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Chapter 05 - ENT 489 [1011] 1

ENT 489 Production Planning and Control

Chapter 05Aggregate Planning

1

Aggregate Planning Chapter Outcome

Ability to explain the aggregate planning focusesAbility to explain the aggregate planning focuses on intermediate range production planning.

Ability to discuss and identify the factors affecting capacity, production costs, capacity change costs and inventory costs.

Ability to describe, demonstrate and organize aggregate planning methods using spreadsheet

2

aggregate planning methods using spreadsheet methods and optimization methods including linear Programming and transportation models.

Aggregate Planning

Also called macro production planning Addresses the problem of deciding how Addresses the problem of deciding how

many employees the firm should retain and, for a manufacturing firm, the quantity and the mix of products to be produced.

3

Aggregate Planning

Objectives :- To react quickly to anticipated changes in To react quickly to anticipated changes in

demand. Retaining a stable workforce Develop a production plan for the firm that

maximizes profit over planning horizon subject to constraints on capacity

4

subject to constraints on capacity

Chapter 05 - ENT 489 [1011] 2

Aggregate Planning

Goal: To plan gross work force levels and set firm-wide production plansand set firm-wide production plans.

Concept is predicated on the idea of an “aggregate unit” of production.

May be actual units, or may be measured in weight (tons of steel),

5

g ( ),volume (gallons of gasoline), time (worker-hours), or dollars of sales. Can even be a fictitious quantity.

Aggregate Planning

Overview of the Problem Suppose that D D D are the Suppose that D1, D2, . . . , DT are the

forecasts of demand for aggregate units over the planning horizon (T periods).

The problem is to determine both work force levels (Wt) and production levels (Pt ) to minimize total costs over the T period

6

minimize total costs over the T period planning horizon.

Aggregate Planning Important Issues

Smoothing Refers to the costs and disruptions that result from making Refers to the costs and disruptions that result from making

changes from one period to the next. Bottleneck Planning

Problem of meeting peak demand because of capacity restrictions.

Planning Horizon Assumed given (T), but what is “right” value? Rolling

horizons and end of horizon effect are both important issues

7

issues. Treatment of Demand

Assume demand is known. Ignores uncertainty to focus on the predictable/systematic variations in demand, such as seasonality.

Aggregate Planning Relevant costs in aggregate planning

Smoothing Costs Smoothing Costs changing size of the work force changing number of units produced

Holding Costs primary component: opportunity cost of

investmentSh t C t

8

Shortage Costs Cost of demand exceeding stock on hand. Why

should shortages be an issue if demand is known?

Chapter 05 - ENT 489 [1011] 3

Aggregate Planning Regular time Costs

Cost of producing one unit of output duringCost of producing one unit of output during regular working hour.

Overtime Costs Production by regular-time employees beyond

the normal workday Assumed to be linear

9

Subcontracting Costs Production of items by an outside supplier Assumed to be linear

Aggregate Planning Idle time Costs

Cost of underutilization of the workplace.Cost of underutilization of the workplace.

10

Aggregate Planning

Aggregate Units The method is based on notion of aggregate The method is based on notion of aggregate

units. They may be Actual units of production Weight (tons of steel) Volume (gallons of gasoline) Dollars (Value of sales)

11

Dollars (Value of sales) Fictitious aggregate units

Aggregate Planning

Aggregate planning can be conducted Spreadsheet Spreadsheet

Zero inventory plan Level work force plan

With backorder Without backorder

Linear Programming

12

g g

Chapter 05 - ENT 489 [1011] 4

Aggregate PlanningJan Feb Mar Apr May Jun Total

1 Days

2 Units/Worker

3 Demand

4 Workers Needed

5 Worker Available

6 Worker Hired

7 Hiring Cost

8 Workers laid off

9 Lay off cost

13

10 Worker used

11 Labor cost

12 Units produced

13 Net inventory

14 Holding cost

15 Backorder cost

16 Total cost

Aggregate Planning

Zero Inventory Plan Produces exactly the demand for each Produces exactly the demand for each

period Required fluctuating work force No cost for inventory eg. Holding cost &

backorder costW k d d

14

Worker needed

Worker needed =Demand / Month

Days / month × units / worker / day

Aggregate Planning

Worker hired Worker hired = max { 0, worker needed – worker available }Worker hired max { 0, worker needed worker available }

Worker laid off Worker laid off = max { 0, worker available – worker needed }

Capacity Capacity = workers × days × units / worker / day

Units produced

15

Units produced Unit produced = min { demand, capacity }

Aggregate Planning Precision Transfer, Inc., makes more than 300

different products, all precision gears. Last p , p gyear, precision made 41,383 gears of various kinds. There were 260 working days and an average of 40 workers. Holding cost is RM 5 per gear per month, new worker can hired at a cost of RM 450 per worker, existing worker

ff f

16

can laid off at a cost of RM 600 per worker. Wages and benefits for a worker are RM 15 per hour. All worker paid for 8 hours per day. Currently 35 workers at Precision.

