Chapter 11 - Aggregate Planning and Master Scheduling
CHAPTER 11
AGGREGATE PLANNING AND MASTER SCHEDULING
Solutions
1.
Given:
Regular cost per unit = $40. Overtime cost per unit = $50. Subcontract cost per unit = $10.
Carrying cost per unit per month = $10 and is assessed on average inventory.
a. We have the following aggregate plan. Calculate the cost of the plan:
Period
Forecast
Output
Regular
Overtime
Subcontract
Jan
300
Feb Mar Apr May Jun
320 320 340 320 320
300
20
0
300
20
0
300
20
0
300
20
0
300
20
0
300
20
0
Period
Forecast
Output
Jan
300
Feb
320
Mar
320
Apr
340
May
320
Jun
320
Total
1,920
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
300
300
300
300
300
300
20
0
20
20
0
0
20
0
0
20
0
-20
20
0
0
20
0
0
1,800
0
120
0
0
0
20
10
0
20
20
20
0
20
20
20
0
20
0
10
0
0
0
0
0
0
0
0
0
60
0
$12,000
$0
$1,000
$0
$12,000
$0
$1,000
$0
$12,000
$0
$1,000
$0
$12,000
$0
$1,000
$0
$12,000
$0
$1,000
$0
$12,000
$0
$1,000
$0
$100
$0
$13,100
$200
$0
$13,200
$200
$0
$13,200
$100
$0
$13,100
$0
$0
$13,000
$0
$0
$13,000
@
@
@
@
40
@
@
10
50
60
$72,000
$0
$6,000
$0
$0
$600
$0
$78,600
Conclusion: Total cost = $78,600.
11-1
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
b. We have the following aggregate plan. Calculate the cost of the plan:
Period
Forecast
Output
Regular
Overtime
Subcontract
Jul Aug Sep
320 340 360
Oct Nov Dec
380 400 400
300
20
20
300
20
40
300
20
30
300
20
40
300
30
60
300
30
70
Period
Forecast
Output
Jul
320
Aug
340
Sep
360
Oct
380
Nov
400
Dec
400
Total
2,200
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
300
300
300
300
300
300
20
20
20
20
30
10
20
40
0
20
40
-20
30
60
-10
30
70
0
1,800
0
140
260
0
0
20
10
0
20
30
25
0
30
30
30
0
30
10
20
0
10
0
5
0
0
0
0
0
90
0
$12,000
$0
$1,000
$1,200
$12,000
$0
$1,000
$1,800
$12,000
$0
$1,000
$2,400
$12,000
$0
$1,000
$2,400
$12,000
$0
$1,500
$3,600
$12,000
$0
$1,500
$4,200
$100
$0
$14,300
$250
$0
$15,050
$300
$0
$15,700
$200
$0
$15,600
$50
$0
$17,150
$0
$0
$17,700
@
@
@
@
40
@
@
10
50
60
$72,000
$0
$7,000
$15,600
$0
$900
$0
$95,500
Conclusion: Total cost = $95,500.
11-2
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
c. Refer back to part b. The manager is considering adding some temporary workers for the
second half of the year. This would increase regular output to a steady 350 units per month,
not use any overtime, and use subcontracting as needed to make up any shortages.
Initial Plan: No Subcontracting
Note: Observe the months with backlog. Those are the months in which we must consider
subcontracting. We can determine the total amount that we will need to subcontract as follows:
Total Forecast – Beginning Inventory – Total Regular Output
Period
Forecast
Output
Jul
320
Aug
340
Sep
360
Oct
380
Nov
400
Dec
400
Total
2,200
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
350
350
350
350
350
350
30
10
-10
-30
-50
-50
2,100
0
0
0
-100
0
30
15
0
30
40
35
0
40
30
35
0
30
0
15
0
0
0
0
50
0
0
0
100
100
150
There are backlogs in November and December. How many units will it take to eliminate these
backlogs?
Total Forecast – Beginning Inventory – Total Regular Output = 2,200 – 0 – 2,100 = 100 units of
backlogs to cover with subcontracting.
We will add subcontracting in those months with backlogs to eliminate the backlogs.
11-3
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Final Plan: Using Subcontracting to Eliminate Backlogs
Period
Forecast
Output
Jul
320
Aug
340
Sep
360
Oct
380
Nov
400
Dec
400
Total
2,200
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
350
350
350
350
350
350
30
10
-10
-30
50
0
50
0
2,100
0
0
100
0
0
30
15
0
30
40
35
0
40
30
35
0
30
0
15
0
0
0
0
0
0
0
0
0
100
0
$14,000
$0
$0
$0
$14,000
$0
$0
$0
$14,000
$0
$0
$0
$14,000
$0
$0
$0
$14,000
$0
$0
$3,000
$14,000
$0
$0
$3,000
$150
$0
$14,150
$350
$0
$14,350
$350
$0
$14,350
$150
$0
$14,150
$0
$0
$17,000
$0
$0
$17,000
@
@
@
@
40
@
@
10
50
60
$84,000
$0
$0
$6,000
$0
$1,000
$0
$91,000
Conclusion: Total cost = $91,000.
11-4
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
2.
Given:
A manager would like to know the total cost of a chase strategy that matches the forecast below
using a steady regular production rate of 200 units per month, a maximum of 20 units per month
of overtime, and subcontracting as needed to make up any shortages. Regular cost per unit =
$35. Overtime cost per unit = $70. Subcontracting cost per unit = $80. We are using a
chase strategy, i.e., we will use overtime or subcontracting in a given month to make up
any shortages in that month.
Month
Forecast
1
230
2
200
3
240
4
240
5
250
6
240
Initial Plan: No Overtime & No Subcontracting
Note: Observe the months with backlog. Those are the months in which we must consider
overtime and subcontracting. Our first option will be overtime ($70 per unit) because it cost less
than subcontracting does ($80 per unit). We can determine the total amount that we will need to
cover using overtime or subcontracting as follows:
Total Forecast – Beginning Inventory – Total Regular Output
Period
Forecast
Output
1
230
2
200
3
240
4
240
5
250
6
240
Total
1,400
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
200
200
200
200
200
200
-30
0
-40
-40
-50
-40
1,200
0
0
0
-200
0
0
0
30
0
0
0
30
0
0
0
70
0
0
0
110
0
0
0
160
0
0
0
200
0
600
There are backlogs in every month. How many units will it take to eliminate these backlogs?
Total Forecast – Beginning Inventory – Total Regular Output = 1,400 – 0 – 1,200 = 200 units of
backlogs to cover with overtime and subcontracting. We will add overtime and subcontracting in
those months with backlogs to eliminate the backlogs.
11-5
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Final Plan: Using Overtime (Maximum of 20 Units in a Period) & Subcontracting
Period
Forecast
Output
1
230
2
200
3
240
4
240
5
250
6
240
Total
1,400
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
200
200
200
200
200
200
20
10
0
0
20
20
0
20
20
0
20
30
0
20
20
0
1,200
0
100
100
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
$7,000
$0
$1,400
$800
$7,000
$0
$0
$0
$7,000
$0
$1,400
$1,600
$7,000
$0
$1,400
$1,600
$7,000
$0
$1,400
$2,400
$7,000
$0
$1,400
$1,600
$0
$0
$9,200
$0
$0
$7,000
$0
$0
$10,000
$0
$0
$10,000
$0
$0
$10,800
$0
$0
$10,000
@
@
@
@
@
@
35
70
80
$42,000
$0
$7,000
$8,000
$0
$0
$0
$57,000
Conclusion: Total cost = $57,000.
11-6
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
3.
Given:
Use regular output of 400 units per month. Use a maximum of 40 units per month of overtime
and subcontracting (no limit) as needed to make up any shortages. Regular cost per unit = $25.
Overtime cost per unit = $40. Subcontracting cost per unit = $60. Carrying cost per unit
per period = $15 and is assessed on average inventory.
Month
Forecast
1
380
2
400
3
420
4
440
5
460
6
480
Initial Plan: No Overtime & No Subcontracting
Note: Observe the months with backlog. Those are the months in which we must consider
overtime and subcontracting. Our first option will be overtime ($40 per unit) because it costs less
than subcontracting does ($60 per unit). We can determine the total amount that we will need to
cover using overtime and subcontracting as follows:
Total Forecast – Beginning Inventory – Total Regular Output
Period
Forecast
Output
1
380
2
400
3
420
4
440
5
460
6
480
Total
2,580
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
400
400
400
400
400
400
20
0
-20
-40
-60
-80
2,400
0
0
0
-180
0
20
10
0
20
20
20
0
20
0
10
0
0
0
0
40
0
0
0
100
0
0
0
180
40
320
There are backlogs in Months 4 - 6. How many units will it take to eliminate these backlogs?
Total Forecast – Beginning Inventory – Total Regular Output = 2,580 – 0 – 2,400 = 180 units of
backlogs to cover with overtime and subcontracting. We will add overtime and subcontracting in
those months with backlogs to eliminate the backlogs.
11-7
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Final Plan: Using Overtime (Maximum of 40 Units per Month) & Subcontracting
Period
Forecast
Output
1
380
2
400
3
420
4
440
5
460
6
480
Total
2,580
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
400
400
400
400
400
400
40
40
40
0
2,400
0
120
60
0
40
0
@
@
@
@
25
@
@
15
40
60
20
0
-20
0
40
20
0
0
20
10
0
20
20
20
0
20
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
$10,000
$0
$0
$0
$10,000
$0
$0
$0
$10,000
$0
$0
$0
$10,000
$0
$1,600
$0
$10,000
$0
$1,600
$1,200
$10,000
$0
$1,600
$2,400
$150
$0
$10,150
$300
$0
$10,300
$150
$0
$10,150
$0
$0
$11,600
$0
$0
$12,800
$0
$0
$14,000
$60,000
$0
$4,800
$3,600
$0
$600
$0
$69,000
Conclusion: Total cost = $69,000.
