Aggregate Planning

Aggregate PlanningAggregate Planning

Aggregate PlanningAggregate Planningin a Supply Chain in a Supply Chain

What is Aggregate planning? What is Aggregate planning? Management optionsManagement options Costs involvedCosts involved Aggregate strategiesAggregate strategies

Level StrategyLevel Strategy Chase StrategyChase Strategy

Aggregate planning using Linear Aggregate planning using Linear ProgrammingProgramming

ExamplesExamples

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The Planning ProcessThe Planning ProcessLong-range plans (over one year)Research and DevelopmentNew product plansCapital investmentsFacility location/expansion

Intermediate-range plans (3 to 18 months)Sales planningProduction planning and budgetingSetting employment, inventory,

subcontracting levelsAnalyzing operating plans

Short-range plans (up to 3 months)Job assignmentsMaterials Requirement PlanningJob schedulingDispatchingOvertimePart-time help

Top executives

Operations managers

Operations managers, supervisors, foremen

ResponsibilityResponsibility Planning tasks and horizonPlanning tasks and horizon

What is Aggregate Planning?What is Aggregate Planning?

Aggregate Planning Aggregate Planning is a is a overall overall production planning production planning process by process by which a company which a company determines determines ideal levels of capacityideal levels of capacity to meet to meet the demandthe demand over a specified over a specified time horizon. ( roughly between time horizon. ( roughly between 3 and 18 months).3 and 18 months).

Example: Steel manufacturing.Example: Steel manufacturing.

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Forecast of demand

Current CapacitiesCosts

Commitments

AGGREGATE PRODUCTION

PLAN

Inventory

Backorder/ Lost sales

Raw material requirement

Machine capacity increase/ decreaseWorkforce level

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GoalGoal: Maximize profits/Minimize costs, : Maximize profits/Minimize costs, meet demand.meet demand.

The Aggregate Planning ProblemThe Aggregate Planning Problem::

““Given the demand forecast for each period in Given the demand forecast for each period in the planning horizon, determine the the planning horizon, determine the production level, inventory level, and the production level, inventory level, and the capacity level for each period that maximizes capacity level for each period that maximizes the firm’s profit over the planning horizonthe firm’s profit over the planning horizon””

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Management options to Management options to meet fluctuating demandmeet fluctuating demand

Build inventories in slack periods in Build inventories in slack periods in anticipation of higher demand later anticipation of higher demand later in the planning horizonin the planning horizon

Carry backorders or tolerate lost Carry backorders or tolerate lost sales during peak periodssales during peak periods

Use overtime in peak periods and Use overtime in peak periods and under time (idle time)in slack under time (idle time)in slack periods, while holding workforce periods, while holding workforce and facilities constant.and facilities constant.

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Vary capacity by changing the size of the Vary capacity by changing the size of the workforce through hiring and firing.workforce through hiring and firing.

Vary capacity through changes in plant Vary capacity through changes in plant and equipment ( long term option)and equipment ( long term option)

Each option involve cost ( tangible and Each option involve cost ( tangible and intangible).intangible).

Aim of Aggregate production planning is to Aim of Aggregate production planning is to choose the best option.choose the best option.

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Capacity OptionsCapacity Options

Changing inventory levelsChanging inventory levels Increase inventory in low demand Increase inventory in low demand

periods to meet high demand in periods to meet high demand in the futurethe future

Increases costs associated with Increases costs associated with storage, insurance, handling, storage, insurance, handling, obsolescence, and capital obsolescence, and capital investment 15% to 40%investment 15% to 40%

Shortages can mean lost sales and Shortages can mean lost sales and poor customer servicepoor customer service

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Varying workforce size by hiring Varying workforce size by hiring or layoffsor layoffs Match production rate to demandMatch production rate to demand

Training and severance costs for Training and severance costs for hiring and laying off workers hiring and laying off workers

New workers may have lower New workers may have lower productivityproductivity

Laying off workers may lower Laying off workers may lower morale and productivitymorale and productivity

