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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
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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
Month Jan Feb Mar Apr May Jun Total
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
Month Jan Feb Mar Apr May Jun Total
Production ( units / worker / day ) = 4
Month Jan Feb Mar Apr May Jun Total
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
Month Jan Feb Mar Apr May Jun Total
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
Month Jan Feb Mar Apr May Jun Total
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
Month Jan Feb Mar Apr May Jun Total
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
Month Jan Feb Mar Apr May Jun Total
Production ( units / worker / day ) = 4
Month Jan Feb Mar Apr May Jun Total
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
Month Jan Feb Mar Apr May Jun Total
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 }
Worker laid off Worker laid off = max { 0, worker available – worker needed }
Workers (total) =Total days × units / worker / day
32
{ , }
Capacity Capacity = workers × days × units / worker / day
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
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 ) = 15 Wages and benefit (RM / worker / day) = 120
Month Jan Feb Mar Apr May Jun Total
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
Units / worker = Production × days in month Eg. Jan :-
Units/worker = 4 × 21 = 84
84 80 92 84 88 88 516
Aggregate Planning
Month Jan Feb Mar Apr May Jun Total
Production ( units / worker / day ) = 4
Month Jan Feb Mar Apr May Jun Total
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
Month Jan Feb Mar Apr May Jun Total
Current workers = 35
4 Worker needed 39 39 39 39 39 39 234
5 Worker available
6 Worker hired8 Worker laid off10 Worker used
Eg. Jan :-W k hi d { 0 k d d k il bl }
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
Worker used = Worker needed
Aggregate Planning Hiring cost ( RM / worker ) = 450 Firing cost ( RM / worker ) = 600
Month Jan Feb Mar Apr May Jun Total
6 Worker hired 4 0 0 0 0 0 4
7 Hiring Cost
8 Worker laid off 0 0 0 0 0 0 09 Lay off Cost
Eg. Jan :-Hi i t k hi i t k 4 450 RM 1800
1800
0
0
0
0
0
0
0
0
0
0
0
1800
0
38
Hiring cost = workers × hiring cost per worker = 4 × 450 = RM 1800 Laid off cost = workers × firing cost per worker = 0 × 600 = RM 0
Aggregate Planning
Month Jan Feb Mar Apr May Jun Total
Wages and benefit (RM / worker / day) = 120
1 Working day 21 20 23 21 22 22 129
10 Worker used 39 39 39 39 39 39 234
11 Labor cost
Eg. Jan :- Labor cost = worker used × wages and benefit × working day
Labor cost = 39 × 120 × 21 = 98280
98280 93600 107640 98280 102960 102960 603720
39
Aggregate Planning
Month Jan Feb Mar Apr May Jun Total
Production ( units / worker / day ) = 4
Month Jan Feb Mar Apr May Jun Total
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
Eg. Jan :- Capacity = worker × days × units / worker / day
Capacity = 39 × 21 × 4 = 3276 Units produce = capacity
Units produce = 3276
Chapter 05 - ENT 489 [1011] 11
Aggregate Planning
Month Jan Feb Mar Apr May Jun Total
Production ( units / worker / day ) = 4
Month Jan Feb Mar Apr May Jun Total
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
Month Jan Feb Mar Apr May Jun Total
Holding cost ( RM / unit / month ) = 5 Backorder cost ( RM / unit / month ) = 15Month Jan Feb Mar Apr May Jun Total
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. Jan :-
N t i t i t i h d it d d d
516
2580
0
42
Net inventory = inventory in hand + unit produce - demandNet inventory = 0 + 3276 – 2760 = 516
Holding cost = Net inventory × holding costHolding cost = 516 × 5 = RM 2580
Aggregate Planning
Month Jan Feb Mar Apr May Jun Total
Holding cost ( RM / unit / month ) = 5 Backorder cost ( RM / unit / month ) = 15Month Jan Feb Mar Apr May Jun Total
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 :-
N t i t i t i h d it d d d
516
2580
0
316
1580
0
43
Net inventory = inventory in hand + unit produce - demandNet inventory = 516 + 3120 – 3320 = 316
Holding cost = Net inventory × holding costHolding cost = 316 × 5 = RM 1580
Aggregate Planning
Month Jan Feb Mar Apr May Jun Total
