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
3. THE PROCESS OF AGGREGATE PLANNING
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
TABLE 1. NECESSARY PRODUCTION PLAN AND PRODUCTION DAYSEXAMPLE OF HOW TO CALCULATE THE FORECASTED DEMAND.
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
TABLE 1. NECESSARY PRODUCTION PLAN AND PRODUCTION DAYSEXAMPLE OF HOW TO CALCULATE THE FORECASTED DEMAND.
Other sources of demand. The quantity needed to satisfy the security stock
9
TABLE 1. NECESSARY PRODUCTION PLAN AND PRODUCTION DAYSEXAMPLE OF HOW TO CALCULATE THE FORECASTED DEMAND.
Necessary production for each month
10
TABLE 1. NECESSARY PRODUCTION PLAN AND PRODUCTION DAYSEXAMPLE OF HOW TO CALCULATE THE FORECASTED DEMAND.
The necessary production for each month
11
TABLE 1. NECESSARY PRODUCTION PLAN AND PRODUCTION DAYSEXAMPLE OF HOW TO CALCULATE THE FORECASTED DEMAND.
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
Strategies to obtain an aggregate plan
Pure (one objective)
Level Strategy
Mixed (multiple objectives)
Objective: maintaining a constant output rate, production rate and therefore constant workforce level over the planning horizon.
3. THE PROCESS OF AGGREGATE PLANNING
27
Level strategy
Level of regular
production
Level of total production
3. THE PROCESS OF AGGREGATE PLANNING
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
Strategies to obtain an aggregate plan
Pure (one objective)
Mixed (multiple objectives)
Mixed Alternative
Objective: sets production equal to forecasted demand.
𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝑃𝑒𝑟𝑖𝑜𝑑
=𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑒𝑑𝑑𝑒𝑚𝑎𝑛𝑑
𝑃𝑒𝑟𝑖𝑜𝑑
3. THE PROCESS OF AGGREGATE PLANNING
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.)(*)
ALTERNATIVE 3: MIXED ALTERNATIVE
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
ALTERNATIVE 3: MIXED ALTERNATIVE
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
ALTERNATIVE 3: MIXED ALTERNATIVE
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
46
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.
50
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