11-8
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
4.
Given:
Use regular output of 550 units per month. Use a maximum of 40 units of overtime per month
and a maximum of 10 units of subcontracting per month to make up any shortages. Regular cost
per unit = $20. Overtime cost per unit = $30. Subcontracting cost per unit = $25.
Carrying cost per unit per month = $10 and is assessed on average inventory. Backlog
(backorder) cost per unit per month = $18.
Month
Forecast
1
540
2
540
3
570
4
590
5
600
6
580
Determine the cost of the aggregate plan given the limits on overtime and subcontracting:
Initial Plan: No Overtime & No Subcontracting
Note: Observe the months with backlog. Those are the months in which we must consider
overtime and subcontracting. Our first option will be subcontracting ($25 per unit) because it
costs less than overtime does ($30 per unit). We can determine the total amount that we will need
to cover using subcontracting and overtime as follows:
Total Forecast – Beginning Inventory – Total Regular Output
Period
Forecast
Output
1
540
2
540
3
570
4
590
5
600
6
580
Total
3,420
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
550
550
550
550
550
550
10
10
-20
-40
-50
-30
3,300
0
0
0
-120
0
10
5
0
10
20
15
0
20
0
10
0
0
0
0
40
0
0
0
90
0
0
0
120
30
250
$11,000
$0
$0
$0
$11,000
$0
$0
$0
$11,000
$0
$0
$0
$11,000
$0
$0
$0
$11,000
$0
$0
$0
$11,000
$0
$0
$0
$50
$0
$11,050
$150
$0
$11,150
$100
$0
$11,100
$0
$720
$11,720
$0
$1,620
$12,620
$0
$2,160
$13,160
@
@
@
@
20
@
@
10
18
30
25
$66,000
$0
$0
$0
$0
$300
$4,500
$70,800
There are backlogs in Months 4 - 6. How many units will it take to eliminate these backlogs?
Total Forecast – Beginning Inventory – Total Regular Output = 3,420 – 0 – 3,300 = 120 units of
backlogs to cover with subcontracting and overtime. We will add subcontracting and overtime in
those months with backlogs to eliminate the backlogs.
11-9
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Final Plan: Using Subcontracting (Maximum of 10 Units per Month) &
Overtime (Maximum of 40 Units per Month)
Period
Forecast
Output
1
540
2
540
3
570
4
590
5
600
6
580
Total
3,420
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
550
550
550
550
550
550
40
10
0
20
10
0
3,300
0
90
30
0
30
0
@
@
@
@
20
@
@
10
18
30
25
10
10
-20
30
10
0
0
10
5
0
10
20
15
0
20
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
$11,000
$0
$0
$0
$11,000
$0
$0
$0
$11,000
$0
$0
$0
$11,000
$0
$900
$250
$11,000
$0
$1,200
$250
$11,000
$0
$600
$250
$50
$0
$11,050
$150
$0
$11,150
$100
$0
$11,100
$0
$0
$12,150
$0
$0
$12,450
$0
$0
$11,850
$66,000
$0
$2,700
$750
$0
$300
$0
$69,750
Conclusion: Total cost = $69,750.
11-10
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
5.
Given:
Regular output capacity is 130 units per month. Regular cost per unit = $60. Overtime cost per
unit = $90. Beginning inventory is 0 units. We have the forecast of engine demand shown below:
Month
Forecast
1
120
2
135
3
140
4
120
5
125
6
125
7
140
8
135
Total
1,040
a. Develop a chase plan that matches the forecast. Calculate the cost of the plan.
Adjust regular time and overtime production to meet demand each period:
Period
Forecast
Output
1
120
2
135
3
140
4
120
5
125
6
125
7
140
8
135
Total
1,040
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
120
130
130
120
125
125
130
130
5
10
10
5
0
0
0
0
0
0
0
0
1,010
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
$7,200
$0
$0
$0
$7,800
$0
$450
$0
$7,800
$0
$900
$0
$7,200
$0
$0
$0
$7,500
$0
$0
$0
$7,500
$0
$0
$0
$7,800
$0
$900
$0
$7,800
$0
$450
$0
$0
$0
$7,200
$0
$0
$8,250
$0
$0
$8,700
$0
$0
$7,200
$0
$0
$7,500
$0
$0
$7,500
$0
$0
$8,700
$0
$0
$8,250
@
@
@
@
@
@
60
90
Conclusion: Total cost = $63,300.
11-11
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Education.
$60,600
$0
$2,700
$0
$0
$0
$0
$63,300
Chapter 11 - Aggregate Planning and Master Scheduling
b. Develop a level plan that uses inventory to absorb fluctuations. Compare the costs of the
level plan to the costs of the chase plan from Part a. Inventory carrying cost per unit per
month = $2. Backlog cost per unit per month = $90. There should be no backlog in the final
month.
Level Plan Regular Production per Month = (Total Forecast – Beginning Inventory) /
Number of Months.
Level Plan Regular Production per Month = (1,040 – 0) / 8 = 130 units per month.
Is this number of units per month feasible? Yes, the regular time capacity is 130 units per
month; therefore, this is the amount that we plan for regular production each month.
Period
Forecast
Output
1
120
2
135
3
140
4
120
5
125
6
125
7
140
8
135
Total
1,040
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
130
130
130
130
130
130
130
130
10
-5
-10
10
5
5
-10
-5
1,040
0
0
0
0
0
10
5.0
0
10
5
7.5
0
5
0
2.5
5
0
5
2.5
0
5
10
7.5
0
10
15
12.5
0
15
5
10.0
0
5
0
2.5
0
50
5
$7,800
$0
$0
$0
$7,800
$0
$0
$0
$7,800
$0
$0
$0
$7,800
$0
$0
$0
$7,800
$0
$0
$0
$7,800
$0
$0
$0
$7,800
$0
$0
$0
$7,800
$0
$0
$0
$10
$0
$7,810
$15
$0
$7,815
$5
$450
$8,255
$5
$0
$7,805
$15
$0
$7,815
$25
$0
$7,825
$20
$0
$7,820
$5
$0
$7,805
@
@
@
@
60
@
@
2
90
90
Conclusion: Cost of chase plan = $63,300. Cost of level plan = $62,950.
The level plan costs $350 less than the chase plan does.
11-12
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Education.
$62,400
$0
$0
$0
$0
$100
$450
$62,950
Chapter 11 - Aggregate Planning and Master Scheduling
6.
Given:
The forecasts for bolts of cloth are shown in the table below. The figures are in hundreds of bolts.
Regular output capacity is 275(00) bolts per month, except for Month 7 when regular output
capacity will be 250(00) bolts. Regular cost per unit (hundred bolts) = $40. Beginning inventory
is 0 bolts.
Month
Forecast (00)
1
250
2
300
3
250
4
300
5
280
6
275
7
270
Total
1,925
a. Develop a chase plan that matches the forecast and compute the total cost of the plan.
Overtime cost per unit (hundred bolts) = $60.
Adjust regular time and overtime production to meet demand each period. Remember:
Regular output capacity in month 7 decreases to 250(00) bolts.
Period
Forecast
Output
1
250
2
300
3
250
4
300
5
280
6
275
7
270
Total
1,925
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
250
275
250
275
275
275
250
25
5
0
0
0
0
0
0
0
1,850
0
75
0
0
0
0
0.0
0
0
0
0.0
0
0
0
0.0
0
0
0
0.0
0
0
0
0.0
0
0
0
0.0
0
0
0
0.0
0
0
0
$10,000
$0
$0
$0
$11,000
$0
$1,500
$0
$10,000
$0
$0
$0
$11,000
$0
$1,500
$0
$11,000
$0
$300
$0
$11,000
$0
$0
$0
$10,000
$0
$1,200
$0
$0
$0
$10,000
$0
$0
$12,500
$0
$0
$10,000
$0
$0
$12,500
$0
$0
$11,300
$0
$0
$11,000
$0
$0
$11,200
25
@
@
@
@
@
@
40
60
20
Conclusion: Total cost = $78,500.
11-13
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Education.
$74,000
$0
$4,500
$0
$0
$0
$0
$78,500
Chapter 11 - Aggregate Planning and Master Scheduling
b. Compute the cost of using regular production with no overtime, but using a subcontractor to
handle the excess above regular capacity at a cost of $50 per hundred bolts. Backlogs are not
allowed. Inventory carrying cost per unit (hundred bolts) per month = $2.
Before solving, compare the cost of regular production to subcontracting:
Regular cost per unit (hundred bolts) = $40.
Subcontracting cost per unit (hundred bolts) = $50.
If we have excess capacity available in the current month, it would cost less to produce a unit
up to four months early using regular production and carry it in inventory [cost = $40 + (4 *
$2) = $48] than it would to subcontract that unit in the current month (cost = $50). As shown
below, regular production will be maxed out each period, thereby requiring some limited
subcontracting.