Holding cost ( RM / unit / month ) = 5 Backorder cost ( RM / unit / month ) = 15Month Jan Feb Mar Apr May Jun Total
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 :-
N t i t i t i h d it d d d
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
Aggregate PlanningMonth Jan Feb Mar Apr May Jun Total
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
15 Backorder cost 0 0 990 4950 1170 0 711016 Total cost
Eg. Jan :-T t l t Hi i t L ff t L b t H ldi t
102660 95180 108630 103230 104130 102960 616790
45
Total cost = Hiring cost + Lay off cost + Labor cost + Holding cost + Backorder costTotal cost = 1800 + 0 + 98280 + 2580 + 0 = 102660
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 }
Worker laid off Worker laid off = max { 0, worker available – worker needed }
Workers (Cumulative) =Cumulative days × units / worker / day
48
Capacity Capacity = workers × days × units / worker / day
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
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 ) = 15 Wages and benefit (RM / worker / day) = 120
Month Jan Feb Mar Apr May Jun Total
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
Units / worker = Production × days in month Eg. Jan :-
Units/worker = 4 × 21 = 84
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
Aggregate PlanningMonth Jan Feb Mar Apr May Jun
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
Aggregate PlanningMonth Jan Feb Mar Apr May Jun
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
Aggregate PlanningMonth Jan Feb Mar Apr May Jun
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
Worker neededCumulative demand
38
55
Workers (Cumulative) =Cumulative demand
Cumulative days × units / worker / day
Workers (Cumulative) =6080
41 × 4= 37.07 ≈ 38
Aggregate PlanningMonth Jan Feb Mar Apr May Jun
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
Worker neededCumulative demand
40
56
Workers (Cumulative) =Cumulative demand
Cumulative days × units / worker / day
Workers (Cumulative) =10050
64 × 4= 39.25 ≈ 40
Chapter 05 - ENT 489 [1011] 15
Aggregate PlanningMonth Jan Feb Mar Apr May Jun
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
Worker neededCumulative demand
40
57
Workers (Cumulative) =Cumulative demand
Cumulative days × units / worker / day
Workers (Cumulative) =13590
85 × 4= 39.97 ≈ 40
Aggregate PlanningMonth Jan Feb Mar Apr May Jun
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
Worker neededCumulative demand
40
58
Workers (Cumulative) =Cumulative demand
Cumulative days × units / worker / day
Workers (Cumulative) =16770
107 × 4= 39.18 ≈ 40
Aggregate PlanningMonth Jan Feb Mar Apr May Jun
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
Worker neededCumulative demand
39
59
Workers (Cumulative) =Cumulative demand
Cumulative days × units / worker / day
Workers (Cumulative) =19670
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
Month Jan Feb Mar Apr May Jun Total
Production ( units / worker / day ) = 4
Month Jan Feb Mar Apr May Jun Total
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
Month Jan Feb Mar Apr May Jun Total
Current workers = 35
4 Worker needed 40 40 40 40 40 40 240
5 Worker available
6 Worker hired8 Worker laid off10 Worker used
Eg. Jan :-W k hi d { 0 k d d k il bl }
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
Worker used = Worker needed
Aggregate Planning Hiring cost ( RM / worker ) = 450 Firing cost ( RM / worker ) = 600
Month Jan Feb Mar Apr May Jun Total
6 Worker hired 5 0 0 0 0 0 5
7 Hiring Cost
8 Worker laid off 0 0 0 0 0 0 09 Lay off Cost
Eg. Jan :-Hi i t k hi i t k 5 450 RM 2250
2250
0
0
0
0
0
0
0
0
0
0
0
2250
0
63
Hiring cost = workers × hiring cost per worker = 5 × 450 = RM 2250 Laid off cost = workers × firing cost per worker = 0 × 600 = RM 0
Aggregate Planning
Month Jan Feb Mar Apr May Jun Total
Wages and benefit (RM / worker / day) = 120
1 Working day 21 20 23 21 22 22 129
10 Worker used 40 40 40 40 40 40 240
11 Labor cost
Eg. Jan :- Labor cost = worker used × wages and benefit × working day
Labor cost = 40 × 120 × 21 = 100800
100800 90600 110400 100800 105600 105600 627800
64
Chapter 05 - ENT 489 [1011] 17
Aggregate Planning
Month Jan Feb Mar Apr May Jun Total
Production ( units / worker / day ) = 4
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
Eg. Jan :- Capacity = worker × days × units / worker / day
