Part 3 . Questions 8-9 For an inventory item, suppose the demand is 1210/month,

Question

Part 3. Questions 8-9

For an inventory item, suppose the demand is 1210/month, lead time is 2.5 weeks, and safety stock is 9. The item cost is $16, the unit ordering cost is $342/order, and the unit carrying cost is $1.30/item/quarter.

Question 8. How many of the statements are true for the optimal inventory policy that minimizes total cost in this problem?

(A) 0   (B) 1   (C) 2   (D) 3   (E) 4

Statement 1. The total annual ordering cost (TOC) is $3593.21

Statement 2. The total annual carrying cost (TCC) is $3593.21

Statement 3. The total annual cost (TC) is $7233.23

Statement 4. The total carrying cost for safety stock per inventory period is $2.50

Question 9. How many statements are true?

(A) 0   (B) 1   (C) 2   (D) 3   (E) 4

Statement 1. EOQ increases as the unit ordering cost decreases

Statement 2. EOQ increases as the unit carrying cost decreases

Statement 3. EOQ increases as the safety stock decreases

Statement 4. EOQ increases as the lead time decreases

Part 4. Questions 9-10

A small manufacturing plant is considering their aggregate plan for the next fiscal year. They are limited to a maximum number of 32 FTEs each quarter. Their forecasted demand for next year is:

Quarter

1

2

3

4

Demand

12000

14200

15400

13200

They do not consider hiring or firing costs but have the following production parameters.

Labor Standard =

1.3 hours/item

Regular Time Labor Cost =

$22/hour

Beginning Annual Inventory Level =

1000

Ending Annual Inventory Level =

1000

Unit Inventory Carrying Cost =

$4/item/quarter

Any overtime labor in a quarter is time and a half.

(Assume 40 hours/week, 52 weeks/year, and 4 quarters/year.)

Question 9. For next fiscal year, find their annual regular time direct labor cost and overtime direct labor cost for a level capacity aggregate planning strategy.

Question 10. For next fiscal year, find their annual regular time direct labor cost and overtime direct labor cost for a chase demand aggregate planning strategy.

Quarter

1

2

3

4

Demand

12000

14200

15400

13200

Explanation / Answer

Answer of Part 3. Questions 8-9

We have following information

Annual demand D= 1210 unit per month * 12 = 14,520 unit per year

Ordering cost S = $ 342 per order

Holding or carrying cost H = $ 1.3 per unit per quarter or $ 1.3* 4 = $5.2 per unit per annum

Lead time = 2.5 weeks

Safety stock = 9

The cost of the item = $16

For minimum cost, first we have to calculate Optimum Order quantity per order which is EOQ

EOQ = sqrt (2* D*S/H) = sqrt(2*14,520*342/5.2) = 1382 units

Total Annual Inventory cost = total ordering cost + total carrying cost

= (D/Q)* S + (H*Q)/2 = (14,520/1382)*342 + (5.2*1382)/2

=$ 3,593.21 + $3593.21 = $ 7,186.42

Here EOQ = Q

Now Optimal number of order per year = annual demand / EOQ = 14,520/1382 = 10.51 orders

And Optimal number of days between two orders = No. of days per year / number of orders per year

= 365 / 10.51 = 35 days or 35/7 = 5 weeks

The total carrying cost for safety stock per inventory period = (safety stock * carrying cost per annum* inventory period) / 52 weeks

= (9 * $ 5.2 * 5 weeks) / 52 weeks = $4.5

Now based on above calculation analyze Question 8. How many of the statements are true for the optimal inventory policy that minimizes total cost in this problem?

(A) 0   (B) 1   (C) 2   (D) 3   (E) 4

Statement 1. The total annual ordering cost (TOC) is $3593.21 (true)

Statement 2. The total annual carrying cost (TCC) is $3593.21 (true)

Statement 3. The total annual cost (TC) is $7233.23 (false, $ 7,186.42)

Statement 4. The total carrying cost for safety stock per inventory period is $2.50 (false, $ 4.5)

There are 2 true statements, therefore option (C) 2. Is the correct answer.

Question 9. How many statements are true?

(A) 0   (B) 1   (C) 2   (D) 3   (E) 4

Statement 1. EOQ increases as the unit ordering cost decreases (false, EOQ and ordering cost are positively correlated to each other therefore if ordering cost will decrease then EOQ will also decrease, see the EOQ formula above)   

Statement 2. EOQ increases as the unit carrying cost decreases (True, EOQ and carrying cost are inversely related to each other therefore if carrying cost will decrease then EOQ will increase, see the EOQ formula above)   

Statement 3. EOQ increases as the safety stock decreases. (false, as they do not have direct correlation, see the EOQ formula above)

Statement 4. EOQ increases as the lead time decreases. (false, as they do not have direct correlation, see the EOQ formula above)

There is 1 true statements, therefore option (B) 1. Is the correct answer

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