Question

Use the following information to answer questions 17-20.

A large hospital uses a certain intravenous solution that it maintains in inventory. Assume the hospital uses reorder point method to control the inventory of this item. Pertinent data about this item are as follows:

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Forecast of demand^a = 1,000 units per week

Forecast error^a, std. dev. =100 units per week

Lead time = 4 weeks

Carrying cost = 25 % per year

Purchase price, delivered = $52 per unit

Replenishment order cost = $20 per order

Stockout cost = $10 per unit

In-stock Probability during the lead time =90%

^a Normally distributed

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Due to possible rounding effect, please pick the closest number in the following options.

Question 17 (1 point)

What is the reorder point?

Question 18 (1 point)

If the hospital orders 400 units each time, what’s the expected number of units out of stock annually?

Question 18 options:

	1248
	2912
	500
	1000

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Use the following information to answer questions 17-20.

A large hospital uses a certain intravenous solution that it maintains in inventory. Assume the hospital uses reorder point method to control the inventory of this item. Pertinent data about this item are as follows:

------------------------------------------------------------

Forecast of demand^a = 1,000 units per week

Forecast error^a, std. dev. =100 units per week

Lead time = 4 weeks

Carrying cost = 25 % per year

Purchase price, delivered = $52 per unit

Replenishment order cost = $20 per order

Stockout cost = $10 per unit

In-stock Probability during the lead time =90%

^a Normally distributed

------------------------------------------------------------

Due to possible rounding effect, please pick the closest number in the following options.

Question 19 (1 point)

If the hospital orders 400 units each time, what’s the total annual costs (holding cost + ordering cost + stock-out cost) excluding purchasing costs?

Question 19 options:

	10000
	21008
	31008
	42016

Save

Use the following information to answer questions 17-20.

A large hospital uses a certain intravenous solution that it maintains in inventory. Assume the hospital uses reorder point method to control the inventory of this item. Pertinent data about this item are as follows:

------------------------------------------------------------

Forecast of demand^a = 1,000 units per week

Forecast error^a, std. dev. =100 units per week

Lead time = 4 weeks

Carrying cost = 25 % per year

Purchase price, delivered = $52 per unit

Replenishment order cost = $20 per order

Stockout cost = $10 per unit

In-stock Probability during the lead time =90%

^a Normally distributed

------------------------------------------------------------

Due to possible rounding effect, please pick the closest number in the following options.

Question 20 (1 point)

If the lead time is normally distributed with a mean of 4 weeks and a standard deviation of 0.5 weeks, what’s the reorder point?

Question 20 options:

	4689
	4129
	5188
	6000

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Answer 1

Reorder Point = Mean Demand*Lead Time + z*SD of Demand*(Lead Time)^(1/2)

ROP = 1000*4 + 1.281552*100*2

ROP = 4256.31

ROP = 4256

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Normal loss function, L(Z) corresponding to 90% service level = 0.048

Expected shortage per cycle (ESC) = L(Z) * σ * (L)^(1/2) = 0.0473*100*(4)^(1/2) = 9.6

Annual shortage = ESC x no. of cycles annually = 9.6 x (52000/400) = 1248

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Shortage cost = Annual shortage x shortage cost per unit = 1248*10 = 12480

Order quantity, Q = 400
Holding cost per unit per annum, H = 52 * 25% = 13
Annual demand, D = 1000 x 52 = 52,000
Ordering cost, S = 20

Cycle stock holding cost = Q * H/ 2 = 400*13/2 = 2600

Ordering cost = (D/Q) * S = (52000 / 400) * 20 = 2600

Safety stock cost = Safey stock * H = 1.28*100*SQRT(4) * 13 = 3328

Total cost = $2,600 + $2,600 + $12,480 + $3,328 = $21,008

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L = 4
σ_L = 0.5

The following formula for ROP will apply.

ROP = d * L + Z * √(σ².L + d².σ_L²)= 1000*4 + 1.28*SQRT((100^2)*4 + (1000*0.5)^2) =4,689