Period
Forecast
Output
1
250
2
300
3
250
4
300
5
280
6
275
7
270
Total
1,925
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
275
275
275
275
275
275
250
25
-25
25
-25
5
0
0
20
0
1,900
0
0
25
0
0
25
12.5
0
25
0
12.5
0
0
25
12.5
0
25
0
12.5
0
0
0
0.0
0
0
0
0.0
0
0
0
0.0
0
50
0
$11,000
$0
$0
$0
$11,000
$0
$0
$0
$11,000
$0
$0
$0
$11,000
$0
$0
$0
$11,000
$0
$0
$250
$11,000
$0
$0
$0
$10,000
$0
$0
$1,000
$25
$0
$11,025
$25
$0
$11,025
$25
$0
$11,025
$25
$0
$11,025
$0
$0
$11,250
$0
$0
$11,000
$0
$0
$11,000
@
@
@
@
40
@
@
2
60
50
Conclusion: It cost less for this aggregate plan than it costs for the plan from Part a.
The difference is $78,500 – $77,350 = $1,150.
11-14
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Education.
$76,000
$0
$0
$1,250
$0
$100
$0
$77,350
Chapter 11 - Aggregate Planning and Master Scheduling
7.
Given:
We have the aggregate forecasts shown below:
Month
Forecast
Mar
50
Apr
44
May
55
Jun
60
Jul
50
Aug
40
Sep
51
Total
350
We have the following additional information:
Regular production cost
Overtime production cost
Regular capacity
Overtime capacity
Subcontracting cost
Subcontracting capacity
Holding cost
Backorder cost
Beginning inventory
$80 per unit
$120 per unit
40 units per month
8 units per month
$140 per unit
12 units per month
$10 per unit per month
$20 per unit
0 units
a. Use regular production. Supplement using inventory, overtime, and subcontracting as
needed. No backlogs allowed.
Step 1: Determine how much regular production to plan each month. Regular capacity is 40
units per month, and each month’s forecast is at least 40 units. Furthermore, we know that
producing a unit using regular production costs less than producing that unit using overtime
production or subcontracting in the current month. Therefore, we know that we will plan on
40 units per month of regular production every month.
Step 2: Compare the costs of overtime production to subcontracting:
Overtime production cost per unit = $120.
Subcontracting cost per unit = $140.
Therefore, using overtime production in the current month always is preferred to
subcontracting in the current month.
If we have excess capacity available in the current month, it would cost less to produce a unit
up to one month early using overtime production and carry it in inventory [cost = $120 + (1 *
$10) = $130] than it would to subcontract that unit in the current month (cost = $140).
11-15
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Period
Forecast
Output
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
@
@
@
@
80
120
140
@
@
10
20
Mar
Apr
May
Jun
Jul
Aug
Sep
50
44
55
60
50
40
51
40
40
40
40
40
40
40
8
2
0
8
0
4
8
3
-4
8
12
0
8
2
0
3
8
3
-3
280
0
51
19
0
0
0
0.0
0
0
4
2.0
0
4
0
2.0
0
0
0
0.0
0
0
0
0.0
0
0
3
1.5
0
3
0
1.5
0
7
0
$3,200
$0
$960
$280
$3,200
$0
$960
$0
$3,200
$0
$960
$420
$3,200
$0
$960
$1,680
$3,200
$0
$960
$280
$3,200
$0
$360
$0
$3,200
$0
$960
$0
$0
$0
$4,440
$20
$0
$4,180
$20
$0
$4,600
$0
$0
$5,840
$0
$0
$4,440
$15
$0
$3,575
$15
$0
$4,175
Total
350
$22,400
$0
$6,120
$2,660
$0
$70
$0
$31,250
Conclusion: Total cost = $31,250.
b. Use a level strategy. Use a combination of backlogs, subcontracting, and inventory to
handle variations in demand. There should be no backlog in the final month.
Step 1: Determine how much regular production to plan each month. Level Plan Regular
Production per Month = (Total Forecast – Beginning Inventory) / Number of Months =
(350 – 0) / 7 = 50 units per month.
However, regular capacity is 40 units per month. Therefore, we will plan on 40 units per
month of regular production every month.
Step 2: Compare the costs of overtime production to subcontracting:
Overtime production cost per unit = $120.
Subcontracting cost per unit = $140.
Therefore, using overtime production in the current month always is preferred to
subcontracting in the current month.
If we have excess capacity available in the current month, it would cost less to produce a unit
up to one month early using overtime production and carry it in inventory [cost = $120 + (1 *
$10) = $130] than it would to subcontract that unit in the current month (cost = $140).
Step 3: Consider whether having a backlog makes sense. Backorder cost = $20 per unit per
month while holding cost = $10 per unit per month. Given the choice of producing a unit one
month early or one month late, we would prefer to produce that unit one month early.
11-16
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Similarly, given the choice of subcontracting a unit one month early or one month late, we
would prefer to subcontract that unit one month early.
Because producing a unit using overtime production costs $20 less than subcontracting does,
we would be indifferent between producing a unit one month late using overtime [cost =
$120 + (1 * $20) = $140] and subcontracting that unit in the current month (cost = $140).
Summary of Rules for This Problem
1. We always prefer using overtime production in the current month over subcontracting in
the current month.
2. If we have excess capacity available in the current month, it would cost less to produce a
unit up to one month early using overtime production and carry it in inventory than it
would to subcontract that unit in the current month.
3. We prefer using overtime one month early over one month late.
4. We prefer using subcontracting one month early over one month late.
5. We are indifferent between producing a unit one month late using overtime and
subcontracting that unit in the current month.
As we apply the rules listed above, we will see that we will maximize overtime production
each month as shown below:
Initial Solution – Using Regular Time & Overtime (No Subcontracting)
Period
Forecast
Output
1
50
2
44
3
55
4
60
5
50
6
40
7
51
Total
350
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
40
40
40
40
40
40
40
8
8
8
8
8
8
8
-2
4
-7
-12
-2
8
-3
280
0
56
0
-14
0
0
0.0
2
0
2
1.0
0
2
0
1.0
5
0
0
0.0
17
0
0
0.0
19
0
0
0.0
11
0
0
0.0
14
2
68
$3,200
$0
$960
$0
$3,200
$0
$960
$0
$3,200
$0
$960
$0
$3,200
$0
$960
$0
$3,200
$0
$960
$0
$3,200
$0
$960
$0
$3,200
$0
$960
$0
$0
$40
$4,200
$10
$0
$4,170
$10
$100
$4,270
$0
$340
$4,500
$0
$380
$4,540
$0
$220
$4,380
$0
$280
$4,440
@
@
@
@
80
120
140
@
@
10
20
$22,400
$0
$6,720
$0
$0
$20
$1,360
$30,500
Looking at the solution above, we see that we have backlogs, including in the last month.
11-17
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
We know that we must not have a backlog in the final month.
How many units do we need to subcontract to ensure that we do not have a backlog in the
final month?
Total Forecast – Beginning Inventory – Total Regular Production – Total Overtime
Production = 350 – 0 – 280 – 56 = 14 units.
The challenge to this problem then becomes how to distribute the 14 units of subcontracting
to minimize total cost as shown below:
Final Solution – Using Regular Time, Overtime, & Subcontracting
Period
Forecast
Output
1
50
2
44
3
55
4
60
5
50
6
40
7
51
Total
350
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
40
40
40
40
40
40
40
8
2
0
8
8
9
-3
8
8
8
4
8
3
-4
-2
8
-3
280
0
56
14
0
0
0
0.0
0
0
4
2.0
0
4
0
2.0
0
0
0
0.0
3
0
0
0.0
5
0
3
1.5
0
3
0
1.5
0
7
8
$3,200
$0
$960
$280
$3,200
$0
$960
$0
$3,200
$0
$960
$420
$3,200
$0
$960
$1,260
$3,200
$0
$960
$0
$3,200
$0
$960
$0
$3,200
$0
$960
$0
$0
$0
$4,440
$20
$0
$4,180
$20
$0
$4,600
$0
$60
$5,480
$0
$100
$4,260
$15
$0
$4,175
$15
$0
$4,175
@
@
@
@
80
120
140
@
@
10
20
$22,400
$0
$6,720
$1,960
$0
$70
$160
$31,310
Conclusion: Total cost = $31,310.
11-18
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
8.
Given:
A planner has developed aggregate forecasts for the next six months shown below:
Month
Forecast
May
4,000
Jun
4,800
Jul
5,600
Use the following information:
Regular production cost
Regular production capacity
Overtime production cost
Subcontracting cost
Holding cost
Beginning inventory
Aug
7,200
Sep
6,400
Oct
5,000
$10 per case
5,000 cases
$16 per case
$20 per case
$1 per case per month
0 cases
a. Use level production. Supplement using overtime as needed. No backlogs are allowed.
Step 1: Determine how much regular production to plan each month. Level Plan Regular
Production per Month = (Total Forecast – Beginning Inventory) / Number of Months =
(33,000 – 0) / 6 = 5,500 units per month. However, regular capacity is 5,000 units per month.
Therefore, we will plan on 5,000 units per month of regular production every month.
Step 2: Supplement with overtime production each month to ensure that there are no backlogs
in every month.
Period
Forecast
Output
May
4,000
Jun
4,800
Jul
5,600
Aug
7,200
Sep
6,400
Oct
5,000
Total
33,000
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
5,000
5,000
5,000
5,000
5,000
5,000
1,600
1,400
@
@
@
@
10
@
@
1
16
20
1,000
200
-600
-600
0
0
30,000
0
3,000
0
0
0
1,000
500
0
1,000
1,200
1,100
0
1,200
600
900
0
600
0
300
0
0
0
0
0
0
0
0
0
2,800
0
$50,000
$0
$0
$0
$50,000
$0
$0
$0
$50,000
$0
$0
$0
$50,000
$0
$25,600
$0
$50,000
$0
$22,400
$0
$50,000
$0
$0
$0
$500
$0
$50,500
$1,100
$0
$51,100
$900
$0
$50,900
$300
$0
$75,900
$0
$0
$72,400
$0
$0
$50,000
$300,000
$0
$48,000
$0
$0
$2,800
$0
$350,800
Conclusion: Total cost = $350,800.
