Demand

Jan Feb Mar

Demand for week 1 459 398 566
Demand for week 2 456 402 602
Demand for week 3 421 505 444
Demand for week 4 464 445 438
Forecasted demand 1,800 1,750 2,050

Costs of Four Production Plans

Jan Feb Mar

Opening stock of finished goods 350
Forecasted demand 1,800 1750 2,050
Working days available per month 22 24 26

Aggregate Production Planning Requirements

Jan Feb Mar

Opening stock of finished goods = 350 360 350
Forecasted demand = 1,800 1750 2050
Safety stock = 20% of forecasted demand = 360 350 410
Production requirement = forecast + safety stock – opening stock = 1,810 1,740 2,110
Closing stock = opening stock + actual prod requirement – forecast = 360 350 410

Cost Information

Production hours available per day 8 Hours per day

Required labour hours 4 Hours per unit
Initial number of labourers in the month of January 40 Labourers
Hiring cost of labourer 150 US$ per labourer
Layoff cost of labourer 250 US$ per labourer
Regular cost of labourer (first 8 hours) 10 US$ per hour
Overtime cost of labourer (beyond 8 hours) 15 US$ per hour
Cost of material 175 US$ per unit
Inventory carrying cost 2 US$ per unit per month
Inventory shortage cost 5 US$ per unit per month
Cost of subcontracting 225 US$ per unit

Options for Production Plans

OPTION 1—CHASE PRODUCTION (PRODUCTION AS PER DEMAND); HIRE AND LAY OFF LABOUR

Jan Feb Mar

Final computed production requirement 1,810 1,740 2,110
Production time needed for each unit in hours 4 4 4
Total production (prod) hours required = prod requirement × prod time per unit 7,240 6,960 8,440
Working days available per month 22 24 26
Working hours available per day 8 8 8
Hours available per labourer per month = working days × working hours per day 176 192 208
Labour available on roll 40 42 37
Labour required = prod hours ÷ hours available per labourer/month 41.14 36.25 40.58
Number of labourers needed (rounding up) 42 37 41
Labour hired = labourers needed ‒ available 2 0 4
Hiring cost per labour 150 150 150
Labour hiring cost = labour × hiring cost per labourer 300 0 600
Number of labourers laid off = labourers available ‒needed 0 5 0
Firing cost per labour 250 250 250
Labour layoff cost = labourers laid off × firing cost per labourer 0 1,250 0
Labour cost per hour for first eight hours 10 10 10
Cost of production = prod hour × labour cost per hour 72,400 69,600 84,400
Total cost = prod cost + hiring cost + layoff cost 72,700 70,850 85,000

OPTION 2—MANAGE AND VARY THE INVENTORY, CONSTANT LABOUR FORCE

Total demand for the year 26,225

Hours per unit of demand 4
Working days available for the year 285
Production hours per day 8
Total production hours needed = demand × hours per unit 104,900
Total production hours available = days × hours per day 2,280
Total number of workers needed = production hours needed ÷ hours available 46

Jan Feb Mar

Opening stock of finished good 350 575 1,034
Working days available per month 22 24 26
Number of labourers available 46 46 46
Working hours available per day 8 8 8
Production hours available = working days × labourers × working hours/day 8,098 8,834 9,570
Production time needed for each unit in hours 4 4 4
Production done = production hours ÷ production time in hours per unit 2,025 2,209 2,393
Forecasted demand 1,800 1,750 2,050
Closing stock = opening stock + production done ‒ forecasted demand 575 1,034 1,377
Shortage (yes or no) No No No
Unit shortage 0 0 0
Marginal shortage cost per unit 5 5 5
Shortage cost = unit shortage × marginal cost of shortage 0 0 0
Safety stock to be maintained 360 350 410
Overstock = closing stock ‒ safety stock 215 684 967
Inventory cost per unit 2 2 2
Inventory cost = overstock × inventory cost per unit 430 1,368 1,934
Labourer cost per hour for first eight hours 10 10 10
Cost of production (prod) = prod hour × lab cost per hour 80,975 88,337 95,698
Total cost = cost of shortage + cost of overstock + cost of production 81,405 89,705 97,632
*(Sum of production requirement × 4 hours/unit) ÷ ( Sum of production hours available × 8 hours/day) =
(26,225 × 4) ÷ (285 × 8) = 46

