Concept explainers
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?
a)
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:
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.
Hence, the cost for Lot for lot is $1,200.
b)
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:
Calculation of EOQ:
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:
Calculation of total holding cost:
Calculation of total cost:
The total cost is calculated by summing the total setup cost and total holding cost.
Hence, the total cost for EOQ is $2,370
c)
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:
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.
Hence, the cost for POQ is $1,100.
d)
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.
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Chapter 14 Solutions
EBK PRINCIPLES OF OPERATIONS MANAGEMENT
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