11-19
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
b. Use a combination of overtime (500 cases per month maximum), inventory, and
subcontracting (500 cases per month maximum) to handle variations in demand. Backlogs are
not allowed.
Step 1: Determine the least cost option out of regular production, overtime production, and
subcontracting:
Regular production = $10 per case.
Overtime production = $16 per case.
Subcontracting = $20 per case.
Holding cost = $1 per case per month.
Regular production costs less than the other two options. Comparing regular time production
to overtime production, we see that it would cost less to meet the demand in the current
month up to five months early using regular time production [cost = $10 + (5 * $1) = $15]
than it would to use overtime production in the current period (cost = $16). Given that we
have only six months, we will maximize regular time production each month at 5,000 units.
Step 2: Compare the costs of overtime production to subcontracting:
Overtime production cost per unit = $16.
Subcontracting cost per unit = $20.
Therefore, using overtime production in the current month always is preferred to
subcontracting in the current month.
If we have excess capacity available in the current month, it would cost less to produce a unit
up to three months early using overtime production and carry it in inventory [cost = $16 + (3
* $1) = $19] than it would to subcontract that unit in the current month (cost = $20).
Period
Forecast
Output
May
4,000
Jun
4,800
Jul
5,600
Aug
7,200
Sep
6,400
Oct
5,000
Total
33,000
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
5,000
5,000
5,000
5,000
5,000
5,000
500
500
500
500
1,500
700
-100
-1,700
500
500
-400
0
30,000
0
2,500
500
0
0
1,500
750
0
1,500
2,200
1,850
0
2,200
2,100
2,150
0
2,100
400
1,250
0
400
0
200
0
0
0
0
0
6,200
0
$50,000
$0
$8,000
$0
$50,000
$0
$8,000
$0
$50,000
$0
$8,000
$0
$50,000
$0
$8,000
$0
$50,000
$0
$8,000
$10,000
$50,000
$0
$0
$0
$750
$0
$58,750
$1,850
$0
$59,850
$2,150
$0
$60,150
$1,250
$0
$59,250
$200
$0
$68,200
$0
$0
$50,000
@
@
@
@
10
@
@
1
16
20
$300,000
$0
$40,000
$10,000
$0
$6,200
$0
$356,200
Conclusion: Total cost = $356,200.
11-20
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
c. Use overtime up to 750 cases per month and inventory to handle variations in demand. No
backlogs allowed.
Step 1: Determine the least cost option out of regular production, overtime production, and
subcontracting:
Regular production = $10 per case.
Overtime production = $16 per case.
Holding cost = $1 per case per month.
Regular production costs less than overtime production costs. Comparing regular time
production to overtime production, we see that it would cost less to meet the demand in the
current month up to five months early using regular time production [cost = $10 + (5 * $1) =
$15] than it would to use overtime production in the current period (cost = $16). Given that
we have only six months, we will maximize regular time production each month at 5,000
units.
Step 2: Supplement with overtime production each month (maximum of 750 units) to ensure
that there are no backlogs in every month. We may have to plan overtime production early to
cover demand in some months. The key to this problem is determining how many units need
to be produced using overtime and then timing the production of those units to minimize total
cost and to ensure that there are no backlogs in every period.
For how many units do we need to use overtime production?
Total Forecast – Beginning Inventory – Total Regular Production = 33,000 – 0 – 30,000 =
3,000 units.
Period
Forecast
Output
May
4,000
Jun
4,800
Jul
5,600
Aug
7,200
Sep
6,400
Oct
5,000
Total
33,000
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
5,000
5,000
5,000
5,000
5,000
5,000
750
750
750
750
1,000
950
150
-1,450
-650
0
30,000
0
3,000
0
0
0
1,000
500
0
1,000
1,950
1,475
0
1,950
2,100
2,025
0
2,100
650
1,375
0
650
0
325
0
0
0
0
0
5,700
0
$50,000
$0
$0
$0
$50,000
$0
$12,000
$0
$50,000
$0
$12,000
$0
$50,000
$0
$12,000
$0
$50,000
$0
$12,000
$0
$50,000
$0
$0
$0
$500
$0
$50,500
$1,475
$0
$63,475
$2,025
$0
$64,025
$1,375
$0
$63,375
$325
$0
$62,325
$0
$0
$50,000
@
@
@
@
10
@
@
1
16
20
$300,000
$0
$48,000
$0
$0
$5,700
$0
$353,700
Conclusion: Total cost = $353,700. We should choose the plan from Part a because it has the
lowest cost ($350,800). The plan from Part a is $2,900 lower.
11-21
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
9.
Given:
We have the information shown below. Subcontracting can handle a maximum of 10 units per
month. Beginning inventory is 0. No backorders are allowed.
Month
Demand
Regular
capacity
Overtime
capacity
1
160
150
2
150
150
3
160
150
4
180
150
5
170
160
6
140
160
10
10
0
10
10
10
Cost per Unit
Regular time
$50
Overtime
$75
Subcontract
$80
Holding per month
$4
Develop a plan that minimizes total cost. The key to solving this problem is meeting demand
when demand exceeds regular capacity. When this happens, we should add overtime production
first, and then add subcontracting if needed. We must be careful to avoid backorders in every
period.
Step 1: Regular production = regular capacity each month.
Step 2: In Months 1 – 5, add overtime production first (cost per unit = $75) and then
subcontracting (cost per unit = $80) so that no backlogs occur.
Period
Forecast
Output
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
@
@
@
@
50
@
@
4
75
80
1
160
2
150
3
160
4
180
5
170
6
140
Total
960
150
150
150
150
160
140
10
10
10
0
10
10
20
10
0
-20
0
0
900
0
40
20
0
0
0
0
0
0
20
10
0
20
20
20
0
20
0
10
0
0
0
0
0
0
0
0
0
40
0
$7,500
$0
$750
$0
$7,500
$0
$750
$800
$7,500
$0
$0
$800
$7,500
$0
$750
$0
$8,000
$0
$750
$0
$7,000
$0
$0
$0
$0
$0
$8,250
$40
$0
$9,090
$80
$0
$8,380
$40
$0
$8,290
$0
$0
$8,750
$0
$0
$7,000
$45,000
$0
$3,000
$1,600
$0
$160
$0
$49,760
Conclusion: The total cost of this plan is $49,760.
11-22
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
10.
Given:
Refer back to the solution in Solved Problem 1 (consider the solution for that problem to be Plan
A). The total cost of Plan A was $20,550. The given information in Solved Problem 1 was:
Current workforce = 20 people, each of whom can produce 10 units of output per period. Regular
production cost per unit = $6. Inventory carrying cost per unit per period = $5. Backlog cost per
unit per period = $10.
Period
Forecast
1
190
2
230
3
260
4
280
5
210
6
170
7
160
8
260
9
180
Total
1,940
Plan B:
Hire one worker at a cost of $200. Make up any shortfall, i.e., reduce backorders, using
subcontracting at $8 per unit, with a maximum of 20 units per period. Ending inventory in period
9 should be 0. Backorders cannot exceed 80 units in any period.
Regular production = regular capacity = (20 + 1) * 10 = 210 units per period.
Therefore, regular production could be used to meet demand of 9 * 210 = 1,890 units. How many
units do we need to subcontract to ensure that we do not have a backlog in the final month?
Total Forecast – Beginning Inventory – Total Regular Production = 1,940 – 0 – 1,890 = 50 units.
The key to this problem is when to plan the 50 units of subcontracting to stay within the
subcontracting limit of 20 units per period, to keep the backlog ≤ 80 units (Month 4 will be a
challenge because it has the peak demand), and to minimize total cost.
Period
Forecast
Output
1
190
2
230
3
260
4
280
5
210
6
170
7
160
8
260
9
180
Total
1,940
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
210
210
210
210
210
210
210
210
210
10
30
20
0
20
-30
-70
0
40
50
-50
30
1,890
0
0
50
0
30
15
0
30
30
30
0
30
0
15
0
0
0
0
70
0
0
0
70
0
0
0
30
0
20
10.0
0
20
0
10.0
30
0
0
0.0
0
80
200
$1,260
$0
$0
$80
$1,260
$0
$0
$160
$1,260
$0
$0
$160
$1,260
$0
$0
$0
$1,260
$0
$0
$0
$1,260
$0
$0
$0
$1,260
$0
$0
$0
$1,260
$0
$0
$0
$1,260
$0
$0
$0
$75
$0
$1,415
$150
$0
$1,570
$75
$0
$1,495
$0
$700
$1,960
$0
$700
$1,960
$0
$300
$1,560
$50
$0
$1,310
$50
$300
$1,610
$0
$0
$1,260
@
@
@
@
6
@
@
5
10
8
Conclusion: Total Cost of Plan B = $14,140 + $200 (cost of hiring 1 worker) = $14,340.
11-23
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
$11,340
$0
$0
$400
$0
$400
$2,000
$14,140
Chapter 11 - Aggregate Planning and Master Scheduling
Plan C:
No additional workers are to be hired. Make up any shortfall, i.e., reduce backorders, using
subcontracting at $8 per unit, with a maximum of 20 units per period. Ending inventory in period
9 should be 0. Backorders cannot exceed 80 units in any period.