OPTION 3—SUBCONTRACT, WITH CONSTANT MINIMUM LABOUR FORCE

Lowest demand figure for the year 1,600

Hours per unit of demand 4
Working days available in the month of April 26
Production hours per day 8
Total production hours needed = demand × hours per unit 6,400
Total production hours available = days × hours per day 208
Total number of workers needed = production hours needed ÷ hours available 31

Cost of subcontracting per unit (US$) 225

Cost of material per unit (US$) 175
Marginal cost of subcontracting = cost of subcontracting ‒ cost of material 50

Jan Feb Mar

Production requirement 1,800 1,750 2,050
Working days available per month 22 24 26
Number of labourers 31 31 31
Working hours per day 8 8 8
Production (prod) hours available = working days × labourers × working hours/day 5,415 5,908 6,400
Production time needed for each unit in hours 4 4 4
Actual prod = prod hours available ÷ hours per unit 1,354 1,477 1,600
Number of units subcontracted = prod requirement ‒ actual production 446 273 450
Marginal cost of subcontracting per unit 50 50 50
Subcontracting cost = marginal sc cost × number of subcontract units 22,308 13,654 22,500
Labourer cost per hour for first eight hours 10 10 10
Cost of production = prod hour × labourer cost per hour 54,154 59,077 64,000
Total cost = cost of prod + cost of subcontracting 76,462 72,731 86,500
*Minimum production requirement in this example is a minimum of 1,600 units. Number of workers required
for June is: (1,600 × 4) ÷ (26 × 8) = 31

OPTION 4—OVERTIME, WITH CONSTANT LEVEL OF LABOUR FORCE (START WITH 40 LABOURERS, JANUARY)

Jan Feb Mar

Opening stock of finished goods 350 310 480
Working days available per month 22 24 26
Working hours per day 8 8 8
Labourers available 40 40 40
Production (prod) hours available = working days per month × number of labourers 7,040 7,680 8,320
Production time needed for each unit in hours 4 4 4
Actual production = prod hours available ÷ hours per unit 1,760 1,920 2,080
Forecasted demand 1,800 1,750 2,050
Closing stock = opening stock + actual prod ‒ forecasted demand 310 480 510
Overtime needed (yes or no) No No No
Overtime production units 0 0 0
Overtime prod hours = overtime prod units × hours per unit 0 0 0
Overtime labourer cost per hour (over eight hours) 15 15 15
Overtime cost of labour for producing beyond regular production 0 0 0
Safety stock to be kept 360 350 410
Overstock = regular prod capacity ‒ safety stock 0 130 100
Inventory cost per unit 2 2 2
Total inventory cost = closing stock × inventory cost per unit 620 960 1,020
Labourer cost per hour for first eight hours 10 10 10
Cost of production = production hour × labour cost per hour 70,400 76,800 83,200
Total cost = cost of prod + inventory cost + overtime labourer cost 71,020 77,760 84,220

OPTION 5—LEVEL PRODUCTION (AVERAGE OF COMPUTED PRODUCTION REQUIREMENTS), HIRE AND LAY OFF LABOURers

Jan Feb Mar

Opening stock of finished goods 350 360 350
Forecasted demand 1,800 1,750 2,050
Safety stock = 20% of forecasted demand 360 350 410
Production requirement = forecast + safety stock ‒ opening stock 1810 1740 2110
Closing stock = opening stock + actual production requirement ‒forecast 360 350 410

Jan Feb Mar

Final computed production requirement 1,810 1,740 2,110
 Jan Feb Mar
Final computed production requirement 1,810 1,740 2,110
Average production carried out every month ‒ level production 2,193 2,193 2,193
Production (prod) time needed for each unit in hours 4 4 4
Total prod hours required = prod requirement × prod time per unit 8,772 8,772 8,772
Working days available per month 22 24 26
Working hours available per day 8 8 8
Hours available per labourer per month = working days × working hours per day 176 192 208
Labourers available on roll 40 50 46
Labourer required = prod hours ÷ hours available per labourer per month 49.84 45.69 42.17
Number of labourers needed (rounding up) 50 46 43
Labourer hired = labourers needed ‒ available 10 0 0
Hiring cost per labourer 150 150 150
Labourer hiring cost = labourer hired × hiring cost per labourer 1,500 0 0
Number of labourers laid off = labourer available ‒ needed 0 4 3
Layoff cost per labourer 250 250 250
Labourer layoff cost = labourer × layoff cost per labourer 0 1,000 750
Labourer cost per hour for first eight hours 10 10 10
Cost of production = prod hour × labourer cost per hour 87,717 87,717 87,717
Total cost = prod cost + hiring cost + layoff cost 89,217 88,717 88,467

