
Concept explainers
a. Given the following
Regular output = $20
Overtime = $30
Subcontract = $25
Average Inventory = $10
Backlog = $18
b. Suppose now that backlogs are not allowed. Modify your plan from part a to accommodate that new condition as economically as possible. The limits on overtime and subcontracting remain the same.
a)

To compute: The total cost of the aggregate plan with backlog
Introduction:The aggregate plan is the output of sales and operations planning. The major concern of aggregate planning is the production time and quantity for the intermediate future. Aggregate planning would encompass a time prospect of approximately 3 to 18 months.
Answer to Problem 4P
Explanation of Solution
Given information:
Regular output is $20, overtime is $30, subcontract is $25, carrying cost is $10, backorder cost is $18, regular production is 550 units per month, maximum overtime unit is of 40 units, and maximum subcontract unit is 10 units.
In addition to this, the following information is given:
Month | 1 | 2 | 3 | 4 | 5 | 6 |
Forecast | 540 | 540 | 570 | 590 | 600 | 580 |
Determine the aggregate plan to compute total cost (without overtime and subcontracting units):
Month | 1 | 2 | 3 | 4 | 5 | 6 | Total | |
Forecast | 540 | 540 | 570 | 590 | 600 | 580 | 3,420 | |
Output | ||||||||
Regular | 550 | 550 | 550 | 550 | 550 | 550 | 3,300 | |
Part-time | ||||||||
Overtime | ||||||||
Subcontract | ||||||||
Difference | 10 | 10 | -20 | -40 | -50 | -30 | -120 | |
Inventory | ||||||||
Beginning | 0 | 10 | 20 | 0 | 0 | 0 | 0 | |
Ending | 10 | 20 | 0 | 0 | 0 | 0 | 0 | |
Average | 5 | 15 | 10 | 0 | 0 | 0 | 0 | |
Backlog | 0 | 0 | 0 | 40 | 90 | 120 | 250 | |
Costs | ||||||||
Regular | 20 | $11,000 | $11,000 | $11,000 | $11,000 | $11,000 | $11,000 | $66,000 |
Part-time | ||||||||
Overtime | 30 | $0 | $0 | $0 | $0 | $0 | $0 | $0 |
Subcontract | 25 | $0 | $0 | $0 | $0 | $0 | $0 | $0 |
Hire/Layoff | ||||||||
Inventory | 10 | $50 | $150 | $100 | $0 | $0 | $0 | $300 |
Backorders | 18 | 0 | 0 | 0 | 720 | 1620 | 2160 | $4,518 |
$11,050 | $11,150 | $11,100 | $11,720 | $12,620 | $13,160 | $70,800 |
Supporting calculation:
Forecast and regular time units were given.
Calculate the difference for the month of 1:
It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 10units.
Calculate the difference for the month of 2:
It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 10 units.
Calculate the difference for the month of 3:
It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is -20 units.
Note: The calculation repeats for all the months.
Backlogs:
As the values of difference between output and forecast are negative, there would be backlogs.
Backlogs for first three months:
It is number of units required in the month. As the differences are non-negative values, the backlog would begin from 4th month. Hence, the backlog for 1st, 2nd, and 3rd month would be0 units.
Backlogs for the month of 4:
It is number of units required in the month. It is calculated by adding the backlog of previous month and the difference between output and forecast of current month. Hence, the backlog is 40 units.
Backlogs for the month of 5:
It is number of units required in the month. It is calculated by adding the backlog of previous month and the difference between output and forecast of current month (without considering the negative sign). Hence, the backlog is 90 units.
Note: The calculation repeats for all the months.
Beginning inventory:
The initial inventory is given as 0. For the remaining months, ending inventory of previous month would be the beginning inventory of present month.
Ending inventory for 1st month:
Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 10 units.
Ending inventory for 2nd month:
Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 20 units.
Ending inventory for 3rd month:
Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 0 units.
Note: The calculation repeats for all the months.
Average inventory for 1st month:
It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 10 units.