Chapter 05 - ENT 489 [1011] 5

Aggregate Planning

Cont.Th F t f th t d d d thThe Forecast for the aggregate demand and the working days is given as Table below

Month Jan Feb Mar Apr May Jun Total

Demand 2760 3320 3970 3540 3180 2900 19670

Working day 21 20 23 21 22 22 129

17

Aggregate Planning

Solution Production ( units / worker / day ) =Production ( units / worker / day ) Hiring cost ( RM / worker ) = Firing cost ( RM / worker ) = Holding cost ( RM / unit / month ) = Backorder cost ( RM / unit / month ) = Wages and benefit (RM / worker / month) =

Si ll i il th t it i

18

Since all gear are similar, the aggregate unit is a gear

Aggregate Planning

Solution Production ( units / worker / day ) = 4Production ( units / worker / day ) Hiring cost ( RM / worker ) = Firing cost ( RM / worker ) = Holding cost ( RM / unit / month ) = Backorder cost ( RM / unit / month ) = Wages and benefit (RM / worker / month) =

L t i i d 41 383 f i ki d Th

4

19

Last year, precision made 41,383 gears of various kinds. There were 260 working days and an average of 40 workers.

Thus Precision made 41,383 gears in 10,400 worker-days.

production =41,383 gears / year

10,400 worker-days / year= 3.98 ≈ 4 gears/worker-days

Aggregate Planning

Solution Production ( units / worker / day ) = 4Production ( units / worker / day ) 4 Hiring cost ( RM / worker ) = Firing cost ( RM / worker ) = Holding cost ( RM / unit / month ) = Backorder cost ( RM / unit / month ) = Wages and benefit (RM / worker / month) =

H ldi t i RM 5 th

5

450600

20

Holding cost is RM 5 per gear per month New worker can hired at a cost of RM 450 per worker Existing worker can laid off at a cost of RM 600 per worker

Chapter 05 - ENT 489 [1011] 6

Aggregate Planning

Solution Production ( units / worker / day ) = 4Production ( units / worker / day ) 4 Hiring cost ( RM / worker ) = 450 Firing cost ( RM / worker ) = 600 Holding cost ( RM / unit / month ) = 5 Backorder cost ( RM / unit / month ) = Wages and benefit (RM / worker / day) =

W d b fit f k RM 15 h All k

1200

21

Wages and benefits for a worker are RM 15 per hour. All worker paid for 8 hours per day.

Wages and benefits = RM 15 × 8 = RM 120 / worker / day Question do not mention backorder

Aggregate Planning Solution

Production ( units / worker / day ) = 4Hi i t ( RM / k ) 450 Hiring cost ( RM / worker ) = 450

Firing cost ( RM / worker ) = 600 Holding cost ( RM / unit / month ) = 5 Backorder cost ( RM / unit / month ) = 0 Wages and benefit (RM / worker / day) = 120


1 Working day 21 20 23 21 22 22 129

2 Units/worker 84 80 92 84 88 88 516

22

2 Units/worker

3 Demand 2760 3320 3970 3540 3180 2900 19670

Units / worker = Production × days in month Eg. Jan :-

Units/worker = 4 × 21 = 84

84 80 92 84 88 88 516

Aggregate Planning


Production ( units / worker / day ) = 4


1 Working day 21 20 23 21 22 22 129

2 Units/worker 84 80 92 84 88 88 516

3 Demand 2760 3320 3970 3540 3180 2900 196704 Worker needed

Worker needed =Demand / Month

D / th it / k / d

33 42 44 43 37 33 232

23

Eg. Jan :- Worker needed = (2760) / { (21) × (4) } = 32.9 ≈ 33 workers

Notes : If the result from calculate is having XX.YY where YY is less then 0.5, the

worker needed is XX + 1

Days / month × units / worker / day

Aggregate Planning


Current workers = 35

4 Worker needed 33 42 44 43 37 33 232

5 Worker available

6 Worker hired8 Worker laid off10 Worker used

Eg. Jan :-W k hi d { 0 k d d k il bl }

0

35

233

9

33

042

2

42

044

0

44

143

0

43

637

0

37

433

11

na

13232

24

Worker hired = max { 0, worker needed – worker available }Worker hired = max { 0, 33 – 35 } = max { 0, -2 } = 0