SUMMARY OF ALL THE FIVE PRODUCTION PLANS

COST HEADS OPTION 1 OPTION 2 OPTION 3

CHASE INVENTORY SUBCONTRACT
Total cost of hiring labourers 9,600
Total cost of laying off labourers 14,750
Total cost of holding inventory 24,278
Total cost of stockout/shortages 0
Total cost of subcontracting 434,327
Total labourer overtime cost
Total cost of production 1,052,600 1,049,000 701,538
Grand total of all cost components 1,076,950 1,073,278 1,135,865
Apr May Jun July Aug Sep Oct Nov Dec Total
794 333 290 499 564 702 788 606 589 6,588
442 572 382 402 478 589 678 719 444 6,166
788 433 467 345 514 602 777 790 561 6,647
676 562 461 454 644 657 557 860 606 6,824
2,700 1,900 1,600 1,700 2,200 2,550 2,800 2,975 2,200 26,225

Apr May Jun July Aug Sep Oct Nov Dec Total

2,700 1,900 1,600 1,700 2,200 2,550 2,800 2,975 2,200 26,225
25 24 26 24 25 24 20 22 23 285

Apr May Jun July Aug Sep Oct Nov Dec Total
410 540 380 320 340 440 510 560 595 5155
2700 1900 1600 1700 2200 2550 2800 2975 2200 26225
540 380 320 340 440 510 560 595 440 5245
2,830 1,740 1,540 1,720 2,300 2,620 2,850 3,010 2,045 26315
540 380 320 340 440 510 560 595 440 5245
Apr May Jun July Aug Sep Oct Nov Dec Total
2,830 1,740 1,540 1,720 2,300 2,620 2,850 3,010 2,045 26,315
4 4 4 4 4 4 4 4 4 4
11,320 6,960 6,160 6,880 9,200 10,480 11,400 12,040 8,180 105,260
25 24 26 24 25 24 20 22 23 285
8 8 8 8 8 8 8 8 8 8
200 192 208 192 200 192 160 176 184 2,280
41 57 37 30 36 46 55 72 69
56.60 36.25 29.62 35.83 46.00 54.58 71.25 68.41 44.46
57 37 30 36 46 55 72 69 45
16 0 0 6 10 9 17 0 0
150 150 150 150 150 150 150 150 150 150
2,400 0 0 900 1,500 1,350 2,550 0 0 9,600
0 20 7 0 0 0 0 3 24
250 250 250 250 250 250 250 250 250 250
0 5,000 1,750 0 0 0 0 750 6,000 14,750
10 10 10 10 10 10 10 10 10 10
113,200 69,600 61,600 68,800 92,000 104,800 114,000 120,400 81,800 1,052,600
115,600 74,600 63,350 69,700 93,500 106,150 116,550 121,150 87,800 1,076,950
Apr May Jun July Aug Sep Oct Nov Dec Total
1,377 978 1,287 2,080 2,589 2,690 2,349 1,390 440
25 24 26 24 25 24 20 22 23 285
46 46 46 46 46 46 46 46 46 46
8 8 8 8 8 8 8 8 8
9,202 8,834 9,570 8,834 9,202 8,834 7,361 8,098 8,466
4 4 4 4 4 4 4 4 4
2,301 2,209 2,393 2,209 2,301 2,209 1,841 2,025 2,117
2,700 1,900 1,600 1,700 2,200 2,550 2,800 2,975 2,200
978 1,287 2,080 2,589 2,690 2,349 1,390 440 357
No No No No No No No No No
0 0 0 0 0 0 0 0 0
5 5 5 5 5 5 5 5 5
0 0 0 0 0 0 0 0 0 0
540 380 320 340 440 510 560 595 440
438 907 1,760 2,249 2,250 1,839 830 0 0
2 2 2 2 2 2 2 2 2
876 1,814 3,520 4,498 4,500 3,678 1,660 0 0 24,278
10 10 10 10 10 10 10 10 10
92,018 88,337 95,698 88,337 92,018 88,337 73,614 80,975 84,656 1,049,000
92,894 90,151 99,218 92,835 96,518 92,015 75,274 80,975 84,656 1,073,278
Apr May Jun July Aug Sep Oct Nov Dec Total
2,700 1,900 1,600 1,700 2,200 2,550 2,800 2,975 2,200 26,225
25 24 26 24 25 24 20 22 23 285
31 31 31 31 31 31 31 31 31
8 8 8 8 8 8 8 8 8
6,154 5,908 6,400 5,908 6,154 5,908 4,923 5,415 5,662
4 4 4 4 4 4 4 4 4
1,538 1,477 1,600 1,477 1,538 1,477 1,231 1,354 1,415
1,162 423 0 223 662 1,073 1,569 1,621 785
50 50 50 50 50 50 50 50 50
58,077 21,154 0 11,154 33,077 53,654 78,462 81,058 39,231 434,327
10 10 10 10 10 10 10 10 10
61,538 59,077 64,000 59,077 61,538 59,077 49,231 54,154 56,615 701,538
119,615 80,231 64,000 70,231 94,615 112,731 127,692 135,212 95,846 1,135,865