Regular production = 200 units per period.
Therefore, regular production could be used to meet demand of 9 * 200 = 1,800 units. How many
units do we need to subcontract to ensure that we do not have a backlog in the final month?
Total Forecast – Beginning Inventory – Total Regular Production = 1,940 – 0 – 1,800 = 140
units. The key to this problem is when to plan the 140 units of subcontracting to stay within the
maximum of 20 units per period, to keep the backlog ≤ 80 units (Period 4 will be a challenge
because it has the peak demand), and to minimize total cost.
Period
Forecast
Output
1
190
2
230
3
260
4
280
5
210
6
170
7
160
8
260
9
180
Total
1,940
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
200
200
200
200
200
200
200
200
200
20
30
20
-10
20
-40
20
-60
20
10
20
50
40
20
-40
20
1,800
0
0
140
0
30
15
0
30
20
25
0
20
0
10
20
0
0
0
80
0
0
0
70
0
0
0
20
0
20
10.0
0
20
0
10.0
20
0
0
0.0
0
70
210
$1,200
$0
$0
$160
$1,200
$0
$0
$160
$1,200
$0
$0
$160
$1,200
$0
$0
$160
$1,200
$0
$0
$160
$1,200
$0
$0
$160
$1,200
$0
$0
$0
$1,200
$0
$0
$160
$1,200
$0
$0
$0
$75
$0
$1,435
$125
$0
$1,485
$50
$200
$1,610
$0
$800
$2,160
$0
$700
$2,060
$0
$200
$1,560
$50
$0
$1,250
$50
$200
$1,610
$0
$0
$1,200
@
@
@
@
6
@
@
5
10
8
Conclusion: Total Cost of Plan C = $14,370.
Comparison of plans:
Plan A: $20,550
Plan B: $14,340
Plan C: $14,370
Conclusion: Plan B has the lowest cost.
11-24
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
$10,800
$0
$0
$1,120
$0
$350
$2,100
$14,370
Chapter 11 - Aggregate Planning and Master Scheduling
11.
Given:
Refer back to the solution in Solved Problem 1. The total cost in that plan was $20,550. The
given information in Solved Problem 1 was: Current workforce = 20 people, each of whom can
produce 10 units of output per period. Regular production cost per unit = $6. Inventory carrying
cost per unit per period = $5. Backlog cost per unit per period = $10. Forecasts are shown below:
Period
Forecast
1
190
2
230
3
260
4
280
5
210
6
170
7
160
8
260
9
180
Total
1,940
Another option is to use part-time workers during seasonal peaks. Cost per unit (hiring + training)
= $11. A maximum of 10 part-time workers can be used, and the same number of part-time
workers must be used in all periods that have part-time workers. The ending inventory in Period 9
should be 10 units. The limit on backlogs is 20 units per period. Try to make up backlogs as soon
as possible.
Regular production = 200 units per period.
Therefore, regular production could be used to meet demand of 9 * 200 = 1,800 units. How many
units do we need part-time workers to produce? Total Forecast + Ending Inventory Goal –
Beginning Inventory – Total Regular Production = 1,940 + 10 – 0 – 1,800 = 150 units. A parttime worker can produce 10 units per period. Therefore, we will need to hire 5 part-time workers.
These 5 part-time workers will produce 50 units per month * 3 months = 150 units.
Period
Forecast
Output
1
190
2
230
3
260
4
280
5
210
6
170
7
160
8
260
9
180
Total
1,940
Regular
Part Time
Overtime
Subcontract
Output – Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
200
200
50
200
50
200
50
200
200
200
200
200
10
20
-10
-30
-10
30
40
-60
20
1,800
150
0
0
10
10
5
0
10
30
20
0
30
20
25
0
20
0
10
10
0
0
0
20
0
10
5
0
10
50
30.0
0
50
0
25.0
10
0
10
5.0
0
125
40
$1,200
$0
$0
$0
$1,200
$550
$0
$0
$1,200
$550
$0
$0
$1,200
$550
$0
$0
$1,200
$0
$0
$0
$1,200
$0
$0
$0
$1,200
$0
$0
$0
$1,200
$0
$0
$0
$1,200
$0
$0
$0
$25
$0
$1,225
$100
$0
$1,850
$125
$0
$1,875
$50
$100
$1,900
$0
$200
$1,400
$25
$0
$1,225
$150
$0
$1,350
$125
$100
$1,425
$25
$0
$1,225
@
@
@
@
6
11
@
@
5
10
8
Conclusion: The total cost of the plan using part-time workers is $13,475. The cost of the plan in
Solved Problem 1 was $20,550. This plan using part-time workers is $7,075 lower.
11-25
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
$10,800
$1,650
$0
$0
$0
$625
$400
$13,475
Chapter 11 - Aggregate Planning and Master Scheduling
12.
Given:
Refer back to the solution in Solved Problem 1. The total cost in that plan was $20,550. The
given information in Solved Problem 1 was: Current workforce = 20 people, each of whom can
produce 10 units of output per period. Regular production cost per unit = $6. Inventory carrying
cost per unit per period = $5. Backlog cost per unit per period = $10. Forecasts are shown below:
Period
Forecast
1
190
2
230
3
260
4
280
5
210
6
170
7
160
8
260
9
180
Total
1,940
Prepare an aggregate plan that uses overtime ($9 per unit, maximum = 25 units per period) and
inventory variation. Try to minimize backlogs. The ending inventory in period 9 should be 0
units, and the limit on backlogs is 60 units per period.
Regular production = 200 units per period.
Therefore, regular production could be used to meet 9 * 200 = 1,800 units. How many units do
we need to use overtime to produce? Total Forecast – Beginning Inventory – Total Regular
Production = 1,940 – 0 – 1,800 = 140 units.
The key to this problem is to schedule OT production (140 units) early to minimize backlogs.
Remember: Maximum overtime is 25 units per period.
Period
Forecast
Output
1
190
2
230
3
260
4
280
5
210
6
170
7
160
8
260
9
180
Total
1,940
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
200
200
200
200
200
200
200
200
200
25
25
25
25
25
15
35
-5
-35
-55
15
45
40
-60
20
1,800
0
140
0
0
35
18
0
35
30
33
0
30
0
15
5
0
0
0
60
0
0
0
45
0
0
0
0
0
40
20.0
0
40
0
20.0
20
0
0
0.0
0
105
130
$1,200
$0
$225
$0
$1,200
$0
$225
$0
$1,200
$0
$225
$0
$1,200
$0
$225
$0
$1,200
$0
$225
$0
$1,200
$0
$135
$0
$1,200
$0
$0
$0
$1,200
$0
$0
$0
$1,200
$0
$0
$0
$88
$0
$1,513
$163
$0
$1,588
$75
$50
$1,550
$0
$600
$2,025
$0
$450
$1,875
$0
$0
$1,335
$100
$0
$1,300
$100
$200
$1,500
$0
$0
$1,200
@
@
@
@
6
@
@
5
10
9
Conclusion: The total units backlogged over this plan = 130. The total cost of this plan is
$13,885. The cost of the plan in Solved Problem 1 was $20,550. This plan using overtime is
$6,665 lower.
11-26
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
$10,800
$0
$1,260
$0
$0
$525
$1,300
$13,885
Chapter 11 - Aggregate Planning and Master Scheduling
13.
Given:
Refer to Example 2. The total cost for Example 2 was $4,640. The forecasts for Example 2 are
shown below:
Period
Forecast
1
200
2
200
3
300
4
400
5
500
6
200
Total
1,800
Subcontracting can be used at a maximum rate of 50 units per period as needed. Overtime is not
allowed. Your plan should have ending inventory of 0 units. Ending backlog must equal 0.
Regular capacity = 280 units per period. Regular production can be less than regular capacity.
Step 1: Determine the least cost option out of regular production and subcontracting.
Regular production cost = $2 per unit.
Subcontracting cost = $6 per unit.
Inventory holding cost = $1 per unit per period (based on average inventory).
Backorder cost = $5 per unit per period.
Regular production costs less than subcontracting does. Comparing regular time production to
subcontracting, we see that it would cost less to meet the demand in the current period up to three
periods early using regular time production [cost = $2 + (3 * $1) = $5] than it would to use
subcontracting in the current period (cost = $6). If we were to produce a unit four periods early
using regular time production [cost = $2 + (4 * $1) = $6], that cost would equal the cost of
subcontracting in the current period ($6).
The cost per unit of producing a unit using regular time production one period late = $2 + (1 x $5)
= $7, which exceeds the cost of subcontracting that unit in the current period. Therefore, given
the choice of meeting demand late using regular time and subcontracting, we would prefer
subcontracting.
Step 2: Determine how much to produce using regular time and how much to subcontract.
Regular time production could be used to meet demand of 6 * 280 = 1,680 units. How many units
do we need to subcontract? Total Forecast – Beginning Inventory – Total Regular Production =
1,800 – 0 – 1,680 = 120 units. The key to this problem is to experiment with the subcontracting to
handle the peak demand period (Period 5) to minimize total cost.
