 0.9772

Using table, z value at 0.9772 = 2

Order Quantity = Expected Demad During Interval + Safety Stock -Amount on Hand

Expected Demad During Interval = mean demand *(fixed interval+lead time) = 4*(5+2) = 28

Safety Stock = z * Standard Deviation * (fixed interval+lead time) = 2*0.4*(5+2) = 2.11

Order Quantity = 28+2.11-22 = 8.11 rounded to 8.

Q0 = 8

keosha answered 3 months ago

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