Average inventory for 2nd month:
It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 15 units.
Average inventory for 3rd month:
It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 10 units.
Note: The calculation repeats for all the months.
Calculate the regular time cost for the 1st month:
Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.
Calculate the regular time cost for the 2nd month:
Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.
Calculate the regular time cost for the 3rdmonth:
Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.
Note: The calculation repeats for all the months.
Calculate the total regular time cost:
It is calculated by adding the regular time cost of all the months.
Hence, the total regular time cost is $66,000.
Calculate the overtime cost for the 1st month:
Overtime cost per unit is given as $30 and overtime unit is given as 0. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $0.
Calculate the overtime cost for the 2nd month:
Overtime cost per unit is given as $30 and overtime unit is given as 0. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $0.
Calculate the overtime cost for the 3rd month:
Overtime cost per unit is given as $30 and overtime unit is given as 0. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $0.
Note: The calculation repeats for all the months.
Calculate the total overtime cost:
It is calculated by adding the overtime cost of all the months.
Hence, the total overtime cost is $0.
Calculate the subcontract cost for 1st month:
Subcontract cost per unit is given as $25 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.
Calculate the subcontract cost for 2nd month:
Subcontract cost per unit is given as $25 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.
Calculate the subcontract cost for 3rd month:
Subcontract cost per unit is given as $25 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.
Note: The calculation repeats for all the months.
Calculate the total subcontract cost:
It is calculated by adding the subcontract cost of all the months.
Hence, the total subcontract cost is $0.
Calculate the inventory cost for 1st month:
It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $50.
Calculate the inventory cost for 2nd month:
It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $150.
Calculate the inventory cost for 3rd month:
It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $100.
Calculate the total inventory cost:
It is calculated by adding the inventory cost of all the months.
Hence, the total inventory cost is $300.
Calculate the backorder cost for first three months:
As there are no backlogs for first three months, there would not be backorder cost.
Calculate the backorder cost for 4th month:
It is calculated by multiplying the backorder cost and the backlog. Hence, the backorder cost is $720.
Calculate the backorder cost for 5th month:
It is calculated by multiplying the backorder cost and the backlog. Hence, the backorder cost is $1,620.
Note: The calculation repeats for all the months.
Calculate the total backorder cost:
It is calculated by adding the backorder cost of all the months.
Hence, the total backorder cost is $4,500.
Calculate the total cost of the plan:
It is calculated by adding the total regular time cost, overtime cost, subcontract cost, and inventory cost.
Hence, the total cost of the plan is $70,800.
b)

To compute: The total cost of the aggregate plan if the backlog is not allowed
Introduction:The aggregate plan is the output of sales and operations planning. The major concern of aggregate planning is the production time and quantity for the intermediate future. Aggregate planning would encompass a time prospect of approximately 3 to 18 months.
Answer to Problem 4P
Explanation of Solution
Given information:
Regular output is $20, overtime is $30, subcontract is $25, carrying cost is $10, backorder cost is $18, regular production is 550 units per month, maximum overtime unit is of 40 units, and maximum subcontract unit is 10 units.