11-27
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Period
Forecast
Output
1
200
2
200
3
300
4
400
5
500
6
200
Total
1,800
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
280
280
280
280
280
280
80
80
20
0
50
-70
50
-170
80
1,680
0
0
120
0
80
40
0
80
160
120
0
160
160
160
0
160
90
125
0
90
0
45
80
0
0
0
0
490
80
$560
$0
$0
$0
$560
$0
$0
$0
$560
$0
$0
$120
$560
$0
$0
$300
$560
$0
$0
$300
$560
$0
$0
$0
$40
$0
$600
$120
$0
$680
$160
$0
$840
$125
$0
$985
$45
$400
$1,305
$0
$0
$560
@
@
@
@
2
@
@
1
5
6
$3,360
$0
$0
$720
$0
$490
$400
$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.
11-28
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
14.
Given:
Plan from Example 3:
Period
1
2
Beg. Inv.
3
Unused cap.
(dummy)
0
0
1
2
60
61
62
0
81
82
0
91
92
0
60
61
0
80
81
0
90
91
0
60
0
80
0
90
0
Total
100
Reg.
100
450
1
50
500
Over.
80
Sub.
90
Reg.
63
Over.
83
Sub.
93
Reg.
66
63
Over.
86
83
Sub.
96
93
50
50
30
90
120
500
2
500
50
50
20
100
120
500
3
500
50
50
100
Demand
550
700
750
100
90
2,090
Verify the transportation solution shown above:
a. Verify that total demand equals total supply:
Total demand = 550 + 700 + 750 = 2,000.
Total supply = 100 + 500 + 50 + 120 + 500 + 50 + 120 + 500 + 50 + 100 = 2,090.
Therefore, the dummy column with demand of 90 has been added to satisfy the requirement
that supply and demand must be equal.
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
1 + 500 units of regular time production in Period 2 + 50 units of overtime production in
Period 2 + 20 units of subcontracting in Period 2.
50 + 50 + 30 + 500 + 50 + 20 = 700.
Period 3 Demand = 750. This demand will be met by 100 units of subcontracting in Period 2
+ 500 units of regular time production in Period 3 + 50 units of overtime production in Period
3 + 100 units of subcontracting in Period 3.
100 + 500 + 50 + 100 = 750.
The dummy demand = 90. That demand is satisfied from subcontracting in Period 1.
11-29
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
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.
450 + 50 = 500.
Overtime capacity of 50 units in Period 1 will be used to meet demand of 50 units in Period
2.
Subcontracting capacity of 120 units in Period 1 will be used to meet demand of 30 units in
Period 2 + dummy demand of 90 units.
30 + 90 = 120.
Regular time capacity of 500 units in Period 2 will be used to meet demand of 500 units in
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.
20 + 100 = 120.
Regular time capacity of 500 units in Period 3 will be used to meet demand of 500 units in
Period 3.
Overtime capacity of 50 units in Period 3 will be used to meet demand of 50 units in Period
3.
Subcontracting capacity of 100 units in Period 3 will be used to meet demand of 100 units in
Period 3.
11-30
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
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
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
Regular capacity: 500 units per month
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 * $2) = $64. That cost is less than using
overtime ($80) or subcontracting ($90) in the current month.
Using regular time up to two months late costs $60 + (2 * $3) = $66. That cost is less than using
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:
11-31
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Solution 1:
Period
1
Beg. Inv.
2
3
Unused cap.
(dummy)
0
0
2
4
60
62
64
0
82
84
0
94
0
100
Reg.
100
450
1
50
500
Over.
80
Sub.
90
92
Reg.
63
60
62
0
Over.
83
80
82
0
Sub.
93
90
92
0
Reg.
66
63
60
0
Over.
86
83
80
0
Sub.
96
93
90
0
50
50
30
90
120
500
2
500
50
50
50
70
120
500
3
500
50
50
100
Demand
Total
550
700
750
1
2
3
100
90
2,090
Solution 2:
Period
Beg. Inv.
Unused cap.
(dummy)
0
0
2
4
60
62
64
0
80
82
84
0
Sub.
90
92
94
0
Reg.
63
60
62
0
Over.
83
80
82
0
Sub.
93
90
92
0
Reg.
66
63
60
0
Over.
86
83
80
0
Sub.
96
93
90
0
100
Reg.
100
400
1
Over.
100
500
50
50
30
90
120
500
2
500
50
50
120
120
500
3
500
50
50
100
Demand
550
Total
700
750
100
90
2,090
Conclusion: Total cost of both plans = $124,960.
11-32
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
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.
Using regular time up to two months late costs $60 + (2 * $3) = $66. That cost is less than using
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 $1 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:
11-33
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Solution 1:
Period
1
Beg. Inv.
2
3
Unused cap.
(dummy)
0
0
1
2
60
61
62
0
81
82
0
91
92
0
60
61
0
80
81
0
91
0
60
0
80
0
90
0
100
Reg.
100
450
1
50
500
Over.
80
Sub.
90
Reg.
63
Over.
83
Sub.
93
90
Reg.
66
63
Over.
86
83
Sub.
96
93
50
50
90
30
120
500
2
500
10
40
50
120
120
440
3
440
50
50
100
Demand
Total
550
700
750
1
2
3
100
30
2,090
Solution 2:
Period
Beg. Inv.
Unused cap.
(dummy)
0
0
1
2
60
61
62
0
80
81
82
0
Sub.
90
91
92
0
Reg.
63
Over.
83
Sub.
93
Reg.
100
Reg.
100
400
1
Over.
100
500
50
50
30
60
30
120
60
61
0
80
81
0
90
91
0
66
63
60
0
Over.
86
83
80
0
Sub.
96
93
90
0
500
2
500
50
50
120
120
440
3
440
50
50
100
Demand
550
Total
700
750
100
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).
11-34
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
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
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 * $2) = $64. That cost is less than using
overtime ($80) or subcontracting ($90) in the current month.
Using regular time up to two months late costs $60 + (2 * $3) = $66. That cost is less than using
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:
11-35
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Solution 1:
Period
1
Beg. Inv.
2
3
Unused cap.
(dummy)
0
0
2
4
60
62
64
0
82
84
0
92
94
0
60
62
0
80
82
0
92
0
60
0
80
0
90
0
100
Reg.
100
450
1
50
500
Over.
80
Sub.
90
Reg.
63
Over.
83
Sub.
93
90
Reg.
66
63
Over.
86
83
Sub.
96
93
50
50
90
30
120
500
2
500
10
40
50
120
120
440
3
440
50
50
100
Demand
Total
550
700
750
1
2
3
100
30
2,090
Solution 2:
Period
Beg. Inv.
Unused cap.
(dummy)
0
0
2
4
60
62
64
0
80
82
84
0
Sub.
90
92
94
0
Reg.
63
Over.
83
Sub.
93
Reg.
100
Reg.
100
400
1
Over.
100
500
50
50
30
60
30
120
60
62
0
80
82
0
90
92
0
66
63
60
0
Over.
86
83
80
0
Sub.
96
93
90
0
500
2
500
50
50
120
120
440
3
440
50
50
100
Demand
550
Total
700
750
100
30
2,090
Conclusion: Total cost for both solutions = $127,000.
11-36
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
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:
There are 28 full-time employees, each of whom can produce 50 wheels per month. David wants
to use a pure level plan. There is no inventory of finished wheels on hand at present, but David
would like to have 300 on hand at the end of April. Big Bike will tolerate back orders of up 200
units per month.
Demand for the next six months:
Month
Nov.
Dec.
20-inch
1,000
900
24-inch
500
500
Total
1,500
1,400
Jan.
600
300
900
Feb.
700
500
1,200
Mar.
1,100
400
1,500
Apr.
1,100
600
1,700
Costs:
Regular: $5.00/unit
Overtime: $7.50/unit
Hiring $300/employee
Layoff: $400/employee
Inventory: $1.00/unit/month
Back order: $6.00/unit/month
Step 1: Determine the total demand for wheels:
(20-inch total + 24-inch total) + desired ending inventory = 8,200 + 300 = 8,500 units.
Step 2: Determine the current total regular time capacity:
Capacity/month = 28 employees * 50 units/employee/month = 1,400 units/month.
6 months * 1,400 units/month = 8,400 units.
Amount short = 8,500 – 8,400 = 100 units.
Step 3: Determine the options to cover this shortage of 100 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
the last month. The key will be to schedule overtime beginning in Month 1 to reduce backorder
costs. If the overtime must be equal in Months 1 – 5, we will use overtime for 100 / 5 = 20 units
per month in Months 1 – 5.
Option 2: Hire more workers. We need to produce 100 / 6 = 16.67 = 17 extra units per month.
How many employees would we need to hire? We would need to hire 1 employee because each
employee can produce up to 50 units per month.
11-37
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Step 4: Compare the costs of Option 1 (keep the same number of employees, produce 1,400 units
per month using regular time, and produce 100 units total using overtime) vs. Option 2 (hire 1
employee and produce 1,417 units each month using regular time).
Option 1: Maintain 28 employees & produce 100 units total using overtime in equal
amounts in Months 1- 5:
Period
Forecast
Output
1
1,500
2
1,400
3
900
4
1,200
5
1,500
6
1,700
Total
8,200
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
1,400
1,400
1,400
1,400
1,400
1,400
20
20
20
20
20
-80
20
520
220
-80
-300
8,400
0
100
0
300
0
0
0
80
0
0
0
60
0
460
230
0
460
680
570
0
680
600
640
0
600
300
450
0
1,890
140
$7,000
$0
$150
$0
$7,000
$0
$150
$0
$7,000
$0
$150
$0
$7,000
$0
$150
$0
$7,000
$0
$150
$0
$7,000
$0
$0
$0
$0
$480
$7,630
$0
$360
$7,510
$230
$0
$7,380
$570
$0
$7,720
$640
$0
$7,790
$450
$0
$7,450
@
@
@
@
@
@
5
7.5
1
6
$42,000
$0
$750
$0
$0
$1,890
$840
$45,480
Conclusion: Total cost using overtime = $45,480.
