Chapter 11 – Aggregate Planning and Master Scheduling
11–31
Education.
Period
1
2
3
4
5
6
Total
Forecast
200
200
300
400
500
200
1,800
Output
Regular
280
280
280
280
280
280
1,680
Part Time
0
Overtime
0
Subcontract
20
50
50
120
Output – Forecast
80
80
0
–70
–170
80
0
Inventory
Beginning
80
160
160
90
0
Ending
80
160
160
90
0
0
Average
40
120
160
125
45
0
490
Backlog
0
0
0
0
80
0
80
Costs:
Regular
@
2
$560
$560
$560
$560
$560
$560
$3,360
Part Time
@
$0
$0
$0
$0
$0
$0
$0
Overtime
@
$0
$0
$0
$0
$0
$0
$0
Subcontract
@
6
$0
$0
$120
$300
$300
$0
$720
Hire/Layoff
$0
Inventory
@
1
$40
$120
$160
$125
$45
$0
$490
Back orders
@
5
$0
$0
$0
$0
$400
$0
$400
Total
$600
$680
$840
$985
$1,305
$560
$4,970
Conclusion: Total cost of this plan is $4,970. Total cost of the plan from Example 2 was $4,640.
The plan from Example 2 is $330 lower.
Chapter 11 – Aggregate Planning and Master Scheduling
14. Given:
Plan from Example 3:
Unused cap.
Period
1
2
3
(dummy)
Total
Beg. Inv.
0
1
2
0
100
100
Reg.
60
61
62
0
1
450
50
500
Over.
80
81
82
0
50
50
Sub.
90
91
92
0
30
90
120
Reg.
63
60
61
0
2
500
500
Over.
83
80
81
0
50
50
Sub.
93
90
91
0
20
100
120
Reg.
66
63
60
0
3
500
500
Over.
86
83
80
0
50
50
Sub.
96
93
90
0
100
100
Demand
550
700
750
90
2,090
Verify the transportation solution shown above:
a. Verify that total demand equals total supply:
b. Verify that all demand is met:
Period 1 Demand = 550. This demand will be met with 100 units of beginning inventory +
450 units of regular time production in Period 1.
100 + 450 = 550.
Period 2 Demand = 700. This demand will be met by 50 units of regular time production in
Period 1 + 50 units of overtime production in Period 1 + 30 units of subcontracting in Period
Chapter 11 – Aggregate Planning and Master Scheduling
c. Verify that all capacity is used:
Beginning inventory of 100 units will be used to meet demand in Period 1.
Regular time capacity of 500 units in Period 1 will be used to meet demand of 450 units in
Period 1 + demand of 50 units in Period 2.
Period 2.
Overtime capacity of 50 units in Period 2 will be used to meet demand of 50 units in Period
2.
Subcontracting capacity of 120 units in Period 2 will be used to meet demand of 20 units in
Period 2 + demand of 100 units in Period 3.
3.
Subcontracting capacity of 100 units in Period 3 will be used to meet demand of 100 units in
Period 3.
11–34
Education.
15. Given:
Refer to Example 3. Inventory carrying costs are now $2 per unit per month. All other costs
remain the same as shown below:
Regular time: $60 per unit
Overtime: $80 per unit
Subcontract: $90 per unit
Step 1: Compare the costs of each option:
Beginning inventory will be used first to meet demand in Month 1.
After that, the least cost option to meet demand in the current month is regular time, followed by
overtime, and then subcontracting.
Using regular time up to two months early costs $60 + (2 * $2) = $64. That cost is less than using
overtime ($80) or subcontracting ($90) in the current month.
Step 2: Begin creating the plan to meet demand each period and to minimize total cost. Note: We
can see that Month 3 has the highest demand and will require all of the regular time and overtime
capacity available in Month 3. Below are two possible solutions:
Chapter 11 – Aggregate Planning and Master Scheduling
11–35
Education.
Solution 1:
Unused cap.
Period
1
2
3
(dummy)
Total
Beg. Inv.
0
2
4
0
100
100
Reg.
60
62
64
0
1
450
50
500
Over.
80
82
84
0
50
50
Sub.
90
92
94
0
30
90
120
Reg.
63
60
62
0
2
500
500
Over.
83
80
82
0
50
50
Sub.
93
90
92
0
50
70
120
Reg.
66
63
60
0
3
500
500
Over.
86
83
80
0
50
50
Sub.
96
93
90
0
100
100
Demand
550
700
750
90
2,090
Solution 2:
Unused cap.
Period
1
2
3
(dummy)
Total
Beg. Inv.
0
2
4
0
100
100
Reg.
60
62
64
0
1
400
100
500
Over.
80
82
84
0
50
50
Sub.
90
92
94
0
30
90
120
Reg.
63
60
62
0
2
500
500
Over.
83
80
82
0
50
50
Sub.
93
90
92
0
120
120
Reg.
66
63
60
0
3
500
500
Over.
86
83
80
0
50
50
Sub.
96
93
90
0
100
100
Demand
550
700
750
90
2,090
Conclusion: Total cost of both plans = $124,960.
11–36
Education.
16. Given:
Refer to Example 3. All costs remain the same as shown below:
Regular time: $60 per unit
Overtime: $80 per unit
Subcontract: $90 per unit
Inventory carrying cost: $1 per unit per month
Back-order cost: $3 per unit per month
Demand:
Period
1
2
3
Demand
550
700
750
Regular capacity: 500 units per month except for Month 3 (440 units). Note how this reduces
the demand in the Dummy column to 30.