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Varying production rate through Varying production rate through overtime or idle timeovertime or idle time Allows constant workforceAllows constant workforce

May be difficult to meet large May be difficult to meet large increases in demandincreases in demand

Overtime can be costly and may Overtime can be costly and may drive down productivitydrive down productivity

Absorbing idle time may be Absorbing idle time may be difficultdifficult

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SubcontractingSubcontracting Temporary measure during Temporary measure during

periods of peak demandperiods of peak demand

May be costlyMay be costly

Assuring quality and timely Assuring quality and timely delivery may be difficultdelivery may be difficult

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Using part-time workersUsing part-time workers Useful for filling unskilled or low Useful for filling unskilled or low

skilled positions, especially in skilled positions, especially in servicesservices

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Demand OptionsDemand Options

Influencing demandInfluencing demand Use advertising or promotion to Use advertising or promotion to

increase demand in low periodsincrease demand in low periods

Attempt to shift Attempt to shift demand to slow demand to slow periodsperiods

May not be May not be sufficient to sufficient to balance demand balance demand and capacityand capacity

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Demand OptionsDemand Options

Back ordering during high- Back ordering during high- demand periodsdemand periods Requires customers to wait for an Requires customers to wait for an

order without loss of goodwill or order without loss of goodwill or the orderthe order

Most effective when there are few Most effective when there are few if any substitutes for the product if any substitutes for the product or serviceor service

Often results in lost salesOften results in lost sales

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Aggregate Planning Aggregate Planning OptionsOptions

OptionOption AdvantagesAdvantages DisadvantagesDisadvantages Some Some CommentsComments

Changing Changing inventory inventory levelslevels

Changes in Changes in human human resources are resources are gradual or gradual or none; no none; no abrupt abrupt production production changes.changes.

Inventory Inventory holding cost holding cost may increase. may increase. Shortages may Shortages may result in lost result in lost sales.sales.

Applies mainly Applies mainly to production, to production, not service, not service, operations.operations.

Varying Varying workforce workforce size by size by hiring or hiring or layoffslayoffs

Avoids the Avoids the costs of other costs of other alternatives.alternatives.

Hiring, layoff, Hiring, layoff, and training and training costs may be costs may be significant.significant.

Used where Used where size of labor size of labor pool is large.pool is large.

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Varying Varying production production rates rates through through overtime overtime or idle or idle timetime

Matches Matches seasonal seasonal fluctuations fluctuations without hiring/ without hiring/ training costs.training costs.

Overtime Overtime premiums; premiums; tired workers; tired workers; may not meet may not meet demand.demand.

Allows Allows flexibility flexibility within the within the aggregate aggregate plan.plan.

Sub-Sub-contractincontractingg

Permits Permits flexibility and flexibility and smoothing of smoothing of the firm’s the firm’s output.output.

Loss of quality Loss of quality control; control; reduced reduced profits; loss of profits; loss of future future business.business.

Applies mainly Applies mainly in production in production settings.settings.

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Using part-Using part-time time workersworkers

Is less costly Is less costly and more and more flexible than flexible than full-time full-time workers.workers.

High turnover/ High turnover/ training costs; training costs; quality suffers; quality suffers; scheduling scheduling difficult.difficult.

Good for Good for unskilled jobs unskilled jobs in areas with in areas with large large temporary temporary labor pools.labor pools.

Influencing Influencing demanddemand

Tries to use Tries to use excess excess capacity. capacity. Discounts Discounts draw new draw new customers.customers.

Uncertainty in Uncertainty in demand. Hard demand. Hard to match to match demand to demand to supply exactly.supply exactly.

Creates Creates marketing marketing ideas. ideas. Overbooking Overbooking used in some used in some businesses.businesses.

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Back Back ordering ordering during during high-high-demand demand periodsperiods

May avoid May avoid overtime. overtime. Keeps capacity Keeps capacity constant.constant.

Customer must Customer must be willing to be willing to wait, but wait, but goodwill is goodwill is lost.lost.