11-38
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Option 2: Hire 1 worker & produce 1,417 units every month using regular time:
Period
Forecast
Output
1
1,500
2
1,400
3
900
4
1,200
5
1,500
6
1,700
Total
8,200
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
1,417
1,417
1,417
1,417
1,417
1,417
-83
17
517
217
-83
-283
8,502
0
0
0
302
0
0
83
0
0
0
66
0
451
226
0
451
668
560
0
668
585
627
0
585
302
444
0
1,855
149
$7,085
$0
$0
$0
$7,085
$0
$0
$0
$7,085
$0
$0
$0
$7,085
$0
$0
$0
$7,085
$0
$0
$0
$7,085
$0
$0
$0
$0
$498
$7,583
$0
$396
$7,481
$226
$0
$7,311
$560
$0
$7,645
$627
$0
$7,712
$444
$0
$7,529
@
@
@
@
@
@
5
7.50
1
6
$42,510
$0
$0
$0
$0
$1,855
$894
$45,259
Conclusion: Total cost of this plan = $45,259 + $300 (cost of hiring 1 employee) = $45,559.
Option 1 (maintaining the same number of employees and using overtime) is the lower cost plan
($45,480) of the two options. The cost of Option 1 (using overtime) is $79 lower.
11-39
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
19.
Given:
Use the industrial pumps information from Figure 11.11:
Forecast
Customer
Orders
1
30
June
2
3
30 30
4
30
5
40
33
20
4
2
10
July
6
7
40 40
8
40
Beginning inventory = 64 units
Lot size = 70 units
Now, change the MPS rule to “schedule production when the projected on-hand inventory would
be less than 10 without production”:
The calculations for MPS and projected on-hand inventory are shown below:
Inventory From
Week Previous Week Requirements*
1
2
3
4
5
6
7
8
64
31
71
41
11
41
71
31
33
30
30
30
40
40
40
40
Net
Inventory
before
MPS
31
1
41
11
–29
1
31
–9
(70)
MPS
Projected
On-hand
Inventory
–
70
–
–
70
70
–
70
31
71
41
11
41
71
31
61
*Requirements equal the larger of forecast and customer orders in each week.
Net Inventory before MPS = Inventory from previous week – Current week’s
requirements.
Projected on-hand inventory = Inventory from previous week – Current week’s
requirements + Current week’s MPS.
Note: We need a MPS quantity whenever Net Inventory before MPS < 10 units.
Example calculations for projected on-hand inventory:
Week 1:
Net Inventory before MPS = 64 – 33 = 31. No MPS is needed.
Projected on-hand inventory = 31 + 0 = 31.
Week 2:
Net Inventory before MPS = 31 – 30 = 1. Warning: This is below the desired level of 10
units. We must plan for 70 units of MPS.
Projected on-hand inventory = 1 + 70 = 71.
The final MPS is shown below:
11-40
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
1
30
June
2
3
30 30
4
30
5
40
33
20
10
4
2
31
71
41
11
31
70
36
Beg. Inv. = 64
Forecast
Customer
Orders
Projected onhand
inventory
MPS
ATP
July
6
40
7
40
8
40
41
71
31
61
70
68
70
70
70
70
ATP (first period) = Beginning inventory + MPS (first period) – sum of customer
orders until (but not including) the period of the next MPS.
ATP (other periods) = MPS (current period) – sum of customer orders until (but
not including) the period of the next MPS.
*We calculate ATP in the first period and in all other periods with MPS
quantities.
ATP (Week 1) = 64 + 0 – (33) = 31
ATP (Week 2) = 70 – (20 + 10 + 4) = 36
ATP (Week 5) = 70 – (2) = 68
ATP (Week 6) = 70 – (0 + 0) = 70
ATP (Week 8) = 70 – (0) = 70
11-41
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
20.
Given:
Update the information from Figure 11.11:
It is now the end of Week 1. Customer orders are 25 for Week 2, 16 for Week 3, 11 for Week 4, 8
for Week 5, and 3 for Week 6. Use the MPS rule of ordering when project on-hand inventory
would be negative without production.
Forecast
Customer
Orders
June
2
3
4
30 30 30
5
40
6
40
25
8
3
16
11
July
7
40
8
40
Beginning inventory = projected on-hand for Week 1 from Figure 11.11 = 31 units
Lot size = 70 units
The calculations for MPS and projected on-hand inventory are shown below:
Inventory From
Week Previous Week Requirements*
2
3
4
5
6
7
8
31
1
41
11
41
1
31
30
30
30
40
40
40
40
Net
Inventory
before
MPS
(70)
MPS
Projected
On-hand
Inventory
1
-29
11
-29
1
-39
-9
–
70
–
70
–
70
70
1
41
11
41
1
31
61
*Requirements equal the larger of forecast and customer orders in each week.
Net Inventory before MPS = Inventory from previous week – Current week’s
requirements.
Projected on-hand inventory = Inventory from previous week – Current week’s
requirements + Current week’s MPS.
Note: We need a MPS quantity whenever Net Inventory before MPS < 0 units (i.e.,
when it is negative).
Example calculations for projected on-hand inventory:
Week 2:
Net Inventory before MPS = 31 – 30 = 1. No MPS is needed.
Projected on-hand inventory = 1 + 0 = 1.
Week 3:
Net Inventory before MPS = 1 – 30 = -29. Warning: This is below the desired level of 0
units. We must plan for 70 units of MPS.
Projected on-hand inventory = -29 + 70 = 41.
The final MPS for Weeks 2 – 8 is shown below:
11-42
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
June
Beg. Inv. = 31 2
3
4
Forecast
30 30 30
Customer
25 16 11
Orders
Projected onhand
1 41 11
inventory
MPS
70
ATP
6 43
July
5
40
6
40
8
3
41
1
70
59
7
40
8
40
31
61
70
70
70
70
ATP (first period) = Beginning inventory + MPS (first period) – sum of customer
orders until (but not including) the period of the next MPS.
ATP (other periods) = MPS (current period) – sum of customer orders until (but
not including) the period of the next MPS.
*We calculate ATP in the first period and in all other periods with MPS
quantities.
ATP (Week 2) = 31 + 0 – (25) = 6
ATP (Week 3) = 70 – (16 + 11) = 43
ATP (Week 5) = 70 – (8 + 3) = 59
ATP (Week 7) = 70 – (0) = 70
ATP (Week 8) = 70 – (0) = 70
11-43
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Chapter 11 - Aggregate Planning and Master Scheduling
21.
Given:
We have the following forecasts and customer orders over the next eight weeks:
Forecast
Customer
Orders
1
50
2
50
3
50
4
50
52
35
20
12
5
50
6
50
7
50
8
50
Beginning inventory = 0 units
Lot size = 75 units
Use the MPS rule of ordering when project on-hand inventory would be negative without
production.
The calculations for MPS and projected on-hand inventory are shown below:
Inventory From
Week Previous Week Requirements*
1
2
3
4
5
6
7
8
0
23
48
73
23
48
73
23
52
50
50
50
50
50
50
50
Net
Inventory
before
MPS
(75)
MPS
Projected
On-hand
Inventory
-52
-27
-2
23
-27
-2
23
-27
75
75
75
–
75
75
–
75
23
48
73
23
48
73
23
48
*Requirements equal the larger of forecast and customer orders in each week.
Net Inventory before MPS = Inventory from previous week – Current week’s
requirements.
Projected on-hand inventory = Inventory from previous week – Current week’s
requirements + Current week’s MPS.
Note: We need a MPS quantity whenever Net Inventory before MPS < 0 units (i.e.,
when it would be negative).
Example calculations for projected on-hand inventory:
Week 1:
Net Inventory before MPS = 0 – 52 = -52. Warning: This is below the desired level of 0
units. We must plan for 75 units of MPS.
Projected on-hand inventory = -52 + 75 = 23.
Week 2:
Net Inventory before MPS = 23 – 50 = -27. Warning: This is below the desired level of
0 units. We must plan for 75 units of MPS.
Projected on-hand inventory = -27 + 75 = 48.
The final MPS is shown below:
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Chapter 11 - Aggregate Planning and Master Scheduling
1
50
2
50
3
50
Week
4
5
50 50
52
35
20
12
23
48
73
23
75
75
75
Beg. Inv. = 0
Forecast
Customer
Orders
Projected onhand
inventory
MPS
22.
6
50
7
50
8
50
48
73
23
48
75
75
Week
5
50
6
50
7
50
8
50
48
73
23
48
75
75
75
75
75
Calculate the ATP for Problem 21:
Beg. Inv. = 0
Forecast
Customer
Orders
Projected onhand
inventory
MPS
ATP
1
50
2
50
3
50
4
50
52
35
20
12
23
48
73
23
75
23
75
40
75
43
75
75
ATP (first period) = Beginning inventory + MPS (first period) – sum of customer
orders until (but not including) the period of the next MPS.
ATP (other periods) = MPS (current period) – sum of customer orders until (but
not including) the period of the next MPS.
*We calculate ATP in the first period and in all other periods with MPS
quantities.
ATP (Week 1) = 0 + 75 – (52) = 23
ATP (Week 2) = 75 – (35) = 40
ATP (Week 3) = 75 – (20 + 12) = 43
ATP (Week 5) = 75 – (0) = 75
ATP (Week 6) = 75 – (0 + 0) = 75
ATP (Week 8) = 75 – (0) = 75
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Chapter 11 - Aggregate Planning and Master Scheduling
23.