Worker laid off = max { 0, worker available – worker needed }Worker laid = max { 0, 35 – 33 } = max { 0, 2 } = 2

Worker used = Worker needed

Chapter 05 - ENT 489 [1011] 7

Aggregate Planning Hiring cost ( RM / worker ) = 450 Firing cost ( RM / worker ) = 600


6 Worker hired 0 9 2 0 0 0 11

7 Hiring Cost

8 Worker laid off 2 0 0 1 6 4 139 Lay off Cost

Eg. Jan :-Hi i t k hi i t k 0 450 RM 0

0

1200

4050

0

900

0

0

600

0

3600

0

2400

4950

7800

25

Hiring cost = workers × hiring cost per worker = 0 × 450 = RM 0 Laid off cost = workers × firing cost per worker = 2 × 600 = RM 1200

Aggregate Planning


Wages and benefit (RM / worker / day) = 120

1 Working day 21 20 23 21 22 22 129

10 Worker used 33 42 44 43 37 33 232

11 Labor cost

Eg. Jan :- Labor cost = worker used × wages and benefit × working day

Labor cost = 33 × 120 × 21 = 83160

83160 100800 121440 108360 97680 87120 598560

26

Aggregate Planning




1 Working day 21 20 23 21 22 22 129

3 Demand 2760 3320 3970 3540 3180 2900 19670

10 Worker used 33 42 44 43 37 33 232

Capacity

12 Unit produce

Eg Jan :-

27722760

33603320

40483970

36123540

32563180

29042900

na19670

27

Eg. Jan :- Capacity = worker × days × units / worker / day

Capacity = 33 × 21 × 4 = 2772 Units produce = min { demand, capacity }

Units produce = min { 2760, 2772 } = 2760

Aggregate Planning


Holding cost ( RM / unit / month ) = 5 Backorder cost ( RM / unit / month ) = 0Month Jan Feb Mar Apr May Jun Total

3 Demand 2760 3320 3970 3540 3180 2900 19670

12 Unit produce 2760 3320 3970 3540 3180 2900 19670

13 Net inventory

14 Holding cost

15 Backorder cost Eg. Jan :-

N t i t i t i h d it d d d

0

0

0

0

0

0

0

0

0

0

0

0

00

0

0

0

0

0

0

0

28

Net inventory = inventory in hand + unit produce - demandNet inventory = 0 + 2760 – 2760 = 0

Holding cost = Net inventory × holding costHolding cost = 0 × 5 = RM 0

If negative net inventory Backorder cost = | Net inventory | × backorder cost

Backorder cost = | 0 | × 0 = RM 0

Chapter 05 - ENT 489 [1011] 8

Aggregate PlanningMonth Jan Feb Mar Apr May Jun Total

7 Hiring cost 0 4050 900 0 0 0 4950

9 L ff t 1200 0 0 600 3600 2400 78009 Lay off cost 1200 0 0 600 3600 2400 7800

11 Labor cost 83160 100800 121440 108360 97680 87120 598560

14 Holding cost 0 0 0 0 0 0 0

15 Backorder cost 0 0 0 0 0 0 016 Total cost

Eg. Jan :-T t l t Hi i t L ff t L b t H ldi t

84360 104850 122340 108960 101280 89520 611310

29

Total cost = Hiring cost + Lay off cost + Labor cost + Holding cost + Backorder costTotal cost = 0 + 1200 + 83160 + 0 + 0 = 84360

