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
½ ½ 500 1250 1000 min 2500 min Product A Product B Price/Prod. time Price ($) Production Time

Replace the price by volume in the above example. Now what is aggregate unit?
½ ½ 500 1250 1000 min 2500 min Product A Product B Volume/Prod. time Volume(cm 3 ) Produc. Time

A plant produces six models of washing machines
What aggregate unit the plant manager can use for planning?
725 5.8 M38 525 5.4 M26 425 5.2 L38 395 5.1 L98 345 4.9 K42 285 4.2 A55 Selling Price ($) Total Production Time (hours) Model Number

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 hierarchy Forecast of aggregate demand for t period Planning horizon Aggregate production Plan : Production and Workforce levels for each period Master Production Schedule : Production levels by item by period Material Requirements Planning : Detailed Time table for production and assembly of Components and subassemblies

Aggregate Production Plan
D 1 , D 2 , …, D T 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
7520 2000 1400 June 5520 2000 2000 May 3520 1200 1200 April 2320 900 900 March 1420 640 640 February 780 780 1280 January Net cumulative demand Net predicted demand Predicted demand

Aggregate Planning: Example Inventory

Cost data
C H : cost of hiring one worker = $ 500
C F : cost of firing one worker = $ 1000
C I : 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: Example Strategy 1 : Chase the demand by changing work force levels Month Number of Working days Number of Units produced Per worker (Bx.14653) Forecast Net demand Min. # of Worker required (D/C) Initial Calculations Table D C B A

Aggregate Planning: Example Total cost = 755(500)+145(1000)+30(80) = 524,900 Month # of Workers # of units per workers # fired # hired Cum. Product. Produc Tion (BxE) Cum. Demand. Inven tory. A B D C F E G H I Aggregate Production/capacity plan

Aggregate Planning: Example Min. Number Of Workers required 411 Strategy 2: Constant work force : Keep the work force level constant throughout the planning horizon Month Cumulative net demand Cumulative # of units produced per worker Ratio (B/C) Required workforce for strategy 2

Aggregate Planning: Example Total cost = (411-300)(500)+5963(80) = 532,540 Month Production Per worker Monthly Production (Bx411) Cumulative production Cumulative Net demand Inven tory Aggregate Production/capacity plan

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: Example Mixed 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

Aggregate Planning: Example Red strategy Blue strategy

Aggregate Planning: Assignment
Figure out the costs of blue and red mixed strategies. What strategy should be used?

Aggregate Production Planning

by 3abooodi on Feb 10, 2010

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Aggregate Production Planning — Presentation Transcript