Presentation aggregate planning

CHAPTER 3:AGGREGATE PRODUCTION PLANNINGAna Gómiz AragónLaura Rodríguez-León RodríguezManuela Valera Ortega

Group 12

Aggregate planning (aggregate scheduling)

Determining the quantity and timing of production for the intermediate future (3 to

18 months).Adjusting production rates, labour levels, inventory levels, overtime work, subcontracting rates...

IN ORDER TO...

Determine the best way to meet forecasted demand and

minimise cost over the planning period

PREVIOUS KNOWLEDGE…

1

1. Introduction to Aggregate Planning

2. Aggregate Planning strategies

3. The process of Aggregate Planning

4. Methods for Aggregate Planning

5. Aggregate Planning in services

CHAPTER 3AGGREGATE PRODUCTION PLANNING

2

Strategies to obtain an aggregate plan

Pure

Mixed

Pure strategies

Chase strateg

y

Level strateg

y

Level strategy

Level of regular

production

Level of total production

3. THE PROCESS OF AGGREGATE PLANNING

3

Strategies to obtain an aggregate

plan

Pure (one objective)

Chase Strategy

Mixed (multiple

objectives)

Objective: sets production equal to forecasted demand.

𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝑃𝑒𝑟𝑖𝑜𝑑

=𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑒𝑑𝑑𝑒𝑚𝑎𝑛𝑑

𝑃𝑒𝑟𝑖𝑜𝑑


4

Assume you are the operations manager of a firm that carries a single family of products. To obtain a unit of the family we need 1.5 hours (standard hours) of workforce and each worker’s shift is 8 h. a day. At this moment, December, the workforce of the firm is 150 workers (50 permanent and 100 temporary) and, although the security stock desired is 500 units, the available stock is zero.

DATA: 1.5 hours per unit (standards h) Worker’s shift 8h a day per Workforce 150 workers

50 permanent 100 temporary

Security stock desired 500 units Available stock 0

EXAMPLE OF AGGREGATE PLANNING

5

Cost information:• Materials per unit of product: 5,000 m.u.• Standard hour of regular time labor: 1,000 m.u.• Standard hour of overtime labor: 1,500 m.u.• Standard hour of idle time: 1,100 m.u.• Hiring: 100,000 m.u./worker• Layoff of a temporary worker: 150,000 m.u.• Subcontracting cost per unit: 1,000 m.u., over the regular production cost

of one unit.• Inventory or carrying cost: 200 m.u./unit and month. Cim = Ciu (Iem +

Ibm)/2• Back order cost: 1,500 m.u./ unit and month.

Other factors that need to be considered to develop an aggregate planning, are the company policies: • There are three shifts and the maximum number of workers that can work

simultaneously is 50. Therefore, there is a maximum of 1,200 h/day (150 workers x 8 h/day and worker).

• The maximum number of overtime hours allowed is 10% of the hours available in regular time.

• Permanent workers cannot be laid off.• All the costs are linear functions.• The daily demand, within each month, is uniform and continuous.

6

TABLE 1. NECESSARY PRODUCTION PLAN AND PRODUCTION DAYSEXAMPLE OF HOW TO CALCULATE THE FORECASTED DEMAND.

Demand forecast for next year, obtained with the information provided by the marketing department

7


Additional information obtained from client portfolios

The demand forecast needs to

be corrected using this information

Orders already placed by the clients in the first two month

Demand that has not been satisfied from previous periods and that need to be

satisfied as soon as possible, so they need to be considered as real demand for

January

8


Other sources of demand. The quantity needed to satisfy the security stock

9


Necessary production for each month

10


The necessary production for each month

11


The production days of each month

12

𝑀𝑎𝑥𝑖𝑚 .𝑑𝑎𝑖𝑙𝑦 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛=150𝑤𝑜𝑟𝑘∗8h/𝑑𝑎𝑦 (𝑎𝑛𝑑𝑤𝑜𝑟𝑘𝑒𝑟 )

1.5h/𝑢𝑛=800𝑢𝑛 /𝑑𝑎𝑦

1,200 h./day

Monthly production equal to the necessary production.