Aggregate Planning

Zero inventory plan

-6-4-202468

10

Chan

ge in

wor

kfor

ce

30

-8Jan Feb Mar Apr May Jun

Month

Aggregate Planning

Level Work Force Plan Use inventory produced in off peak periods Use inventory produced in off-peak periods

to satisfy demand in peak periods Same number of workers is used in each

period Hiring cost or lay off cost only involved in

first month only

31

first month only

Aggregate Planning

Worker neededTotal demand

Worker hired Worker hired = max { 0, worker needed – worker available }


Workers (total) =Total days × units / worker / day

32

{ , }


Chapter 05 - ENT 489 [1011] 9

Aggregate Planning

Units produced Unit produced = capacityUnit produced capacity

Unit produced (Last month) Units produce = cumulative demand – unit being produced

33

Aggregate Planning

By consider pervious example and backorder cost is RM 15 /unit / monthbackorder cost is RM 15 /unit / month

Plan a level work force plan

34





1 Working day 21 20 23 21 22 22 129

2 Units/worker 84 80 92 84 88 88 516

35

2 Units/worker

3 Demand 2760 3320 3970 3540 3180 2900 19670



84 80 92 84 88 88 516

Aggregate Planning




1 Working day 21 20 23 21 22 22 129

2 Units/worker 84 80 92 84 88 88 516

3 Demand 2760 3320 3970 3540 3180 2900 196704 Worker needed 39 39 39 39 39 39 234

Workers (Total) =Total demand

T t l d it / k / d

36

Total days × units / worker / day

Workers (Total) =19670

129 × 4= 38.12 ≈ 39

Chapter 05 - ENT 489 [1011] 10

Aggregate Planning



4 Worker needed 39 39 39 39 39 39 234

5 Worker available



4

35

039

0

39

039

0

39

039

0

39

039

0

39

039

0

39

039

4

na

0234

37

Worker hired = max { 0, worker needed – worker available }Worker hired = max { 0, 39 – 35 } = max { 0, 4 } = 4

Worker laid off = max { 0, worker available – worker needed }Worker laid = max { 0, 35 – 39 } = max { 0, -4 } = 0




6 Worker hired 4 0 0 0 0 0 4

7 Hiring Cost



1800

0

0

0

0

0

0

0

0

0

0

0

1800

0

38


Aggregate Planning



1 Working day 21 20 23 21 22 22 129

10 Worker used 39 39 39 39 39 39 234

11 Labor cost


Labor cost = 39 × 120 × 21 = 98280

98280 93600 107640 98280 102960 102960 603720

39

Aggregate Planning




1 Working day 21 20 23 21 22 22 129

3 Demand 2760 3320 3970 3540 3180 2900 19670

10 Worker used 39 39 39 39 39 39 234

Capacity

12 Unit produce

Eg Jan :-

32763276

31203120

35883588

32763276

34323432

40


Capacity = 39 × 21 × 4 = 3276 Units produce = capacity

Units produce = 3276

Chapter 05 - ENT 489 [1011] 11

Aggregate Planning




1 Working day 21 20 23 21 22 22 129

3 Demand 2760 3320 3970 3540 3180 2900 19670

10 Worker used 39 39 39 39 39 39 234

Capacity 3276 3120 3588 3276 3432

12 Unit produce 3276 3120 3588 3276 3432

Eg June :-

34322978

na19670

41

Eg. June :- Capacity = worker × days × units / worker / day

Capacity = 39 × 22 × 4 = 3432 Units produce = cumulative demand – unit being produced

Units produce = 19670 – (3276 + 3120 + 3588 + 3276 + 3432) = 2978

Aggregate Planning



3 Demand 2760 3320 3970 3540 3180 2900 19670

12 Unit produce 3276 3120 3588 3276 3432 2978 19670

13 Net inventory

14 Holding cost



516

2580

0

42



Aggregate Planning



3 Demand 2760 3320 3970 3540 3180 2900 19670

12 Unit produce 3276 3120 3588 3276 3432 2978 19670

13 Net inventory

14 Holding cost

15 Backorder cost Eg. Feb :-


516

2580

0

316

1580

0

43



Aggregate Planning



3 Demand 2760 3320 3970 3540 3180 2900 19670

12 Unit produce 3276 3120 3588 3276 3432 2978 19670

13 Net inventory

14 Holding cost

15 Backorder cost Eg. Mar :-


516

2580

0

316

1580

0

-330

0

4950

-780

1170

0

0

0

na

4160

7110

-66

0

990

44

Net inventory = inventory in hand + unit produce - demandNet inventory = 316 + 3588 – 3970 = -66

Backorder cost = | Net inventory | × backorder costBackorder cost = | -66 | × 15 = RM 990

