Aggregate Production Planning

Aggregate Planning

• It is about translating demand forecasts into production and capacity levels over a fixed planning horizon

• Assumes the demand forecast is fairly accurate.

• It generally uses an aggregate unit of production

Conflicting Objectives in AP• Objective 1 : React quickly to anticipated changes

in demand– Called “chase” strategy– Involves frequent and large changes in the size of the

labor force– May not be the best strategy in the long-run– Cost of firing and hiring

• Objective 2 : Retaining a stable workforce– Leads in to inventory build-ups during low demand

periods or to idle time increases.• Objective 3: Plan that maximize profit s.t

constraints on capacity

Aggregate Unit of Production

• Aggregate planning is usually based on an aggregate unit of production

• If the products are similar, an “average” item can represent the aggregate unit

• If there are variety of products then the aggregate unit may be– Weights (tons of steel)– Volume (gallons of gasoline)– Amount of work required (hours of labor)– Dollar value (value of the inventory in dollar)

Aggregate Unit of Production : Example• Two products made of steel

• It takes the same amount of time to produce a one $ worth of product.

• Aggregate unit 1 $ worth of output• Forecasted demand in aggregate unit = (forecast for prod. A*500

+ Forecast for prod. B*1250)• Example; (200 units*500 + 150 units*1250)=287500 $ worth of

product is needed. 287500*2=575000 min. of production time is needed

Production Time

Price ($) Price/Prod. time

Product A

Product B

1000 min

2500 min

500

1250

½

½

Aggregate Unit of Production : Example

• Replace the price by volume in the above example. Now what is aggregate unit?

Produc. Time Volume(cm3) Volume/Prod. time

Product A

Product B

1000 min

2500 min

500

1250

½

½

S. Nahmias, Production and Operations Analysis


• A plant produces six models of washing machines

• What aggregate unit the plant manager can use for planning?

Model Number

Total Production

Time (hours)

Selling Price

($)

A55 4.2 285

K42 4.9 345

L98 5.1 395

L38 5.2 425

M26 5.4 525

M38 5.8 725



• Can we use one dollar of output as aggregate unit?– Selling values are not consistent with the worker hours

required

– The ratio of selling price to total worker hours required differs from one model to the other

• Say that we have an almost constant percentage of sales in total sales across the models (32%, 21%, 17%, 14%, 10%, 6% respectively)



• A valid aggregate unit is a weighed average of hours required, weighted by percent sales– Fictitious machine

= .32(4.2)+.21(4.9)+.17(5.1)+.14(5.2)+.10(5.4)+ .06(5.8) = 4.856 hours of labor

• An aggregate forecast can be obtained in the same way. • # of fictitious machines demanded = .32*fore. for

A55+.21*fore. for (K42) +…. + .06* fore. for M38• If variety of products, sales dollars is good

approximation as an aggregate unit


Planning Steps hierarchyForecast of aggregate demand for t period

Planning horizon

Aggregate production Plan : Production and Workforce levels for each period

Master Production Schedule : Productionlevels by item by period

Material Requirements Planning : Detailed Time table for production and assembly of

Components and subassemblies

Aggregate Production Plan

• D1, D2, …, DT demand forecasts for next T planning periods

• A period is usually a month

• Demands are known constants

• Goal of APP: determine aggregate production quantities and the levels of resources required to achieve these production goals


Issues in Aggregate Planning

• Smoothing ; refers to the cost of changing production and workforce level between periods– Firing and hiring costs

• Hard to find the real costs– Trade-off between cost of changing workforce and saving in inventory

costs

• Bottleneck problems ; Inability to respond to sudden changes in demand as a result of capacity restrictions– High demand in one period– Breakdown of a vital piece of equipment


Issues in Aggregate Planning

• Planning Horizon ; number of periods for which the demand forecast and aggregate planning are done– If it is too small ; current aggregate plan may lead into

not meeting the demand beyond planning horizon

– If it is too large ; forecasts into far future will be less accurate

– End-of-horizon effect

– Rolling schedules are used in practice


Costs in Aggregate Planning• Smoothing cost

– Hiring cost ; advertising, interviewing, training– Firing cost ; severance penalty, decline in worker morale, lack

of labor force in future– Mostly assumed to be a linear function of the number of

workers

• Holding cost– Major part is the opportunity cost of tied up money in

inventories– Assumed to be linear in the level of inventory (end-of period

or average inventory– It is in $/item/planning period


Costs in Aggregate Planning

• Shortage costs– Cost of not meeting demand on time (from inventory).