Apr May Jun July Aug Sep Oct Nov Dec Total
510 0 20 500 720 520 0 0 0
25 24 26 24 25 24 20 22 23 285
8 8 8 8 8 8 8 8 8
40 40 40 40 40 40 40 40 40
8,000 7,680 8,320 7,680 8,000 7,680 6,400 7,040 7,360
 4 4 4 4 4 4 4 4 4
2,000 1,920 2,080 1,920 2,000 1,920 1,600 1,760 1,840
2,700 1,900 1,600 1,700 2,200 2,550 2,800 2,975 2,200
-190 20 500 720 520 -110 -1,200 -1,215 -360
Yes No No No No Yes Yes Yes Yes
190 0 0 0 0 110 1,200 1,215 360
760 0 0 0 0 440 4,800 4,860 1,440
15 15 15 15 15 15 15 15 15
11,400 0 0 0 0 6,600 72,000 72,900 21,600 184,500
540 380 320 340 440 510 560 595 440
0 0 180 380 80 0 0 0 0 Have calculated as Closing Stock - Safety Stock
2 2 2 2 2 2 2 2 2
0 40 1,000 1,440 1,040 0 0 0 0 6,120 Why??
10 10 10 10 10 10 10 10 10
80,000 76,800 83,200 76,800 80,000 76,800 64,000 70,400 73,600 912,000
91,400 76,840 84,200 78,240 81,040 83,400 136,000 143,300 95,200 1,102,620

Apr May Jun July Aug Sep Oct Nov Dec Total
410 540 380 320 340 440 510 560 595 5,155
2,700 1,900 1,600 1,700 2,200 2,550 2,800 2,975 2,200 26,225
540 380 320 340 440 510 560 595 440 5,245
2830 1740 1540 1720 2300 2620 2850 3010 2045 26,315
540 380 320 340 440 510 560 595 440 5,245

Apr May Jun July Aug Sep Oct Nov Dec Total
2,830 1,740 1,540 1,720 2,300 2,620 2,850 3,010 2,045 26,315
MONTHS 12
AVERAGE PROD / MONTH 2,193
 Apr May Jun July Aug Sep Oct Nov Dec Total
2,830 1,740 1,540 1,720 2,300 2,620 2,850 3,010 2,045 26,315
2,193 2,193 2,193 2,193 2,193 2,193 2,193 2,193 2,193 26,315
4 4 4 4 4 4 4 4 4
8,772 8,772 8,772 8,772 8,772 8,772 8,772 8,772 8,772
25 24 26 24 25 24 20 22 23
8 8 8 8 8 8 8 8 8
200 192 208 192 200 192 160 176 184
43 44 46 43 46 44 46 55 50
43.86 45.69 42.17 45.69 43.86 45.69 54.82 49.84 47.67
44 46 43 46 44 46 55 50 48
1 2 0 3 0 2 9 0 0
150 150 150 150 150 150 150 150 150
150 300 0 450 0 300 1,350 0 0 4,050
0 0 3 0 2 0 0 5 2
250 250 250 250 250 250 250 250 250
0 0 750 0 500 0 0 1,250 500 4,750
10 10 10 10 10 10 10 10 10
87,717 87,717 87,717 87,717 87,717 87,717 87,717 87,717 87,717 1,052,600
87,867 88,017 88,467 88,167 88,217 88,017 89,067 88,967 88,217 1,061,400

OPTION 4 OPTION 5
OVERTIME LEVEL
4,050
4,750
6,120

184,500
912,000 1,052,600
1,102,620 1,061,400
osing Stock - Safety Stock