Adjusting capacity by varying workforce levels through hiring or laying off (use of idle time due to restrictions in the layoff of permanent workers) and backorders. REGULAR PRODUCTION = necessary production with the

limit of the maximum daily production

Total number of workers

Worker’s shift

Standard hours needed to obtain a unit of the family

ALTERNATIVE 1:CHASE STRATEGY

13

FEB: 800 * 20 = 16,000 un. We need 15,000 un.

MAR: 800 * 22 = 17,600 un. We need 10,000 un.

APR: 800 * 20 = 16,000 un. We need 5,000 un.

MAY: 800 * 22 = 17,600 un. We need 5,000 un.

JUN: 800 * 21 = 16,800 un. We need 5,000 un.

JUL: 800 * 20 = 16,000 un. We need 10,000 un.

AUG: 800 * 22 = 17,600 un. We need 5,000 un.

SEP: 800 * 22 = 17,600 un. We need 5,000 un.

OCT: 800 * 20 = 16,000 un. We need 10,000 un.

NOV: 800 * 21 = 16,800 un. We need 15,000 un.

DEC: 800 * 20 = 16,000 un. We need 20,000 un.

The production days of each monthMaxim. Daily production

Nece

ssary

pro

du

ctio

n f

or

each

m

on

th

𝐽𝐴𝑁=800𝑢𝑛𝑑𝑎𝑦

×20𝑑𝑎𝑦𝑠=16,000𝑢𝑛

Maxim. Daily production The production days of each month

We only need 15,000 un. (Production Necessity)

14

HOURS OF REGULAR PRODUCTION = Regular production * h/un.

JAN, FEB , NOV:

15,000 un. * 1.5 h./un.=22,500 h.

MAR, JUL, OCT:

10,000 un. * 1.5 h./un.=15,000 h.

APR, MAY, JUN, AUG, SEP:

5,000 un. * 1.5 h./un.= 7,500 h.

DEC:

16,000 un. (maximum possible)* 1.5 h./un.= 24,000 h.

Forecast Standard hours needed to obtain a unit of the family

20,000

15

WORKFORCE

JAN: 22,500 h. / (8 h./day and work. * 20 days) = 140.625 = 141 work.

FEB: 22,500 / (8 * 20) = 140.625 = 141 work.

MAR: 15,000 / (8 * 22) = 85.23 = 86 work.

ABR: 7,500 / (8 * 20) = 46.875 = 47 work. X

MAY: 7,500 / (8 * 22) = 42.61 = 43 work. X

JUN: 7,500 / (8 * 21) = 44.64 = 45 work. X

JUL: 15,000 / (8 * 20) = 93.75 = 94 work.

AUG: 7,500 / (8 * 22) = 42.61 = 43 work. X

SEP: 7,500 / (8 * 22) = 42.61 = 43 work. X

OCT: 15,000 / (8 * 20) = 93.75 = 94 work.

NOV: 22,500 / (8 * 21) = 133.93 = 134 work.

DEC: 24,000 / (8 * 20) = 150 work.

50 workers; permanent workforceWorkforce 150

workers• 50 permanent • 100 temporaty

Note: The idle hours from the rounding are not considered to calculate the corresponging costs

16

REGULAR PRODUCTION COST =

JAN: 1,000 m.u. / h.

22,500 h. * 1,000 m.u./ h. = 22,500,000 m.u. = 22,500 t.m.u.

The same way for the remaining months. VARIATION IN THE WORKFORCE =

Difference between the number of workers in this month and the previous one.

If positive, it implies hiring. If negative, it implies laying off.

JAN: 141 workwers /JAN – 150 work./BEGINNING(Dec) = -9 work.

17

FEB: 141-141 = 0 work.

MAR: 86-141 = -55 work.

APR: 50-86 = -36 work.

MAY: 50-50 = 0 work.

JUN: 50-50 = 0 work.

JUL: 94-50 = 44 work.

AUG: 50-94 = -44 work.

SEP: 50-50 = 0 work.

OCT: 94-50= 44 work.

NOV: 134-94= 40 work.

DEC: 150-134= 16 work.

18

COST OF HIRING AND LAYING OFF =

Cost of Hiring= 100,000 m.u. / work.Cost of Layoff =150,000 m.u./ work.