Backlogging or lost sale– Usually assumed to be linear in number of items

• Regular time costs– Cost of producing one unit in regular time

• Overtime or subcontracting costs– Cost of producing one unit item in over time or through

subcontracting production to an outside supplier

• Idle time costs


Aggregate Planning: Example

• Example 3.2 (Nahmias’ Book) Densepack ; a disk drive producer

• Has 300 workers employed at the moment• Ending inventory in December 500 units• Would like to have 600 unit at the end of June• Inventory requirements and on-hand inventories

are dealt with by adding/ subtracting them to expected demand



• Demand data

Predicted demand

Net predicted demand

Net cumulative

demand

January 1280 780 780

February 640 640 1420

March 900 900 2320

April 1200 1200 3520

May 2000 2000 5520

June 1400 2000 7520


Inventory

A feasible aggregate plan

0

2000

4000

6000

8000

1 2 3 4 5 6

Month

Cu

mu

lati

ve

nu

mb

er

of

un

its

Cumulative Net Dem. Cumulative prod.



• Cost data– CH: cost of hiring one worker = $ 500

– CF: cost of firing one worker = $ 1000

– CI: cost of holding one unit of inventory one month = $ 80

• K ; Number of aggregate units produced by one worker in one day– It was observed that 76 workers produced 245 disk drives in

22 days

– K = 245/(76x22) = .14653


Aggregate Planning: ExampleStrategy 1 : Chase the demand by changing

work force levels

January 20 2.931 780 267February 24 3.517 640 182March 18 2.638 900 342April 26 3.810 1200 316May 22 3.224 2000 621June 15 2.198 2000 910

Month

Number of Working

days

Number of Units produced

Per worker(Bx.14653)

ForecastNet demand

Min. # of Worker required

(D/C)

Initial Calculations Table

DCBA


January 267 33 2.931 783 783 780 3February 183 85 3.517 640 1423 1420 3

March 342 160 2.638 902 2325 2320 5April 316 27 3.810 1200 3525 3520 5May 621 306 3.224 2002 5527 5520 7June 910 289 2.198 2000 7527 7520 7

Totals 755 145 30

Month# of

Workers

# of unitsper

workers#

fired#

hiredCum.

Product.

ProducTion

(BxE)

Cum.Demand.

Inventory.

A B DC FE G H I

Aggregate Production/capacity plan

Total cost = 755(500)+145(1000)+30(80) = 524,900


Aggregate Planning: ExampleStrategy 2: Constant work force : Keep the work

force level constant throughout the planning horizon

January 780 2.931 267February 1420 6.448 221

March 2320 9.086 256April 3520 12.896 274May 5520 16.120 343June 7520 18.318 411

A B C D

Month

Cumulativenet

demand

Cumulative# of unitsproduced per worker

Ratio(B/C)

Required workforce for strategy 2

Min. NumberOfWorkersrequired

411


January 2.931 1205 1205 780 425February 3.517 1445 2650 1420 1230

March 2.638 1084 3734 2320 1414April 3.810 1566 5300 3520 1780May 3.224 1325 6625 5520 1105June 2.198 903 7528 7520 8

Total 5963A B C D E F

Month

ProductionPer

worker

MonthlyProduction

(Bx411)Cumulativeproduction

CumulativeNet

demandInventory

Aggregate Production/capacity plan

Total cost = (411-300)(500)+5963(80) = 532,540

Are we missing anything?? :P


• What are the total cost of salary paid to workers in each strategy (assuming 2500 per month for each worker)– 6,598,924 for strategy 1 + 524,900 = 7,124,824– 6,165,000 for strategy 2 + 532,540 = 6,697,540

• Strategy 2 costs about 425,000 less and also avoids some hard-to-determine costs of changing workforce levels frequently


Aggregate Planning: ExampleMixed Strategies

• Instead of pure strategies (chase and constant workforce), we can have mixed strategies.

• Any mixed strategy can be represented by combination of lines on the plot.

• Lines represent constant work force• Any line combination not going below the

cumulative demand curve is a feasible aggregate plan


Feasible aggregate plans

0

2000

4000

6000

8000

1 2 3 4 5 6

Month

Cumu

lativ

e nu

mber

of

uni

ts

Cumulative Net Dem.

Feasible aggregate plans

0

2000

4000

6000

8000

1 2 3 4 5 6

MonthCu

mulat

ive

numb

er

of u

nits

Cumulative Net Dem.

Red strategy Blue strategy

Aggregate Planning: Assignment

• Figure out the costs of blue and red mixed strategies. What strategy should be used?

Business

Aggregate Production Planning