Beginning inventory: 100 units
Step 1: Compare the costs of each option:
Beginning inventory will be used first to meet demand in Month 1.
After that, the least cost option to meet demand in the current month is regular time, followed by
overtime, and then subcontracting.
Using regular time up to two months early costs $60 + (2 * $1) = $62. That cost is less than using
overtime ($80) or subcontracting ($90) in the current month.
Step 2: Begin creating the plan to meet demand each period and to minimize total cost. Note: We
can see that Month 3 has the highest demand and will require all of the regular time and overtime
capacity available in Month 3.
Below are two possible solutions:
Chapter 11 – Aggregate Planning and Master Scheduling
11–37
Education.
Solution 1:
Unused cap.
Period
1
2
3
(dummy)
Total
Beg. Inv.
0
1
2
0
100
100
Reg.
60
61
62
0
1
450
50
500
Over.
80
81
82
0
50
50
Sub.
90
91
92
0
90
30
120
Reg.
63
60
61
0
2
500
500
Over.
83
80
81
0
10
40
50
Sub.
93
90
91
0
120
120
Reg.
66
63
60
0
3
440
440
Over.
86
83
80
0
50
50
Sub.
96
93
90
0
100
100
Demand
550
700
750
30
2,090
Solution 2:
Unused cap.
Period
1
2
3
(dummy)
Total
Beg. Inv.
0
1
2
0
100
100
Reg.
60
61
62
0
1
400
100
500
Over.
80
81
82
0
50
50
Sub.
90
91
92
0
30
60
30
120
Reg.
63
60
61
0
2
500
500
Over.
83
80
81
0
50
50
Sub.
93
90
91
0
120
120
Reg.
66
63
60
0
3
440
440
Over.
86
83
80
0
50
50
Sub.
96
93
90
0
100
100
Demand
550
700
750
30
2,090
Conclusion: Total cost for both solutions = $126,650. Total cost for Example 3 = $124,730. The
original solution for Example 3 is $1,920 lower ($126,650 – $124,730).
11–38
Education.
17. Given:
Use the same information as in Problem 16, except now the inventory carrying cost = $2 per unit
per period.
Regular time: $60 per unit
Overtime: $80 per unit
Subcontract: $90 per unit
Inventory carrying cost: $2 per unit per month
Back-order cost: $3 per unit per month
Demand:
Period
1
2
3
Demand
550
700
750
overtime ($80) or subcontracting ($90) in the current month.
Given an option of producing a unit one month early or one month late, we prefer to produce it
one month early because the carrying cost is $2 per unit per month while the back-order cost is $3
per unit per month.
Step 2: Begin creating the plan to meet demand each period and to minimize total cost. Note: We
can see that Month 3 has the highest demand and will require all of the regular time and overtime
capacity available in Month 3.
Below are two possible solutions:
Chapter 11 – Aggregate Planning and Master Scheduling
11–39
Education.
Solution 1:
Unused cap.
Period
1
2
3
(dummy)
Total
Beg. Inv.
0
2
4
0
100
100
Reg.
60
62
64
0
1
450
50
500
Over.
80
82
84
0
50
50
Sub.
90
92
94
0
90
30
120
Reg.
63
60
62
0
2
500
500
Over.
83
80
82
0
10
40
50
Sub.
93
90
92
0
120
120
Reg.
66
63
60
0
3
440
440
Over.
86
83
80
0
50
50
Sub.
96
93
90
0
100
100
Demand
550
700
750
30
2,090
Solution 2:
Unused cap.
Period
1
2
3
(dummy)
Total
Beg. Inv.
0
2
4
0
100
100
Reg.
60
62
64
0
1
400
100
500
Over.
80
82
84
0
50
50
Sub.
90
92
94
0
30
60
30
120
Reg.
63
60
62
0
2
500
500
Over.
83
80
82
0
50
50
Sub.
93
90
92
0
120
120
Reg.
66
63
60
0
3
440
440
Over.
86
83
80
0
50
50
Sub.
96
93
90
0
100
100
Demand
550
700
750
30
2,090
Conclusion: Total cost for both solutions = $127,000.
11–40
Education.
18. a. Initially, David should develop one aggregate plan for the next six months to determine his
output rate, employment levels and changes, inventory levels and changes, back orders, and
subcontracting. This will help him to achieve a plan that will utilize resources more
effectively and efficiently to satisfy expected demand. For the first two months though, David
will need to disaggregate his plan into a short-run master schedule for each size wheel.
Adjustments will be made in the planning process as needs arise over time and the planning
horizon gets shorter.
b. and c.
Given:
Demand for the next six months:
Month
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
20-inch
1,000
900
600
700
1,100
1,100
24-inch
500
500
300
500
400
600
Total
1,500
1,400
900
1,200
1,500
1,700
Costs:
Regular: $5.00/unit
Overtime: $7.50/unit
Step 1: Determine the total demand for wheels:
(20-inch total + 24-inch total) + desired ending inventory = 8,200 + 300 = 8,500 units.
Option 1: Keep the same number of employees (28), but produce 100 units using overtime.
Under this plan, the amount produced using overtime should be the same each month except for