JAN: 9 work. * 150,000 m.u./ work. = 1,350,000 u.m. = 1,350 t.m.u.

MAR: 55 work. * 150,000 m.u./ work. = 8,250,000 m.u.

APR: 36 work. * 150,000 m.u./ work. = 5,400,000 m.u.

AUG: 44 work. * 150,000 m.u./ work. = 6,600,000 m.u.

JUL: 44 work. * 100,000 m.u./ work. = 4,400,000 m.u.

OCT: 44 work. * 100,000 m.u./ work.= 4,400,000 m.u.

NOV: 40 work. * 100,000 m.u./ work. = 4,000,000 m.u.

DEC: 16 work. * 100,000 m.u./ work. = 1,600,000 m.u.FEB, MAY, JUN, SEP: 0 t.m.u.

19

FINAL INVENTORY i =

If the final inventory < 0 = there is some production that is not satisfied and backordered.

DEC: 0 + 16,000 un– 20,000 un. = -4,000 un.

Necessary production of month i – final inventory (month i-1) = necessary production

Necessary production

Regular production

Production which is not satisfied and

backordered

20

COST OF INVENTORY PER MONTH

(Cim) = Ciu*(Iem+Ibm)/2 (or else (Cim)=Ciu*Iem)

COST OF BACKORDER =

un. and month (demand not covered)* m.u./un. and month

COST OF INVENTORY= 200 m.u./un. and month.

COST OF BACKORDER= 1,500 m.u./un. and month

DIC: |- 4,000 un.| * 1,500 m.u./un. and month = 6,000 t.m.u.

We don´t have it

Final inventory

21

APR: Workers needed: 47

Permanent workers: 50

Therefore we have 3 workers in idle time:

3 workers * 20 days * 8 h./day and work. =

480 h. (idle)

COST OF IDLE TIME (1,100 m.u./h.):

480 h. * 1,100 m.u./h. = 528 t.m.u.

MAY: hours: 7*22*8 = 1,232; cost:1,232*1,100 = 1,355.2 t.m.u.

JUN: hours: 5*21*8 = 840; cost: 840* 1,100 = 924 t.m.u.

COST OF IDLE TIME=

Note: The idle hours from the rounding are not considered to calculate the corresponging costs

22

COST OF IDLE TIME=

We will have idle time everytime we have rounding of workers

JAN: Hours with current workforce

141 work. * 20 days * 8 h./day and work. =

22,560 h.

Hours regular production: 22,500 h.

Hours of idle time: 22,560 – 22,500 = 60 h.

COST OF IDLE TIME (1,100 m.u./h.):

ABR: 50*20*8 - 7,500 = 500;

Cost= 500*1,100 = 550 t.m.u.

60 h. * 1,100 m.u./h. = 66 t.m.u.

23

TC = 174,000 + 36,000 + 6,000 + 5,517.6 = 221,517.6 t.m.u.

Units produced on time for the customers (necessary production):JAN: 15,000 un.; FEB: 15,000 un.; MAR: 10,000; APR: 5,000 un.; MAY: 5,000 un.; JUN: 5,000 un.; JUL: 10,000 un.; AUG: 5,000 un.; SEP: 5,000 un.; OCT: 10,000 un.; NOV: 15,000 un.; DEC: 20,000 un./NEEDED -4,000/Inventory = 16,000;

TOTAL COST=

CUSTOMER SATISFACTION=

TOTAL sum = 116,000 un.

SERVICE LEVEL =

24

EXAMPLE OF AGGREGATE PLANNING

TABLE 2. ALTERNATIVE 1: CHASE STRATEGY

J F M A MY J JL AU S O N D TOTAL

Forecast 9.000 15.000 10.000 5.000 5.000 5.000 10.000 5.000 5.000 10.000 15.000 20.000 114.000

Orders placed 10.000 1.800

Backordered units 4.500

Security Stock 500

Necessary Production 15.000 15.000 10.000 5.000 5.000 5.000 10.000 5.000 5.000 10.000 15.000 20.000 120.000

Cumulative Production 15.000 30.000 40.000 45.000 50.000 55.000 65.000 70.000 75.000 85.000 100.000 120.000 120.000

