Chapter 14, Problem 27P

Grace Greenberg, production planner for Science and Technology Labs, in New Jersey, has the master production plan shown below:

Lead time = 1 period; setup cost = $200; holding cost = $10 per week; stockout cost = $10 per week. Develop an ordering plan and costs for Grace, using these techniques:

a) Lot-for-lot.

b) EOQ.

c) POQ.

d) Which plan has the lowest cost?

Summary Introduction

To determine: The ordering plan and cost for Lot for lot.

Introduction:

Lot for Lot:

The lot for lot method of requirements plan is the process where the planned order release will be equal to the net requirement of the period.

Net requirements plan:

The net requirements plan is the plan which is established on the gross requirements plan formed by deducting the stock on and the scheduled receipts. If the total requirement is below the safety stock levels, a planned order is made based on the given lot sizing technique.

Answer to Problem 27P

The cost for Lot for lot is $1,200.

Explanation of Solution

Given information:

	Period (weeks)
Item A	1	2	3	4	5	6	7	8	9	10	11	12	Total
Gross requirements		35		40		10			25	10		45	165

Holding cost = $10 / week

Setup cost = $200

Lead time = 1 period

Stockout cost = $10 / week

Lot for lot:

Net requirements plan:

	Period (weeks)
Item A	1	2	3	4	5	6	7	8	9	10	11	12	Total
Gross requirements		35		40		10			25	10		45	165
Scheduled receipt
On hand (0)		0		0		0			0	0		0
Ending inventory		0		0		0			0	0		0	0
Net requirement		35		40		10			25	10		45
Planned order receipt		35		40		10			25	10		45
Planned order release	35		40		10			25	10		45

Week 2:

The gross requirement is 35 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 35. The lead time is 1 week. Therefore, the planned order release will be 35 in week 1 which will be the planned order receipt in week 2.

Week 4:

The gross requirement is 40 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 40. The lead time is 1 week. Therefore, the planned order release will be 40 in week 3 which will be the planned order receipt in week 4.

Week 6:

The gross requirement is 10 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 10. The lead time is 1 week. Therefore, the planned order release will be 10 in week 5 which will be the planned order receipt in week 6.

Week 9:

The gross requirement is 25 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 25. The lead time is 1 week. Therefore, the planned order release will be 25 in week 8 which will be the planned order receipt in week 9. There is no ending inventory.

Week 10:

The gross requirement is 10 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 10. The lead time is 1 week. Therefore, the planned order release will be 10 in week 9 which will be the planned order receipt in week 10.

Week 12:

The gross requirement is 45 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 45. The lead time is 1 week. Therefore, the planned order release will be 45 in week 11 which will be the planned order receipt in week 12. There is no ending inventory.

Number of planned orders = 6

Inventory holding units= 0

Formula to calculate total cost of the plan:

$\text{Total cost}=\left(\text{Number of planned orders}\times \text{Setup cost}\right)+\left(\text{Inventory holding period}\times \text{Holding cost}\right)$

Calculation of total cost:

The total cost is calculated by adding the product of number of planned order and setup cost with the product of inventory holding period and holding cost.

$\begin{array}{c}\text{Total cost}=\left(6\times \$200\right)+\left(0\times \$10\right)\\ =\$1,200+\$0\\ =\$1,200\end{array}$

Hence, the cost for Lot for lot is $1,200.

Summary Introduction

To determine: The ordering plan and cost for EOQ.

Introduction:

Economic order quantity (EOQ):

The economic order quantity is the number of units a firm must add to their stock while making each order. The notion of EOQ is to reduce the total cost of inventory of the firm.

Net requirements plan:

The net requirements plan is the plan which is established on the gross requirements plan formed by deducting the stock on and the scheduled receipts. If the total requirement is below the safety stock levels, a planned order is made based on the given lot sizing technique.

Answer to Problem 27P

The cost for EOQ is $2,370.