Chapter 05 - ENT 489 [1011] 12


7 Hiring cost 1800 0 0 0 0 0 1800

9 L ff t 0 0 0 0 0 0 09 Lay off cost 0 0 0 0 0 0 0

11 Labor cost 98280 93600 107640 98280 102960 102960 603720

14 Holding cost 2580 1580 0 0 0 0 4160



102660 95180 108630 103230 104130 102960 616790

45


Aggregate Planning

Level work force plan

-300-200-100

0100200300400500600

Net I

nven

tory

(Uni

ts)

46

-400Jan Feb Mar Apr May Jun

Month

Aggregate Planning

Level Work Force Plan (no backorder) Use inventory produced in off peak periods Use inventory produced in off-peak periods

to satisfy demand in peak periods Same number of workers is used in each

period Use maximum worker over the period for

single month

47

single month Hiring cost or lay off cost only involved in

first month only

Aggregate Planning

Worker needed (Cumulative)Cumulative demand

Worker hired Worker hired = max { 0, worker needed – worker available }


Workers (Cumulative) =Cumulative days × units / worker / day

48


Chapter 05 - ENT 489 [1011] 13

Aggregate Planning

Units produced Unit produced = capacityUnit produced capacity

Unit produced (Last month) Units produce = cumulative demand – unit being produced

49

Aggregate Planning

By considering pervious example with backorder cost RM 15 / unit / monthbackorder cost RM 15 / unit / month

Plan a level work force plan without backorder

50





1 Working day 21 20 23 21 22 22 129

2 Units/worker 84 80 92 84 88 88 516

51

2 Units/worker

3 Demand 2760 3320 3970 3540 3180 2900 19670



84 80 92 84 88 88 516

Aggregate PlanningMonth Jan Feb Mar Apr May Jun

Working day 21 20 23 21 22 22

Sum of days

Demand 2760 3320 3970 3540 3180 2900

Sum of demand

Workers

Sum of daysEg

21 41 64 85 107 129

52

Eg. Jan :- Sum of days = 21 Feb :- Sum of days = 21 + 20 = 41 Mar :- Sum of days = 41 + 23 = 64

Chapter 05 - ENT 489 [1011] 14


Working day 21 20 23 21 22 22

Sum of days 21 41 64 85 107 129

Demand 2760 3320 3970 3540 3180 2900

Sum of demand

Workers

Sum of demandEg

2760 6080 10050 13590 16770 19670

53

Eg. Jan :- Sum of demand = 2760 Feb :- Sum of demand = 2760 + 3320 = 6080 Mar :- Sum of demand = 6080 + 3970 = 10050


Working day 21 20 23 21 22 22

Sum of days 21 41 64 85 107 129

Demand 2760 3320 3970 3540 3180 2900

Sum of demand 2760 6080 10050 13590 16770 19670

Workers

Worker neededCumulative demand

33

54

Workers (Cumulative) =Cumulative demand

Cumulative days × units / worker / day

Workers (Cumulative) =2760

21 × 4= 32.86 ≈ 33


Working day 21 20 23 21 22 22

Sum of days 21 41 64 85 107 129

Demand 2760 3320 3970 3540 3180 2900

Sum of demand 2760 6080 10050 13590 16770 19670

Workers 33


38

55




41 × 4= 37.07 ≈ 38


Working day 21 20 23 21 22 22

Sum of days 21 41 64 85 107 129

Demand 2760 3320 3970 3540 3180 2900

Sum of demand 2760 6080 10050 13590 16770 19670

Workers 33 38


40

56




64 × 4= 39.25 ≈ 40

Chapter 05 - ENT 489 [1011] 15


Working day 21 20 23 21 22 22

Sum of days 21 41 64 85 107 129

Demand 2760 3320 3970 3540 3180 2900

Sum of demand 2760 6080 10050 13590 16770 19670

Workers 33 38 40


40

57




85 × 4= 39.97 ≈ 40


Working day 21 20 23 21 22 22

Sum of days 21 41 64 85 107 129

Demand 2760 3320 3970 3540 3180 2900

Sum of demand 2760 6080 10050 13590 16770 19670

Workers 33 38 40 40


40

58




107 × 4= 39.18 ≈ 40


Working day 21 20 23 21 22 22

Sum of days 21 41 64 85 107 129

Demand 2760 3320 3970 3540 3180 2900

Sum of demand 2760 6080 10050 13590 16770 19670

Workers 33 38 40 40 40


39

59




129 × 4= 38.12 ≈ 39

Aggregate Planning

Since maximum worker needed is 40 So company will use 40 workers for this So company will use 40 workers for this