Production Days 20 20 22 20 22 21 20 22 22 20 21 20 250

Regular Production 15.000 15.000 10.000 5.000 5.000 5.000 10.000 5.000 5.000 10.000 15.000 16.000 116.000

Overtime Production

Hours of Regular Prod. 22.500 22.500 15.000 7.500 7.500 7.500 15.000 7.500 7.500 15.000 22.500 24.000

Workforce 141 141 86 47/50 43/50 45/50 94 43/50 43/50 94 134 150

Cost of Regular Prod. 22.500 22.500 15.000 7.500 7.500 7.500 15.000 7.500 7.500 15.000 22.500 24.000 174.000

Variation of Workforce -9 0 -55 -36 0 0 44 -44 0 44 40 16

Cost of Hiring/Layoff 1.350 8.250 5.400 4.400 6.600 4.400 4.000 1.600 36.000

Overtime Hours

Cost of Overtime

Subcontracting Cost

Final Inventory 0 0 0 0 0 0 0 0 0 0 0 -4.000

Cost of inventory/backorder 6.000 6.000

Cost of idle time 528 1.355 924 1.355 1.355 5.518

Total cost 221.518

25

Factors to take into account:

Frequent layoffs could generate:

Insecurity.

Decrease in motivation.

Decrease in work satisfaction, and therefore, in productivity.

It may affect to the predictions made when elaborating the plan.

26



Level Strategy

Mixed (multiple objectives)

Objective: maintaining a constant output rate, production rate and therefore constant workforce level over the planning horizon.


27

Level strategy

Level of regular

production

Level of total production


28

The workforce and, therefore, the daily regular production will remain constant.

The production is adjusted by inventory variations.

REGULAR PRODUCTION = daily regular production x production days

ALTERNATIVE 2:LEVEL OF REGULAR PRODUCTION

Total necessary production

Total production days

29

FEB: 480*20 = 9,600 un. < 15,000 un.

MAR: 480*22 = 10,560 un. < 15,000 un.

APR: 480*20 = 9,600 un. < 10,000 un.

MAY: 480*22 = 10,560 un. > 5,000 un.

JUN: 480*21 = 10,080 un. > 5,000 un.

JUL: 480*20 = 9,600 un. < 10,000 un.

AUG: 480*22 = 10,560 un. > 5,000 un.

SEP: 480*22 = 10,560 un. > 5,000 un.

OCT: 480*20 = 9,600 un. < 10,000 un.

NOV: 480*21 = 10,080 un. < 15,000 un.

DEC: 480*20 = 9,600 un. < 20,000 un.

Production days per monthDaily regular production

Nece

ssary

pro

du

ctio

n p

er

month

Daily regular production Production days per month

Necessary production per month

30

HOURS OF REGULAR PRODUCTION = Regular production x h./un.

JAN, FEB, APR, JUL, OCT, DEC:

9,600 un. x 1.5 h./un. = 14,400 h.

MAR, MAY, AUG, SEP:

10,560 un. x 1.5 h./un. = 15,840 h.

JUN, NOV:

10,080 un. x 1.5 h./un. = 15,120 h.

31

Hours of regular production Standard hour of regular time labour

COST OF REGULAR PRODUCTION (WORKFORCE) = h. x m.u./h.

WORKFORCE =

Number of h./day = 480 un./day x 1.5 h./un. = 720 h./day

Number of workers = = 90 workers

The same for all the remaining months.

JAN

Daily regular production is always

480 un./day

32

VARIATION OF WORKFORCE = work. (i) – work. (i-1)

Difference between the number of workers in one month and the previous one. - If positive, it will imply hiring. - If negative, it will imply layoff.

JAN: 90 workers (JAN) – 150 workers (BEGINNING) = -60 workersFEB: 90 workers (FEB) – 90 workers (JAN) = 0 workers

The same for all the remaining months.

COST OF HIRING AND LAYOFF = m.u./worker x worker

Cost of hiring = 100,000 m.u./workerCost of layoff = 150,000 m.u./worker

JAN: 60 workers x 150,000 m.u./worker = 9,000 t.m.u.

Cost of hiring/layoff is zero in the remaining months.

33

FINAL INVENTORY i =

= final inventory (i-1) + regular production i – necessary production i

If the final inventory is less than zero, then there is production not satisfied and therefore backordered.