Explanation of Solution

Given information:

	Period (weeks)
Item A	1	2	3	4	5	6	7	8	9	10	11	12	Total
Gross requirements		35		40		10			25	10		45	165

Holding cost = $10 / week

Setup cost = $200

Lead time = 1 period

Stockout cost = $10 / week

Formula to calculate EOQ:

$\text{EOQ}=\sqrt{\frac{2\times \text{Total gross requirements}\times \text{Setup cost}}{\text{Holding cost}\times \text{Number of periods}}}$

Calculation of EOQ:

$\begin{array}{c}\text{EOQ}=\sqrt{\frac{2\times 165\times 200}{10\times 12}}\\ =\sqrt{\frac{66000}{120}}\\ =\sqrt{550}\\ =23.45\text{ units}\end{array}$

The EOQ can be rounded off to 23 units.

Net requirements plan:

	Period (weeks)
Item A	1	2	3	4	5	6	7	8	9	10	11	12	Total
Gross requirements		35		40		10			25	10		45	165
Scheduled receipt
On hand (0)		0	11	11	17	17	7	7	7	5	18	18
Ending inventory		11	11	17	17	7	7	7	5	18	18	19	137
Net requirement		35		29		0			18	5		27
Planned order receipt		46		46		0			23	23		46
Planned order release	46		46					23	23		46

Week 2:

The gross requirement is 35 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 35. The lead time is 1 week. Therefore, the planned order release will be 46 (1 Lot = 23) in week 1 which will be the planned order receipt in week 2. The ending inventory is 11 which will be available at week 3.

Week 3:

The on hand inventory is 11. Since there is no requirement, the ending inventory at week 3 is 11 which will be available at week 4.

Week 4:

The gross requirement is 40 (1 assembly). The on hand inventory is 11. Hence, the net requirement is 29. The lead time is 1 week. Therefore, the planned order release will be 46 (1 Lot = 23) in week 3 which will be the planned order receipt in week 4. The ending inventory is 17 which will be available at week 5.

Week 5:

The on hand inventory is 17. Since there is no requirement, the ending inventory at week 5 is 17 which will be available at week 6.

Week 6:

The gross requirement is 10 (1 assembly). The on hand inventory is 17. Hence, the net requirement is 0. Therefore there will be no planned order assembly. The ending inventory is 7 which will be available at week 7.

Week 7:

The on hand inventory is 7. Since there is no requirement, the ending inventory at week 7 is 7 which will be available at week 8.

Week 8:

The on hand inventory is 7. Since there is no requirement, the ending inventory at week 8 is 7 which will be available at week 9.

Week 9:

The gross requirement is 25 (1 assembly). The on hand inventory is 7. Hence, the net requirement is 18. The lead time is 1 week. Therefore, the planned order release will be 23 (1 Lot = 23) in week 8 which will be the planned order receipt in week 9. The ending inventory is 5 which will be available at week 10.

Week 10:

The gross requirement is 10 (1 assembly). The on hand inventory is 5. Hence, the net requirement is 5. The lead time is 1 week. Therefore, the planned order release will be 23 (1 Lot = 23) in week 9 which will be the planned order receipt in week 10. The ending inventory is 18 which will be available at week 11.

Week 11:

The on hand inventory is 18. Since there is no requirement, the ending inventory at week 11 is 18 which will be available at week 12.

Week 12:

The gross requirement is 45 (1 assembly). The on hand inventory is 18. Hence, the net requirement is 27. The lead time is 1 week. Therefore, the planned order release will be 46 (1 Lot = 23) in week 11 which will be the planned order receipt in week 12. The ending inventory is 19 which will be available in the next week.

Number of planned order releases = 5

Total Ending inventory = 137

Calculation of total setup cost:

$\begin{array}{c}\text{Total setup cost}=\text{Number of planned order releases}\times \text{Setup cost}\\ =5\times \$200\\ =\$1,000\end{array}$

Calculation of total holding cost:

$\begin{array}{c}\text{Total holding cost}=\text{Total ending inventory}\times \text{Holding cost}\\ =137\times \$10\\ =\$1,370\end{array}$

Calculation of total cost:

The total cost is calculated by summing the total setup cost and total holding cost.