Many Many companies companies back order.back order.

Costs involvedCosts involved

1.1. Procurement CostProcurement Cost

2.2. Production CostProduction Cost

3.3. Inventory holding costInventory holding cost

4.4. Back orders/ Lost salesBack orders/ Lost sales

5.5. Cost of Increasing/Decreasing work forceCost of Increasing/Decreasing work force

6.6. Cost of overtime/ under timeCost of overtime/ under time

7.7. Costs to vary production rates.Costs to vary production rates.

Inputs for an aggregate plan Inputs for an aggregate plan

Specify the planning horizon (typically 3-18 Specify the planning horizon (typically 3-18 months)months)

Aggregate planner requires the following Aggregate planner requires the following informationinformation Demand forecast in each period Demand forecast in each period Production costsProduction costs

labor costs, regular time ($/hr) and overtime ($/hr)labor costs, regular time ($/hr) and overtime ($/hr) subcontracting costs ($/hr or $/unit)subcontracting costs ($/hr or $/unit) cost of changing capacity: hiring or layoff ($/worker) cost of changing capacity: hiring or layoff ($/worker)

and cost of adding or reducing machine capacity and cost of adding or reducing machine capacity ($/machine)($/machine)

Labor/machine hours required per unitLabor/machine hours required per unit Inventory holding cost ($/unit/period)Inventory holding cost ($/unit/period) Stockout or backlog cost ($/unit/period)Stockout or backlog cost ($/unit/period) Constraints: limits on overtime, layoffs, capital available, Constraints: limits on overtime, layoffs, capital available,

stockouts and backlogs stockouts and backlogs

Outputs of Aggregate PlanOutputs of Aggregate Plan

Production quantity from regular time, Production quantity from regular time, overtime, and subcontracted time:overtime, and subcontracted time: used to used to determine number of workers and supplier purchase determine number of workers and supplier purchase levelslevels

Inventory held:Inventory held: used to determine how much used to determine how much warehouse space and working capital is neededwarehouse space and working capital is needed

Backorder/stock out quantity:Backorder/stock out quantity: determines the determines the customer service levels.customer service levels.

Machine capacity increase/decrease:Machine capacity increase/decrease: used to used to determine if new production equipment needs to be determine if new production equipment needs to be purchasedpurchased

Aggregate Planning Aggregate Planning StrategiesStrategies

Chase strategyChase strategy – using capacity – using capacity as the leveras the lever

Level strategyLevel strategy – using inventory – using inventory as the leveras the lever

Mixed strategyMixed strategy – a combination – a combination of the two strategiesof the two strategies

Chase StrategyChase Strategy (using capacity as (using capacity as lever)lever)

Production rate is synchronized with demand by varying Production rate is synchronized with demand by varying machine capacity or hiring and laying off workers as the machine capacity or hiring and laying off workers as the demand rate varies.demand rate varies.

Drawbacks:Drawbacks: In practice, it is often difficult to vary capacity and In practice, it is often difficult to vary capacity and

workforce on short noticeworkforce on short notice Expensive if cost of varying capacity is highExpensive if cost of varying capacity is high Negative effect on workforce moraleNegative effect on workforce morale

When to use:When to use:

Inventory holding costs are high and costs of changing Inventory holding costs are high and costs of changing capacity are low.capacity are low.

Favored by many service organization.Favored by many service organization.

Level StrategyLevel Strategy (using inventory as lever)(using inventory as lever)

Maintain stable machine capacity and workforce Maintain stable machine capacity and workforce levels with a constant output ratelevels with a constant output rate

Shortages and surpluses result in fluctuations in Shortages and surpluses result in fluctuations in inventory levels over timeinventory levels over time

Drawback:Drawback: Large inventories and backlogs may accumulate.Large inventories and backlogs may accumulate.