JAN: FI = 0 + 9,600 – 15,000 = -5,400 un.

FEB: FI = -5,400 + 9,600 – 15,000 = -10,800 un.

MAR: FI = -10,800 + 10,560 – 10,000 = -10,240 un.

APR: FI = -10,240 + 9,600 – 5,000 = -5,640 un.

MAY: FI = -5,640 + 10,560 – 5,000 = -80 un.

JUN: FI = -80 + 10,080 – 5,000 = 5,000 un.

JUL: FI = 5,000 + 9,600 – 10,000 = 4,600 un.

AUG: FI = 4,600 + 10,560 – 5,000 = 10,160 un.

SEP: FI = 10,160 + 10,560 – 5,000 = 15,720 un.

OCT: FI = 15,720 + 9,600 – 10,000 = 15,320 un.

NOV: FI = 15,320 + 10,080 – 15,000 = 10,400 un.

DEC: FI = 10,400 + 9,600 – 20,000 = 0 un.

Final inventory

Nece

ssary

pro

du

ctio

n p

er

month

Regular production per month

34

JAN: 5,400 un. x 1,500 m.u./un. month = 8,100 t.m.u./month

FEB: 16,200 t.m.u.

MAR: 15,360 t.m.u.

APR: 8,460 t.m.u.

MAY: 120 t.m.u.

JUN: = 500 t.m.u.

JUL: 960 t.m.u.

AUG: 1,476 t.m.u.

SEP: 2,588 t.m.u.

OCT: 3,104 t.m.u.

NOV: 2,572 t.m.u.

DEC: 1,040 t.m.u.

COST OF INVENTORY AND BACKORDERCost of backorder = un. and month (demand not satisfied) x m.u./un. and month

Cost of inventory per month (Cim) =

Cost

of

back

ord

er

Cost

of

inven

tory

Negative final inventory (production not satisfied)

Inventory or carrying costs

Final inventory

Backorder costs

35

TOTAL COST

TC = 180,000 + 9,000 + 60,480 = 249,480 t.m.u.

CUSTOMER SATISFACTION (SERVICE LEVEL) =

SERVICE LEVEL =

UNITS PRODUCED ON TIME FOR THE CUSTOMERS = units needed - inventory

JAN: 9,600 un.

FEB: 4,200 un.

MAR: -240 un.

APR: -640 un.

MAY: 4,920 un.

JUN: 5,000 un.

TOTAL = 87,840 un.

JUL: 10,000 un.

AUG: 5,000 un.

SEP: 5,000 un.

OCT: 10,000 un.

NOV: 15,000 un.

DEC: 20,000 un.

The Alternative 1 is more

convenient

Cost of regular production Cost of hiring and layoff

Cost of inventory and backorder

36

37

TABLE 2. ALTERNATIVE 2: LEVEL OF REGULAR PRODUCTION

J F M A MY J JL AU S O N D TOTAL

Necessary Prod. Plan 15.000 15.000 10.000 5.000 5.000 5.000 10.000 5.000 5.000 10.000 15.000 20.000

120.000

Cum. Plan 15.000 30.000 40.000 45.000 50.000 55.000 65.000 70.000 75.000 85.000100.00

0120.00

0120.00

0

Prod. Days 20 20 22 20 22 21 20 22 22 20 21 20 250

Regular Prod. 9.600 9.600 10.560 9.600 10.560 10.080 960 10.560 10.560 9.600 10.080 9.600120.00

0

Overtime Prod.

Subcontracting (units)

Hours of Regular Prod. 14.400 14.400 15.840 14.400 15.840 15.120 14.400 15.840 15.840 14.400 15.120 14.400

Workforce 90 90 90 90 90 90 90 90 90 90 90 90

Cost of Regular Production 14.400 14.400 15.840 14.400 15.840 15.120 14.400 15.840 15.840 14.400 15.120 14.400

180.000

Variation of workforce -60 0 0 0 0 0 0 0 0 0 0 0

Cost of hiring and layoff 9.000 9.000

Overtime H.