Given:
The forecasts and customer orders for the next five periods are shown below:
Period
Forecast
Customer Orders
1
80
82
2
80
80
3
60
60
4
60
40
5
60
20
Beginning inventory = 20 units.
The company uses a chase strategy for determining production lot size, except there is an upper
limit on the lot size of 70 units. The desired safety stock is 10 units. Note: A negative projected
on-hand can occur.
The calculations for MPS and projected on-hand inventory are shown below:
Inventory From
Week Previous Week Requirements*
1
2
3
4
5
20
8
-2
8
10
82
80
60
60
60
Net
Inventory
before
MPS
Max. of
(70)
MPS
Projected
On-hand
Inventory
-62
-72
-62
-52
-50
70
70
70
62
60
8
-2
8
10
10
*Requirements equal the larger of forecast and customer orders in each week.
Net Inventory before MPS = Inventory from previous week – Current week’s
requirements.
Projected on-hand inventory = Inventory from previous week – Current week’s
requirements + Current week’s MPS.
Note: We need a MPS quantity whenever Net Inventory before MPS < 10 units.
Calculations for projected on-hand inventory:
Week 1:
Net Inventory before MPS = 20 – 82 = -62. Warning: This is below the desired safety
stock of 10 units. We need 72 units to increase projected on-hand inventory to the desired
safety stock of 10 units; however, the MPS is capped at 70. Therefore, we plan a MPS of
70.
-62 + 70 = 8.
Week 2:
Net Inventory before MPS = 8 – 80 = -72. Warning: This is below the desired safety
stock of 10 units. We need 82 units to increase projected on-hand inventory to the desired
safety stock of 10 units; however, the MPS is capped at 70. Therefore, we plan a MPS of
70.
-72 + 70 = -2.
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Week 3:
Net Inventory before MPS = -2 – 60 = -62. Warning: This is below the desired safety
stock of 10 units. We need 72 units to increase projected on-hand inventory to the desired
safety stock of 10 units; however, the MPS is capped at 70. Therefore, we plan a MPS of
70.
-62 + 70 = 8.
Week 4:
Net Inventory before MPS = 8 – 60 = -52. Warning: This is below the desired safety
stock of 10 units. We need 62 units to increase projected on-hand inventory to the desired
safety stock of 10 units. Therefore, we plan a MPS of 62.
-52 + 62 = 10.
Week 5:
Net Inventory before MPS = 10 – 60 = -50. Warning: This is below the desired safety
stock of 10 units. We need 60 units to increase projected on-hand inventory to the desired
safety stock of 10 units. Therefore, we plan a MPS of 60.
-50 + 60 = 10.
The final MPS is shown below:
Beg. Inv. = 20
1
80
2
80
Week
3
4
60 60
5
60
40
20
10
10
62
22
60
40
Forecast
Customer
82 80 60
Orders
Projected onhand
8 -2 8
inventory
MPS
70 70 70
ATP
8 -10 10
ATP (first period) = Beginning inventory + MPS (first period) – sum of customer orders
until (but not including) the period of the next MPS.
ATP (other periods) = MPS (current period) – sum of customer orders until (but not
including) the period of the next MPS.
*We calculate ATP in the first period and in all other periods with MPS quantities.
ATP (Week 1) = 20 + 70 – (82) = 8
ATP (Week 2) = 70 – (80) = -10
ATP Week 3 = 70 – (60) = 10
ATP (Week 4) = 62 – (4) = 22
ATP (Week 5) = 60 – (20) = 40
11-47
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Case: Eight Glasses a Day
Given:
Forecasts:
Month
Forecast
May Jun Jul Aug Sept Oct Total
50
60
70
90
80
70
420
Costs (all costs are in thousands of dollars):
Regular production cost = $1 per tankload
Regular production capacity = 60 tankloads
Overtime production cost = $1.6 per tankload
Subcontracting cost = $1.8 per tankload
Holding cost = $2 per tankload per month
Beginning inventory = 0 tankloads
Backlogs are not allowed.
1.
Select the plan that has the lowest costs:
Strategy 1: Level production supplemented by up to 10 tankloads a month from overtime.
Total Demand = 420 units. We have regular time capacity = 60 tankloads per month = 6 months *
6 tankloads/month = 360 tankloads over the 6-month plan. We will need to use overtime for 420
– 360 = 60 tankloads. Given that overtime is limited to 10 tankloads/month, we will plan
overtime of 10 tankloads each month. The plan using overtime is shown below:
Period
Forecast
Output
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
@
@
@
@
@
@
1
1.6
1.8
2
May
50
Jun
60
Jul
70
Aug
90
Sept
80
Oct
70
Total
420
60
60
60
60
60
60
10
10
10
10
10
10
20
10
0
-20
-10
0
360
0
60
0
0
20
10
0
20
30
25
0
30
30
30
0
30
10
20
0
10
0
5
0
0
0
0
0
90
0
$60
$0
$16
$0
$60
$0
$16
$0
$60
$0
$16
$0
$60
$0
$16
$0
$60
$0
$16
$0
$60
$0
$16
$0
$20
$0
$96
$50
$0
$126
$60
$0
$136
$40
$0
$116
$10
$0
$86
$0
$0
$76
$360
$0
$96
$0
$0
$180
$0
$636
Conclusion: Total cost = $636,000.
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Strategy 2: Level production with a combination of overtime, inventory, and
subcontracting.
Total Demand = 420 units. We have regular time capacity = 60 tankloads per month = 6 months *
6 tankloads/month = 360 tankloads over the 6-month plan. We will need to use overtime or
subcontracting for 420 – 360 = 60 tankloads. Overtime is limited to 10 tankloads/month. The key
is to focus on the peak month (August).
Overtime costs $1.6 per tankload while subcontracting costs $1.8 per tankload. Therefore, in a
given month, we prefer using overtime over subcontracting. When would it make sense to use
subcontracting instead of overtime? If we use overtime 1 month early to meet demand in the
current month, the cost per tankload = $1.6 + $2 = $3.6. Therefore, if the choice is to produce a
tankload 1 month early or to subcontract it in the current month, we prefer to subcontract it in the
current month. This means that if we exhaust overtime in the current month, we would prefer to
subcontract in the current month over using overtime in earlier months to meet the excess demand
in the current month.
Period
Forecast
Output
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
@
@
@
@
@
@
1
1.6
1.8
2
May
50
Jun
60
Jul
70
Aug
90
Sept
80
Oct
70
Total
420
60
60
60
60
60
60
10
10
0
10
0
360
0
30
30
0
20
0
10
0
-10
10
20
0
0
10
5
0
10
10
10
0
10
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
$60
$0
$0
$0
$60
$0
$0
$0
$60
$0
$0
$0
$60
$0
$16
$36
$60
$0
$16
$18
$60
$0
$16
$0
$10
$0
$70
$20
$0
$80
$10
$0
$70
$0
$0
$112
$0
$0
$94
$0
$0
$76
$360
$0
$48
$54
$0
$40
$0
$502
Conclusion: Total cost = $502,000.
11-49
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
Strategy 3: Level production supplemented by up to 15 tankloads a month from overtime.
Total Demand = 420 units. We have regular time capacity = 60 tankloads per month = 6 months *
6 tankloads/month = 360 tankloads over the 6-month plan. We will need to use overtime for 420
– 360 = 60 tankloads. The key is to focus on the peak month (August). The plan using a
maximum of 15 tankloads of overtime in a period is shown below:
Period
Forecast
Output
Regular
Part Time
Overtime
Subcontract
Output - Forecast
Inventory
Beginning
Ending
Average
Backlog
Costs:
Regular
Part Time
Overtime
Subcontract
Hire/Layoff
Inventory
Back orders
Total
@
@
@
@
@
@
1
1.6
1.8
2
May
50
Jun
60
Jul
70
Aug
90
Sept
80
Oct
70
Total
420
60
60
60
60
60
60
5
15
15
15
10
10
5
5
-15
-5
0
360
0
60
0
0
0
10
5
0
10
15
13
0
15
20
18
0
20
5
13
0
5
0
3
0
0
0
0
0
50
0
$60
$0
$0
$0
$60
$0
$8
$0
$60
$0
$24
$0
$60
$0
$24
$0
$60
$0
$24
$0
$60
$0
$16
$0
$10
$0
$70
$25
$0
$93
$35
$0
$119
$25
$0
$109
$5
$0
$89
$0
$0
$76
$360
$0
$96
$0
$0
$100
$0
$556
Conclusion: Total cost = $556,000.
Summary of Strategies & Costs:
1) Level production with overtime (maximum of 10 tankloads/month): $636,000
2) Level production with overtime (maximum of 10 tankloads/month & subcontracting): $502,000
3) Level production with overtime (maximum of 15 tankloads/month): $556,000
Conclusion: Strategy 2 is preferred because it has the lowest cost ($502,000).
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Education.
Chapter 11 - Aggregate Planning and Master Scheduling
2.
Suppliers would need to know projections of initial demand and demand growth over time, and
product characteristics that would relate to new materials and new methods so they could prepare
for the new line. They, in turn, would need to collaborate with their suppliers. Transportation
partners would need to be made aware of changes in transportation requirements. Information
sharing is important to ensure that supply partners can adjust to the changes. However, ideally,
supply chain partners should be consulted prior to committing to a new line so that they can
contribute ideas and any cautions.
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