In addition to this, the following information is given:
Month | 1 | 2 | 3 | 4 | 5 | 6 |
Forecast | 540 | 540 | 570 | 590 | 600 | 580 |
Determine the total cost of the plan (considering overtime and subcontract):
Month | 1 | 2 | 3 | 4 | 5 | 6 | Total | |
Forecast | 540 | 540 | 570 | 590 | 600 | 580 | 3,420 | |
Output | ||||||||
Regular | 550 | 550 | 550 | 550 | 550 | 550 | 3,300 | |
Part-time | ||||||||
Overtime | 30 | 40 | 20 | 90 | ||||
Subcontract | 10 | 10 | 10 | 30 | ||||
Difference | 10 | 10 | -20 | 0 | 0 | 0 | 0 | |
Inventory | ||||||||
Beginning | 0 | 10 | 20 | 0 | 0 | 0 | 30 | |
Ending | 10 | 20 | 0 | 0 | 0 | 0 | 30 | |
Average | 5 | 15 | 10 | 0 | 0 | 0 | 30 | |
Backlog | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Costs | ||||||||
Regular | 20 | $11,000 | $11,000 | $11,000 | $11,000 | $11,000 | $11,000 | $66,000 |
Part-time | ||||||||
Overtime | 30 | $0 | $0 | $0 | $900 | $1,200 | $600 | $2,700 |
Subcontract | 25 | $0 | $0 | $0 | $250 | $250 | $250 | $750 |
Hire/Layoff | ||||||||
Inventory | 10 | $50 | $150 | $100 | $0 | $0 | $0 | $300 |
Backorders | 18 | 0 | 0 | 0 | 0 | 0 | 0 | $0 |
$11,050 | $11,150 | $11,100 | $12,150 | $12,450 | $11,850 | $69,750 |
Supporting calculation:
Forecast and regular time units are given. It is given maximum units of overtime is 20 units and maximum subcontract unit is 10 units. The added units should make the difference from a negative value to 0.
Calculate the difference for the month of 1:
It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 10 units.
Calculate the difference for the month of 2:
It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 10 units.
Calculate the difference for the month of 3:
It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is -20 units.
Note: The calculation repeats for all the months.
Beginning inventory:
The initial inventory is given as 0. For the remaining months, ending inventory of previous month would be the beginning inventory of present month.
Ending inventory for 1st month:
Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 10 units.
Ending inventory for 2nd month:
Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 20 units.
Ending inventory for 3rd month:
Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 0 units.
Note: The calculation repeats for all the months.
Average inventory for 1st month:
It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 10 units.
Average inventory for 2nd month:
It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 15 units.
Average inventory for 3rd month:
It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 10 units.
Note: The calculation repeats for all the months.
Calculate the regular time cost for the 1st month:
Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.
Calculate the regular time cost for the 2nd month:
Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.
Calculate the regular time cost for the 3rdmonth:
Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.
Note: The calculation repeats for all the months.
Calculate the total regular time cost:
It is calculated by adding the regular time cost of all the months.
Hence, the total regular time cost is $66,000.
Calculate the overtime cost for 1st month:
Overtime cost per unit is given as $30 and overtime unit is given as 0. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $0.
Calculate the overtime cost for the 2nd month:
Overtime cost per unit is given as $30 and overtime unit is given as 0. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $0.
Calculate the overtime cost for the 3rd month:
Overtime cost per unit is given as $30 and overtime unit is given as 0. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $0.
Calculate the overtime cost for the 4th month:
Overtime cost per unit is given as $30 and overtime unit is given as 30. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $900.
Note: The calculation repeats for all the months.
Calculate the total overtime cost:
It is calculated by adding the overtime cost of all the months.
Hence, the total overtime cost is $2,700.
Calculate the subcontract cost for 1st month:
Subcontract cost per unit is given as $25 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.
Calculate the subcontract cost for 2nd month:
Subcontract cost per unit is given as $25 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.
Calculate the subcontract cost for 3rd month:
Subcontract cost per unit is given as $25 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.
Calculate the subcontract cost for 3rd month:
Subcontract cost per unit is given as $25 and subcontract unit is given as 10. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $250.
Note: The calculation repeats for all the months.
Calculate the total subcontract cost:
It is calculated by adding the subcontract cost of all the months.
Hence, the total subcontract cost is $0.
Calculate the inventory cost for 1st month:
It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $50.
Calculate the inventory cost for 2nd month:
It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $150.
Calculate the inventory cost for 3rd month:
It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $100.
Calculate the total inventory cost:
It is calculated by adding the inventory cost of all the months.
Hence, the total inventory cost is $300.
Calculate the total cost of the plan:
It is calculated by adding the total regular time cost, overtime cost, subcontract cost, and inventory cost.
Hence, the total cost of the plan is $69,750.
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Chapter 11 Solutions
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