$\begin{array}{c}\text{Total cost}=\$1,000+\$1370\\ =\$2,370\end{array}$

Hence, the total cost for EOQ is $2,370

Summary Introduction

To determine: The ordering plan and cost for POQ.

Introduction:

Periodic order quantity (POQ):

The POQ is the standard quantity of units that will be ordered over a fixed period of time. This method is followed when the usage of raw materials is consistent and is predictable.

Net requirements plan:

The net requirements plan is the plan which is established on the gross requirements plan formed by deducting the stock on and the scheduled receipts. If the total requirement is below the safety stock levels, a planned order is made based on the given lot sizing technique.

Answer to Problem 27P

The cost for POQ is $1,100.

Explanation of Solution

Given information:

	Period (weeks)
Item A	1	2	3	4	5	6	7	8	9	10	11	12	Total
Gross requirements		35		40		10			25	10		45	165

Holding cost = $10 / week

Setup cost = $200

Lead time = 1 period

Stockout cost = $10 / week

Net requirements plan:

The planned ordered release in the POQ plan is planned in a way such that the demand for next two periods is satisfied.

Net requirements plan:

	Period (weeks)
Item A	1	2	3	4	5	6	7	8	9	10	11	12	Total
Gross requirements		35		40		10			25	10		45	165
Scheduled receipt
On hand (0)		0	0	0	0	0	0	0	0	10	0	0
Ending inventory		0	0	0	0	0	0	0	10	0	0	0	10
Net requirement		35		40		10			25			45
Planned order receipt		35		40		10			35			45
Planned order release	35		40		10			35			45

Week 2:

The gross requirement is 35 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 35. The lead time is 1 week. Therefore, the planned order release will be 35 in week 1 which will be the planned order receipt in week 2. There is no ending inventory.

Week 4:

The gross requirement is 40 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 40. The lead time is 1 week. Therefore, the planned order release will be 40 in week 3 which will be the planned order receipt in week 4. There is no ending inventory.

Week 6:

The gross requirement is 10 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 10. Therefore, the planned order release will be 10 in week 5 which will be the planned order receipt in week 6. There is no ending inventory.

Week 9:

The gross requirement is 25 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 25. The lead time is 1 week. Therefore, the planned order release will be 35 in week 8 which will be the planned order receipt in week 9. The ending inventory is 10 which will be available at week 10.

Week 10:

The gross requirement is 10 (1 assembly). The on hand inventory is 10. Hence, the net requirement is 0. Therefore there will be no planned order inventory.

Week 12:

The gross requirement is 45 (1 assembly). The on hand inventory is 0. Hence, the net requirement is 45. The lead time is 1 week. Therefore, the planned order release will be 45 in week 11 which will be the planned order receipt in week 12. There is no ending inventory.

Number of planned orders = 5

Inventory holding units= 10

Formula to calculate total cost of the plan:

$\text{Total cost}=\left(\text{Number of planned orders}\times \text{Setup cost}\right)+\left(\text{Inventory holding period}\times \text{Holding cost}\right)$

Calculation of total cost:

The total cost is calculated by adding the product of number of planned order and setup cost with the product of inventory holding period and holding cost.

$\begin{array}{c}\text{Total cost}=\left(5\times \$200\right)+\left(10\times \$10\right)\\ =\$1,000+\$100\\ =\$1,100\end{array}$

Hence, the cost for POQ is $1,100.

Summary Introduction

To determine: The plan which has the lowest cost.

Answer to Problem 27P

The plan which has the lowest cost is POQ.

Explanation of Solution

The total cost for Lot for lot is $1,200. The total cost for EOQ is $2,370. The total cost for POQ is $1,100. The total cost is less for POQ when compared with EOQ and Lot for lot. ($1,100 < $2,370, $1,200)

Hence, the plan which has the lowest cost is POQ.