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
Month Jan Feb Mar Apr May Jun Total
1 Working day 21 20 23 21 22 22 129
Production ( units / worker / day ) = 4
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
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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
Month Jan Feb Mar Apr May Jun Total
1 Working day 21 20 23 21 22 22 129
Production ( units / worker / day ) = 4
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
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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
Month Jan Feb Mar Apr May Jun Total
Holding cost ( RM / unit / month ) = 5 Backorder cost ( RM / unit / month ) = 15Month Jan Feb Mar Apr May Jun Total
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
15 Backorder cost Eg. Jan :-
H ldi t N t i t h ldi t
3000
0
2400
0
950
0
0
0
0
0
0
0
6350
0
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Holding cost = Net inventory × holding costHolding cost = 600 × 5 = RM 3000
Aggregate PlanningMonth Jan Feb Mar Apr May Jun Total
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
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
106050 98400 111350 100800 105600 105600 627800
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Total cost = Hiring cost + Lay off cost + Labor cost + Holding cost + Backorder costTotal cost = 1800 + 0 + 98280 + 2580 + 0 = 102660
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
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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
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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
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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
80
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
81
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
82
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
83
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
Month Jan Feb Mar Apr May Jun Total
Demand 2760 3320 3970 3540 3180 2900 19670
85
Demand 2760 3320 3970 3540 3180 2900 19670
Working day 21 20 23 21 22 22 129
Aggregate Planning
86
Aggregate Planning
87
Aggregate Planning
Selecting the target cell to obtain the
88
Selecting the target cell to obtain the objective >> minimize cost
Chapter 05 - ENT 489 [1011] 23
Aggregate Planning
Press the follo ing b tton
89
Press the following button
Aggregate Planning
By holding Ctrl key then selecting following cell
After selecting above cell then press this
90
key
Aggregate Planning
Press the add button to add constraint
91
Aggregate Planning
92
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
93
p pbutton and when finish edit then press OK button
Aggregate Planning
Press OPTIONS button and select assume non-negative analysisassume non-negative analysis
94
Aggregate Planning
When finish then press SOLVE button The solver results window will appear The solver results window will appear
then press OK button
95
Aggregate Planning
96
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)
97
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
98
Need to round up value
Aggregate PlanningAggregate Planning
End of part A
99
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
100
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
101
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
102
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
103
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
104
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
105
CtI 2 2 2
Aggregate Planning
200 300 400
106
By key in the demand accordingly to question
200 300 400
Aggregate Planning
50
107
Then key in initial inventory of 50 cases
Aggregate Planning
75
108
Now fill in final inventory of 75 cases
75
Chapter 05 - ENT 489 [1011] 28
Aggregate Planning
350
350
300
109
Now key in the capacity accordingly to question
Aggregate Planning
1050
110
Now total the available capacity
Aggregate Planning
75
111
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
113
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
114
Now key in the cost to produce Since each week will having RM 200 inventory
cost
Aggregate PlanningAggregate Planning
End of chapter
115