Cost of overtime

Cost of subcontracting

Final Inventory -5.400 -10.800 -10.240 -5.640 -80 5.000 4.600 10.160 15.720 15.320 10.400 0

Cost of inventory and backorder 8.100 16.200 15.360 8.460 120 492 960 1.476 2.588 3.104 2.572 1.040 60.480

Cost of idle time

Total cost 249.48

0

Factors to take into account to satisfy the necessary production when using just regular production is not possible:

Cost of regular production:1,000 m.u./h. x 1.5 h./un. = 1,500 m.u./un.

Backordering costs 1,500 m.u./(un. month)and a decrease in the customer service level

Subcontracting leads to an incremental cost of 1,000 m.u./u.n.

Production on overtime leads to an incremental cost of:

Therefore, if there is lack of capacity, we have to use the alternative with lower incremental cost with respect to the regular production unit cost:

First, we will produce on overtime. Secondly, subcontracting. The last option, backordering.

38



Mixed (multiple objectives)

Mixed Alternative

Objective: sets production equal to forecasted demand.

𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝑃𝑒𝑟𝑖𝑜𝑑

=𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑒𝑑𝑑𝑒𝑚𝑎𝑛𝑑

𝑃𝑒𝑟𝑖𝑜𝑑


39

ALTERNATIVE 3: MIXED ALTERNATIVE

Objective: reduce () Total Cost of the first option.

Using the hiring and layoff rationally

We will maintain a constant workforce of 52 workers to avoid the cost of hiring and layoff…

in April, May, June, July, August and September

The remaining months we will use variation in the workforce if possible, avoiding the overtime production and subcontracting.

40

We start by laying off 9 workers and staying with 141 workers needed to produce 15,000 un. required in JAN and FEB

In MAR we layoff 55 workers (variation of the workforce,141-86) and we keep 86 workers to produce 10,000 units needed in that month.

In APR, MAY, JUN, JUL, AUG and SEP we layoff 34 workers and level the workforce with 52 workers (86-34) to face the total demand (or necessary production) in such interval (35,000 un.)(*)


Months Layoff Remaining workers

Units to produce

Jan and Feb 9 workers 141 workers 15,000 un.

Month Layoff Remaining workers

Units to produce

March 55 workers 86 workers 10,000 un.

Months Layoff Remaining workers

Units to produce

Apr, May, Jun, Jul, Aug and

Sep

34 workers 52 workers 35,000 un.

41


In OCT we hire 42 workers, having then a workforce of 94 (52+42) workers needed to satisfy the 10,000 un. of production of that month.

In NOV we hire 35 workers, having a total of 129 (94+35) workers, although a priori we need 134 workers to produce the 15.000 un. required that month which would require to hire 40 workers. The remaining units of production needed 15,000 un. -14,448 un. (21,672 h./1.5 h./un.), will be covered with available inventory, 2,228 (Iim)-1,676 (Ifm) =552, and therefore in DEC inventory will be 0.

The lack of production will be covered using overtime, and if it is not possible, subcontracting.

Month Hire Remaining workers

Units to produce

Oct 42 workers 94 workers 10,000 un.

Month Hire Remaining workers

Units to produce

Nov 35 workers 129 workers 15.000 un.

42

(*) from April to September…

NECESSARY PROD. 5,000 + 5,000 + 5,000 +10,000 + 5,000 + 5,000 = 35,000 un.

NECESSARY WORK HOURS 35,000 un. * 1.5 h./un. = 52,500 h.

NUMBER OF PRODUCTION DAYS 20 + 22 + 21 + 20 + 22 + 22 = 127 days

DAYLY HOURS NEEDED

WORKERS NEEDED A DAY


43

FEB: 141*8h *20. = 22,560 h.

MAR: 86 *8h *22 = 15,136 h.

APR: 52 *8h *20 = 8,320 h.

MAY: 52 *8h *22 = 9,152 h.

JUN: 52 *8h *21 = 8,736 h.

JUL: 52 *8h *20 = 8,320 h.

AUG: 52 *8h *22 = 9,152 h.

SEP: 52 *8h *22 = 9,152 h.

OCT: 94 *8h *20 = 15,040 h.

NOV: 129 *8h *21 = 21,672 h.

DEC: 129 *8h *20 = 20,640 h.