six-month period

60

Chapter 05 - ENT 489 [1011] 16

Aggregate Planning




1 Working day 21 20 23 21 22 22 129

2 Units/worker 84 80 92 84 88 88 516

3 Demand 2760 3320 3970 3540 3180 2900 196704 Worker needed 40 40 40 40 40 40 240

61

Aggregate Planning



4 Worker needed 40 40 40 40 40 40 240

5 Worker available



5

35

040

0

40

040

0

40

040

0

40

040

0

40

040

0

40

040

5

na

0240

62

Worker hired = max { 0, worker needed – worker available }Worker hired = max { 0, 40 – 35 } = max { 0, 5 } = 5

Worker laid off = max { 0, worker available – worker needed }Worker laid = max { 0, 35 – 40 } = max { 0, -5 } = 0




6 Worker hired 5 0 0 0 0 0 5

7 Hiring Cost



2250

0

0

0

0

0

0

0

0

0

0

0

2250

0

63


Aggregate Planning



1 Working day 21 20 23 21 22 22 129

10 Worker used 40 40 40 40 40 40 240

11 Labor cost


Labor cost = 40 × 120 × 21 = 100800

100800 90600 110400 100800 105600 105600 627800

64

Chapter 05 - ENT 489 [1011] 17

Aggregate Planning



1 Working day 21 20 23 21 22 22 129

3 Demand 2760 3320 3970 3540 3180 2900 19670

10 Worker used 40 40 40 40 40 40 240

Capacity

12 Unit produce13 Net inventory

Eg Jan :-

3360

3360

32003200

36803680

600 480 190

65


Capacity = 40 × 21 × 4 = 3360 Units produce = capacity

Units produce = 3360 Net inventory = in hand inventory + unit produce - demand

Net inventory = 0 + 3360 – 2760 = 600

Aggregate Planning

Recall back the worker needed for each monthMonth Jan Feb Mar Apr May Jun

Workers 32.86 37.07 39.25 39.97 39.18 38.12

Since Apr give the maximum value Then start from Apr the net inventory will equal

to zero As the production already meet the market

66

As the production already meet the market demand

Aggregate Planning


1 Working day 21 20 23 21 22 22 129


g y

3 Demand 2760 3320 3970 3540 3180 2900 19670

10 Worker used 40 40 40 40 40 40 240

Capacity 3360 3200 3680

12 Unit produce 3360 3200 368013 Net inventory 600 480 190

Eg. Apr :-Capacity worker × days × units / worker / day

33603350

0

67

Capacity = worker × days × units / worker / dayCapacity = 40 × 21 × 4 = 3360

Units produce = capacity Units produce = 3360

Net inventory = in hand inventory + unit produce - demand Net inventory = 190 + 3360 – 3540 = 10

Since start Apr net inventory = 0, unit produce = 3360 – 10 = 3350

Aggregate Planning


1 Working day 21 20 23 21 22 22 129


g y

3 Demand 2760 3320 3970 3540 3180 2900 19670

10 Worker used 40 40 40 40 40 40 240

Capacity 3360 3200 3680 3550

12 Unit produce 3360 3200 3680 354013 Net inventory 600 480 190 0

Eg. May :-Capacity worker × days × units / worker / day

3520

31800

3520

29000

na

19670na

68

Capacity = worker × days × units / worker / dayCapacity = 40 × 22 × 4 = 3520

Units produce = capacity Units produce = 3520

Net inventory = in hand inventory + unit produce - demand Net inventory = 0 + 3520 – 3180 = 340

Since start Apr net inventory = 0, unit produce = 3520 – 340 = 3180

Chapter 05 - ENT 489 [1011] 18

Aggregate Planning



3 Demand 2760 3320 3970 3540 3180 2900 19670

12 Unit produce 3360 3200 3680 3350 3180 2900 19670

13 Net inventory 600 480 190 0 0 0 na

14 Holding cost


H ldi t N t i t h ldi t

3000

0

2400

0

950

0

0

0

0

0

0

0

6350

0

69



7 Hiring cost 2250 0 0 0 0 0 2250

9 L ff t 0 0 0 0 0 0 09 Lay off cost 0 0 0 0 0 0 0

11 Labor cost 100800 90600 110400 100800 105600 105600 619200

14 Holding cost 3000 2400 950 0 0 0 0



106050 98400 111350 100800 105600 105600 627800

70


Aggregate Planning

Level work force plan (no backorder)700

0

100

200

300

400

500

600

700

Net I

nven

tory

(Uni

ts)

