Question

PLEASE HELP ME WITH QUESTIONS 5 - 8 - 10 ! THANK YOU!

Consider a basic economic order quantity (EOQ) model with the
following characteristics:
Item cost:			$15
Item selling price:			$20
Monthly demand:			500 units (constant)
Annual holding cost:			$1.35 per unit
Cost per order:			$18
Order lead time:			5 working days
Firm's work year:			300 days (50 weeks @ 6 days per week)
Safety stock:			15% of monthly demand
For this problem, determine the values of:

Question 1

Q* the optimal order quantity and reorder point.

a. 500 and 175

b. 400 and 100

c. none of the other

d. 400 and 75

e. 400 and 175

Question 2

M, the maximum quantity in inventory.

a. None of the other

b. 500

c. 675

d. 575

e. 475

Question 3

T, the cycle time in working days.

a. 15

b. 25

c. 32

d. None of the other

e. 20

Question 4

Total annual inventory cost.

a. $540.00

b. None of the other

c. $90,641.25

d. $675.00

e. $90,540.00

Question 5

What is the annual ordering cost?

a. $270.00

b. $216.00

c. $18.00

d. None of the other.

e. $1,080.00

Question 6

Suppose the vendor demands purchases in multiples of 500 only.  What is the increase in total annual inventory cost that this causes?

a. $67.50

b. $0.00

c. None of the other

d. $337.50

e. $13.50

Question 7

What is the average lead time demand?

a. 8 units

b. 75 units

c. 16 units

d. 100 units

e. None of the other

Question 8

If the standard deviation of the lead time demand is 10 units, what is the cycle service level with the given safety stock

a. 95%

b. 100%

c. 75%

d. 99%

e. None of the other

Question 9

If the standard deviation of the lead time demand is 10 units, what would be the safety stock if cycle service level is 99%?

a. 175

b. 100

c. None of the other

d. 123

e. 75

Question 10

Assuming cycle service level of over 99% is not advisable, what is the annual cost of carrying un-necessary safety stock?

a. $1,350.00

b. $1,800.00

c. $414.00

d. None of the other

e. $70.20

Answer 1

Annual demand, D = 500*12 = 6000

Holding cost, h = $1.35

Order cost, S =$18

EOQ = sqrt (2DS/h) = sqrt(2*6000*18/1.35) = 400

Daily demand = 6000/300 = 20 units

Reorder point = Average demand during lead time (5 days) + Safety stock = 20*5 +15%*500 = 175

Answer = Option e.

Q5 Annual ordering cost = D/Q * 18 = 6000/400*18 = $270 (Option a)

Q6. Difference in Q/2 quantities = (500/2 - 400/2) = 50

Difference in holding costs = 50 * 1.35 =$67.5

Q7. Average lead time demand = Daily demand * Lead time = 20*5 = 100 units

Q8. Safety Stock = Z* Std deviation * sqrt (lead time)

Z = Safety stock / (Std deviation * Sqrt (5)) = 75 / (10*Sqrt(5)) = 3.5

For Z=3.5, Service level = 100% (Refer standard normal distribution table)

Q9 . For 99% service level, Z = 2.33

Safety Stock = Z* Std deviation * sqrt (lead time) = 2.33*10*sqrt(5) = 52

Answer = 52 (none of the other)

Q10. Since more than 99% service leve is not advisable. We have 52 units of Safety Stock.

Annual safety stock cost = 52 * 1.35 = $70.20