When to use:When to use: Should be used when inventory holding and Should be used when inventory holding and

backlog costs are relatively lowbacklog costs are relatively low

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Roofing Supplier Example Roofing Supplier Example ( Using level strategy)( Using level strategy)

MonthMonth Expected DemandExpected DemandProduction Production

DaysDaysDemand Per Day Demand Per Day

(computed)(computed)

JanJan 900900 2222 4141

FebFeb 700700 1818 3939

MarMar 800800 2121 3838

AprApr 1,2001,200 2121 5757

MayMay 1,5001,500 2222 6868

JuneJune 1,1001,100 2020 5555

6,2006,200 124124

= = 50= = 50 units per day units per day6,2006,200

124124

Average Average requirementrequirement ==

Total expected demandTotal expected demand

Number of production daysNumber of production days

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Roofing Supplier Example Roofing Supplier Example 11

Figure 13.3Figure 13.3

70 70 –

60 60 –

50 50 –

40 40 –

30 30 –

0 0 –JanJan FebFeb MarMar AprApr MayMay JuneJune == MonthMonth

2222 1818 2121 2121 2222 2020 == Number ofNumber ofworking daysworking days

Pro

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ate

per

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ion

rat

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ork

ing

day

Level production using average Level production using average monthly forecast demandmonthly forecast demand

Forecast demandForecast demand

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Cost InformationCost Information

Inventory carrying costInventory carrying cost $ 5$ 5 per unit per month per unit per month

Subcontracting cost per unitSubcontracting cost per unit $10$10 per unit per unit

Average pay rateAverage pay rate $ 5$ 5 per hour per hour ($40($40 per per dayday))

Overtime pay rateOvertime pay rate$ 7$ 7 per hour per hour

((above above 88 hours per hours per dayday))

Labor-hours to produce a unitLabor-hours to produce a unit 1.61.6 hours per unit hours per unit

Cost of increasing daily production Cost of increasing daily production rate (hiring and training)rate (hiring and training)

$300$300 per unit per unit

Cost of decreasing daily production Cost of decreasing daily production rate (layoffs)rate (layoffs)


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Table 13.3Table 13.3


Inventory carry costInventory carry cost $ 5$ 5 per unit per month per unit per month










Plan 1 – constant workforce

Plan 1 – constant workforce

Month

Production at 50 Units per

Day

Demand Forecas

t

Monthly Inventor

y Change

Ending Inventor

y

Jan 1,100 900 +200 200

Feb 900 700 +200 400

Mar 1,050 800 +250 650

Apr 1,050 1,200 -150 500

May 1,100 1,500 -400 100

June 1,000 1,100 -100 0

1,850Total units of inventory carried over from onemonth to the next = 1,850 units

Workforce required to produce 50 units per day = 10 workers

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Month

Production at 50 Units per

DayDemand Forecast

Monthly Inventory Change

Ending Inventory

Jan 1,100 900 +200 200

Feb 900 700 +200 400

Mar 1,050 800 +250 650

Apr 1,050 1,200 -150 500

May 1,100 1,500 -400 100

June 1,000 1,100 -100 0

1,850Total units of inventory carried over from one

month to the next = 1,850 units

Workforce required to produce 50 units per day = 10 workers

Costs Calculations

Inventory carrying $9,250 (= 1,850 units carried x $5 per unit)

Regular-time labor 49,600 (= 10 workers x $40 per day x 124 days)

Other costs (overtime, hiring, layoffs, subcontracting) 0

Total cost$58,850

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Figure 13.4Figure 13.4

Cu

mu

lati

ve d

eman

d u

nit

sC

um

ula

tive

dem

and

un

its

7,000 7,000 –

6,000 6,000 –

5,000 5,000 –

4,000 4,000 –

3,000 3,000 –

2,000 –

1,000 –

–JanJan FebFeb MarMar AprApr MayMay JuneJune

Cumulative forecast Cumulative forecast requirementsrequirements

Cumulative level Cumulative level production using production using average monthly average monthly