71

0Jan Feb Mar Apr May Jun

Month

Aggregate PlanningWhen compare three plan

Zero inventory plan Zero inventory plan Total cost = RM 611310

Level work force plan Total cost = RM 616790

Level work force plan (no backorder) Total cost = RM 627800

72

All this three plan can be mix into a plan. The decision is more like trial and error

to reduce total cost

Chapter 05 - ENT 489 [1011] 19

Aggregate Planning

Advantages of spreadsheet Immediately see result Immediately see result Easy to change

Disadvantages of spreadsheet Trial and error Quality depends on creativity of person

73

y p y pusing spreadsheet

Aggregate Planning

Linear Programming T = planning horizon length in period T = planning horizon length, in period t = index of periods, t = 1,2,…,T Dt = forecasted number of units demanded

in period t. nt = number of units that can be made by

k i i d t

74

one worker in period t

Aggregate Planning CP

t = cost to produce one unit in period t. CW

t = cost to one worker in period t C t cost to one worker in period t. CH

t = cost to hide one worker in period t. CL

t = cost to lay off one worker in period t. CI

t = cost to hold one unit in inventory for period t.CB f

75

CBt = cost to backorder one unit for period t.

Aggregate Planning Pt = number of units produced in period t Wt = number of workers available in period t Wt number of workers available in period t Ht = number of workers hired in period t Lt = number of workers laid off in period t It = number of units held in inventory at end

of period tf f

76

Bt = number of units backordered at end of period t

Chapter 05 - ENT 489 [1011] 20

Aggregate Planning

In period t, Wt workers, and each can produce n units in the period meaningproduce nt units in the period, meaning can produce no more than ntWt units in period t. Mathematically, the unit produced is Pt ≤ nt Wt t = 1,2,…,T

77

Aggregate Planning

Let W0 as the initial number of workers, the number of workers available is athe number of workers available is a function of the initial number plus the number hired and minus the number lay off. For later period, Wt = Wt-1 + Ht - Lt t = 1,2,…,T

78

Aggregate Planning

net inventory this period = net inventory last period + production= net inventory last period + production this period - demand this period

If the net inventory is positive, physically is inventory, but if it is negative, that is a backorder position

79

p

Aggregate Planning

These two conditions cannot occur simultaneously Let the net inventory atsimultaneously. Let the net inventory at time t be It - Bt , Either It ≥ 0 or Bt ≥ 0 , but at least one of them must be zero. The relationship, called the material or inventory balance equation, is

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It - Bt = It-1 - Bt-1 + Pt - Dt t = 1,2,…,T

Chapter 05 - ENT 489 [1011] 21

Aggregate Planning

The total cost is the sum of productioncosts hiring and lay-off costs inventorycosts, hiring and lay-off costs, inventoryholding costs, backorder costs over unitto produce and the cost per worker timesthe number of workers.

Production costs per unit that do not

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change from period to period can bedeleted from model. The total cost for aplan is

Aggregate Planning

The total cost for a plan is

TBILHWP

For the linear programming model, the mathematical expression is given as

t

tBtt

Itt

Ltt

Htt

Wtt

Pt BCICLCHCWCPC

1

T

BILHWP BCICLCHCWCPC

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Pt, Wt, Ht, Lt, It ≥ 0 t = 1,2,…,T

Minimize

t

tBtt

Itt

Ltt

Htt

Wtt

Pt BCICLCHCWCPC

1

Aggregate Planning

By consider previous example where backorder is allowedbackorder is allowed

Software MS Excel is used

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Aggregate Planning

84

Chapter 05 - ENT 489 [1011] 22

Aggregate Planning Fill in the data for the problem

Production ( units / worker / day ) = 4 Hiring cost ( RM / worker ) = 450 Hiring cost ( RM / worker ) = 450 Firing cost ( RM / worker ) = 600 Holding cost ( RM / unit / month ) = 5 Backorder cost ( RM / unit / month ) = 15 Wages and benefit (RM / worker / day) = 120