Production days per month

Daily regular production

Nr. of workers Production days per month

Hours of regular production per month

44

JAN: 141 workers * 8 h./(day and work) * 20 days = 22,560 h.

Hours of regular production per month

HOURS OF REGULAR PRODUCTION

REGULAR PRODUCTION

JAN: 22,560 h.e. / 1.5 h.e./un. = 15,040 un. > 15,000 un.

Hours of regular production Standard hours needed to obtain a unit of the family

Forecast

FEB: 22,560 h.e. / 1,5 h.e./un. = 15,040 un. > 15,000

MAR: 15,136 h.e. / 1,5 h.e./un. = 10,090 un. > 10,000

APR: 8,320 h.e. / 1,5 h.e./un. = 5,546 un. > 5,000

MAY: 9,152 h.e. / 1,5 h.e./un. = 6,101 un. > 5,000

JUN: 8,736 h.e. / 1,5 h.e./un. = 5,824 un. > 5,000

JUL: 8,320 h.e. / 1,5 h.e./un. = 5,546 un. < 10,000

AUG: 9,152 h.e. / 1,5 h.e./un. = 6,101 un. > 5,000

SEP: 9,152 h.e. / 1,5 h.e./un. = 6,101 un. > 5,000

OCT: 15,040 h.e. / 1,5 h.e./un. = 10,026 un. > 10,000

NOV: 21,672 h.e. / 1,5 h.e./un. = 14,448 un. < 15,000

DEC: 20,640 h.e. / 1,5 h.e./un. = 13,760 un. < 20,000

Overtime production

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OVERTIME PRODUCTION Necessary ProductionInventory available

JULY: Demand not satisfied = 10,000 – 5,546 – 2,601 = 1,813 un.

1,813 un. * 1.5 h./un. = 2,719.5 h. additional

Available overtime hours = 0.1 * 8320 h. = 832 overtime hours

Overtime hours (min between 832 and 2,719.5 = 832)

Overtime production: 832 O.H./1.5 h./un.) = 554 un.

There are still some necessary production not satisfied that we have to subcontract

1,813 un.- 554 un.=1,259 un.

Correct the slides!Inventory available = 2601

10% union contract

Hours of regular production

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OVERTIME PRODUCTION Necessary ProductionInventory available

NOV: Demand not satisfied = 15,000 – 14,448 – 2,228 = 1,676 un.

There is demand not satisfied but we can compensate it with the inventory available so we do not need to work overtime

DEC: Demand not satisfied = 20,000 – 13,760 – 1,676 = 4,564 un

4,564 un. * 1.5 h./un. = 6,846 h. additional

Available overtime hours = 0.1 * 20,640 h. = 2,064 overtime hours

Overtime hours (min between 6,846 and 2,064 = 2,064) Overtime production: 2,064 O.H./1.5 h./un.) = 1,376 un. There are still some necessary production not satisfied

that we have to subcontract

4,564 un.- 1376 un. = 3,188 un.

Necessary ProductionInventory available

10% union contract Hours of regular production

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FEB: 22,560 h. * 1,000 m.u./h. = 22,560 t.m.u

MAR: 15,136 h. * 1,000 m.u./h. = 15,136 t.m.u

APR: 8,320 h. * 1,000 m.u./h. = 8,320 t.m.u MAY: 9,152 h. * 1,000 m.u./h. = 9,152 t.m.u JUN: 8,736 h. * 1,000 m.u./h. = 8,736 t.m.u JUL: 8,320 h. * 1,000 m.u./h. = 8,320 t.m.u AUG: 9,152 h. * 1,000 m.u./h. = 9,152 t.m.u SEP: 9,152 h. * 1,000 m.u./h. = 9,152 t.m.u OCT: 15,040 h. * 1,000 m.u./h. = 15,040

t.m.u NOV: 21,672 h. * 1,000 m.u./h. = 21,672

t.m.u DEC: 20,640 h. * 1,000 m.u./h. = 20,640

t.m.u

COST OF REGULAR PRODUCTION

JAN:.

22,560 h. * 1,000 m.u./ h. = 22,560,000 m.u. = 22,500 t.m.u.

The same way for the remaining months.

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1,000 m.u. / h

h. * m.u./h.

