Chapter 05 - ENT 489 [1011] 1 ENT 489 Production Planning and Control Chapter 05 Aggregate Planning 1 Aggregate Planning Chapter Outcome Ability to explain the aggregate planning focuses Ability 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
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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),
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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
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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
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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
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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
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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.
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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
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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
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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
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
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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
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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
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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
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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
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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
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Chapter 05 - ENT 489 [1011] 22
Aggregate Planning Fill in the data for the problem
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
105
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
107
Then key in initial inventory of 50 cases
Aggregate Planning
75
108
Now fill in final inventory of 75 cases
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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
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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