Demand 2760 3320 3970 3540 3180 2900 19670

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Demand 2760 3320 3970 3540 3180 2900 19670

Working day 21 20 23 21 22 22 129

Aggregate Planning

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Aggregate Planning

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Aggregate Planning

Selecting the target cell to obtain the

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Selecting the target cell to obtain the objective >> minimize cost

Chapter 05 - ENT 489 [1011] 23

Aggregate Planning

Press the follo ing b tton

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Press the following button

Aggregate Planning

By holding Ctrl key then selecting following cell

After selecting above cell then press this

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key

Aggregate Planning

Press the add button to add constraint

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Aggregate Planning

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Chapter 05 - ENT 489 [1011] 24

Aggregate Planning

Continue to add all constraint with press ADD buttonADD button

During last constraint then press OK button.

If would like to edit the go to solver parameter window and press CHANGE

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p pbutton and when finish edit then press OK button

Aggregate Planning

Press OPTIONS button and select assume non-negative analysisassume non-negative analysis

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Aggregate Planning

When finish then press SOLVE button The solver results window will appear The solver results window will appear

then press OK button

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Aggregate Planning

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Chapter 05 - ENT 489 [1011] 25

Aggregate PlanningWhen compare with previous

spreadsheet methodp Zero inventory plan

Total cost = RM 611310 Level work force plan

Total cost = RM 616790 Level work force plan (no backorder)

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p ( ) Total cost = RM 627800

Linear programming Total cost = RM 600191.56

Aggregate Planning

Advantages of Linear Programming Optimize the problem Can be solve large problem

Disadvantages of Linear Programming The value obtain is not practical Need to round up value

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Need to round up value

Aggregate PlanningAggregate Planning

End of part A

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Aggregate Planning

Transportation model Production planning problem with constant

work force Faster then linear programming Larger problems are more readily solved Minimizes the cost of shipping a single

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pp g gproduct from several plants to several customers

Chapter 05 - ENT 489 [1011] 26

Aggregate Planning

Cost of shipping a unit of product from each supply point to each demand point and thesupply point to each demand point, and the total supply must equal the total demand

Dummy supply or demand point can be added as needed

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Aggregate Planning

Let n W the capacity (in units) during period t ntWt = the capacity (in units) during period t

Dt = forecasted number of units demanded in period t

Ctp = the cost to produce one unit in period t

CtI = the cost to hold one unit in inventory for

period t

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Assume total capacity over the horizon is at least as large as total demand

Aggregate Planning

Case study A production plan for Klean, Inc., needs to

plan production for the next three months. Expected demand for their degreaser is 200, 300 and 400 cases for the next three months. There is an initial inventory of 50 cases and a final inventory of 75 cases is

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cases and a final inventory of 75 cases is desired. Capacity for the next three months is 350 300 and 350 cases.

Aggregate Planning

Klean projects that it costs RM 1000, RM 1100 d RM 1200 t d1100 and RM 1200 to produce a case the next three months. Due to the volatile nature of he degreaser, it costs RM 200 per month to store a case. Data, with costs stated in multiplies of RM 100, are

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summarized in follow table.

Chapter 05 - ENT 489 [1011] 27

Aggregate Planning

t 1 2 3ntWt 350 300 350Dt 200 300 400Ct

P 10 11 12

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CtI 2 2 2

Aggregate Planning

200 300 400

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By key in the demand accordingly to question

200 300 400

Aggregate Planning

50

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Then key in initial inventory of 50 cases

Aggregate Planning

75

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Now fill in final inventory of 75 cases

75

Chapter 05 - ENT 489 [1011] 28

Aggregate Planning

350

350

300

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Now key in the capacity accordingly to question

Aggregate Planning

1050

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Now total the available capacity

Aggregate Planning

75

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Now total the demand We will get 975 it still excess 75 to 1050 cases

Aggregate Planning

500 2 4 6 0

50

112

Now fill in the beginning inventory While for the holding cost due to inventory is

RM 200 for each period

Chapter 05 - ENT 489 [1011] 29

Aggregate Planning

150

300

350

50 75 75

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Now analysis capacity for period 1, since demand is 200 so inventory for period 1 is 200 - 50 = 150

And the following is

Aggregate Planning

10

11

12

12

13

14

14

15

16 0

0

0

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Now key in the cost to produce Since each week will having RM 200 inventory

cost

Aggregate PlanningAggregate Planning

End of chapter

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