JAN: 141 -150 = -9 work. (layoff) MAR: 86-141 = -55 work. (layoff) APR: 52-86 = -34 work. (layoff) OCT: 94-52 = 42 work. (hiring) NOV: 129-94 = 35 work. (hiring)

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VARIATIONS OF THE WORKFORCE (HIRING AND LAYOFF)

trab. (i) – trab. (i-1)

Difference between the number of workers in this month and the previous one.

If positive, If negative it implies hiring., it implies laying off.

COST OF HIRING AND LAYING OFF =

Cost of Hiring= 100,000 m.u. / work.Cost of Layoff =150,000 m.u./ work.

JAN: 9 layoff * 150,000 m.u./ work. = 1,350,000 u.m. = 1,350 t.m.u.

MAR: 55 layoff. * 150,000 m.u./ work. = 8,250,000 m.u.

APR: 34 layoff. * 150,000 m.u./ work. = 5,100,000 m.u.

OCT: 42 hired. * 100,000 m.u./ work.= 4,200,000 m.u.

NOV: 35 hired. * 100,000 m.u./ work. = 3,500,000 m.u.

FEB, MAY, JUN, SEP: 0 t.m.u.

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COST OF OVERTIMEm.u./O.H.*O.H.

JUL: 1,500 m.u./O.H. *832 O.H. = 1,248 t.m.u.

DEC: 1,500 m.u./O.H.* 2,064 O.H.= 3,096 t.m.u. Cost of

overtime

COST OF SUBCONTRACTING

Subcon. un.* (1.000 m.u. + cost of regular production).

JUL: Units to subcontract = 1,813 un. - 554 un. = 1,259 un.

Cost of regular production: 1,000 m.u./h. * 1.5 h./un. = 1,500 m.u./un.

Demand not satisfied

Production on overtime

Cost of subcontracting:

1,259 un.* (1,000 m.u./un. + 1,500 m.u./un.) = 3,147.5 t.m.u.DEC: Units to subcontract: 6,240 un.- 1,376-1,676 un.=3,188 un.

Cost of subcontracting:

3,188 un.* (1,000 m.u. + 1,500 m.u.) = 7,970 t.m.u.

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JAN: F.I.= 0 + 15,040 – 15,000 = 40 un. FEB: F.I. = 80 un. MAR: F.I. = 170 un. APR: F.I. = 716 un. MAY: F.I. = 1,817 un. JUN: F.I. = 2,641 un. JUL: F.I. = -1,813 un.

(satisfied with overtime and subcontracting) = 0 AUG: F.I. = 1,110 un. SEP: F.I. = 2,202 un. OCT: F.I. = 2,228 un. NOV: F.I. = 1,676 un. DIC: F.I. = -4,564 un.

(satisfied with overtime and subcontracting) = 0

FINAL INVENTORYfinal inventory (i-1) + regular production i – necessary production i

If the final inventory is lower than zero, then there is still some demand not satisfied and therefore backordered

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JAN: 200 m.u.*(40+0)/2 = 4 t.m.u.

FEB: 12 t.m.u. MAR: 25t.m.u. APR: 88.6t.m.u.

MAY: 253.3 t.m.u. JUN: 445.8t.m.u. JUL: 264.1 t.m.u.

AUG: 110.1 t.m.u. SEP: 330.3t.m.u. OCT: 443t.m.u.

NOV: 390.4 t.m.u. DEC: 167.6t.m.u.

COST OF INVENTORY AND BACKORDERCost of backorder = un. and month (production not satisfied)* m.u./un. and month. There are no backordered units since we have used overtime and subcontracting

Cost of inventory per month (Cim) = Ciu*(Iem+Ibm)/2

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TC = 170,440 + 22,400 + 4,344 + 11,117.5 + 2,534.2 = 210,835.7 t.m.u.

TOTAL COST

CUSTOMER SATISFACTION

SERVICE LEVEL

The incremental cost is lower than for alternative 1 and the service level is 100%.

This alternative leads to a lower

cost but it is not the optimal

TABLE 4. ALTERNATIVE 3: MIXED STRATEGY

For your attention

Presentation aggregate planning

Business

Transcript of Presentation aggregate planning