Question

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. Four weeks are required to fill an order for letterhead stationery. Ordering cost is $2, and annual holding cost is 40 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

boxes

b.	If the copy center reorders when the supply on hand is 22 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 21 boxes on hand, and an acceptable stockout risk for the order cycle is .0351? (Round "z" value to 2 decimal places and final answer to the nearest whole number.)

Q0

Answer 1

Following details are provided :

Annual demand = D = 500 / week x 52 weeks = 26000 weeks

Ordering cost = Co = $2

Annual unit holding cost = Ch = $0.40 per box

Economic Order Quantity ( EOQ )

= Square root ( 2 x Co x D / Ch )

= Square root ( 2 x 2 x 26000 / 0.40 )

= 509.90 ( 510 rounded to nearest whole number )

ECONOMIC ORDER QUANTITY = 510 BOX

Standard deviation of weekly demand = 1.5 weeks

Lead time i.e. time required to fill an order = 4 weeks

Therefore, standard deviation of demand during lead time = Sd = 1.5 x Square root ( 4 ) = 1.5 x 2 = 3 boxes

Let z value corresponding to the relevant service level = Z1

Therefore , Safety stock = Z1 x Standard deviation of demand during lead time = 3.Z1

Therefore , reorder point

= Mean weekly demand x Lead time ( weeks ) + safety stock

= 5 x 4 + 3.Z1

= 20 + 3.Z1

It is given that , reorder point = 22

Therefore ,

22 = 20 + 3.Z1

Or, Z1 = 2/3

Or, Z1 = 0.666 ( 0.67 rounded to nearest whole number )

Corresponding probability for Z = 0.67 as derived from standard normal distribution table = 0.74857

Therefore , In stock probability = service level = 0.74857

Therefore , risk of stockout = 1 – 0.74857 = 0.2514

RISK = 0.2514

In stock probability = 1 – stockout risk = 1 – 0.0351 = 0.9649

Corresponding Z value for in stock probability of 0.9649 = NORMSINV ( 0.9649 ) = 1.81

It is given :

Review period = 7 weeks

Lead time = 4 weeks

Therefore , Protection period = Review period + Lead time = 7 + 4 = 11 weeks

Standard deviation of weekly demand = 1.5 boxes

Therefore , Standard deviation of demand during protection period

= Standard deviation of weekly demand x square root ( Protection period )

= 1.5 x square root ( 11 )

= 1.5 x 3.316

= 4.974

Hence , safety stock = Z value x Standard deviation of demand during protection period = 1.81 x 4.974 = 9.002 ( 9 rounded to nearest whole number)

Therefore , Reorder point ( when there is zero stock at hand )

= Weekly demand x Protection period ( weeks ) + Safety stock

= 5 x 11 + 9

= 55 + 9

= 64

Number of boxes to be ordered if there are 21 boxes on hand

= Reorder point – 21

= 64 – 21

= 43

43 BOXES SHOULD BE ORDERED