forecast forecast requirementsrequirements

Reduction Reduction of inventoryof inventory

Excess inventoryExcess inventory

6,200 units6,200 units

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JanJan 900900 2222 4141

FebFeb 700700 1818 3939

MarMar 800800 2121 3838

AprApr 1,2001,200 2121 5757

MayMay 1,5001,500 2222 6868

JuneJune 1,1001,100 2020 5555

6,2006,200 124124

Minimum requirementMinimum requirement = 38 = 38 units per day units per day

Plan 2 – subcontracting

Plan 2 – subcontracting

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70 70 –

60 60 –

50 50 –

40 40 –

30 30 –



Pro

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ork

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day

Level production Level production using lowest using lowest

monthly forecast monthly forecast demanddemand

Forecast demandForecast demand

34














35














In-house production = 38 units per day x 124 days

= 4,712 units

Subcontract units = 6,200 - 4,712= 1,488 units

36














In-house production = 38 units per day x 124 days

= 4,712 units

Subcontract units = 6,200 - 4,712= 1,488 units

Costs Calculations

Regular-time labor $37,696 (= 7.6 workers x $40 per day x 124 days)

Subcontracting 14,880 (= 1,488 units x $10 per unit)

Total cost $52,576

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JanJan 900900 2222 4141

FebFeb 700700 1818 3939

MarMar 800800 2121 3838

AprApr 1,2001,200 2121 5757

MayMay 1,5001,500 2222 6868

JuneJune 1,1001,100 2020 5555

6,2006,200 124124

Production = Expected DemandProduction = Expected DemandPlan 3 – hiring and firing

Plan 3 – hiring and firing

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70 70 –

60 60 –

50 50 –

40 40 –

30 30 –



Pro

du

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ate

per

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ork

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day Forecast demand and Forecast demand and

monthly productionmonthly production

39














40














Month

Forecast (units)

Daily Prod Rate

Basic Production

Cost (demand x 1.6 hrs/unit

x $5/hr)

Extra Cost of Increasing Production

(hiring cost)

Extra Cost of Decreasing Production (layoff cost)

Total Cost

Jan 900 41 $ 7,200 — — $ 7,200

Feb 700 39 5,600 —$1,200

(= 2 x $600)6,800

Mar 800 38 6,400 —$600

(= 1 x $600)7,000

Apr 1,200 57 9,600$5,700

(= 19 x $300)— 15,300

May 1,500 68 12,000$3,300

(= 11 x $300)— 15,300

June 1,100 55 8,800 —$7,800

(= 13 x $600)16,600

$49,600 $9,000 $9,600 $68,200


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Comparison of Three Comparison of Three PlansPlans


CostCost Plan 1Plan 1 Plan 2Plan 2 Plan 3Plan 3

Inventory Inventory carryingcarrying $ 9,250$ 9,250 $ 0$ 0 $ 0$ 0

Regular laborRegular labor 49,60049,600 37,69637,696 49,60049,600

Overtime laborOvertime labor 00 00 00

HiringHiring 00 00 9,0009,000

LayoffsLayoffs 00 00 9,6009,600

SubcontractingSubcontracting 00 14,88014,880 00

Total costTotal cost $58,850$58,850 $52,576$52,576 $68,200$68,200

Plan 2 is the lowest cost optionPlan 2 is the lowest cost option

Aggregate planning using Linear Aggregate planning using Linear ProgrammingProgramming

Case Study: Red Tomato Gardening Case Study: Red Tomato Gardening Tools Inc.Tools Inc.

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The demand is highly seasonal for The demand is highly seasonal for gardening tools.gardening tools.

Red Tomato’s options for handling Red Tomato’s options for handling seasonality areseasonality are Adding workers during peak seasonAdding workers during peak season SubcontractingSubcontracting Building up inventory during slow monthsBuilding up inventory during slow months Building up backorders ( orders delivered late Building up backorders ( orders delivered late

to customers)to customers) Starting Point: Build a Demand Forecast.Starting Point: Build a Demand Forecast.

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Aggregate Planning using Linear ProgrammingAggregate Planning using Linear ProgrammingCase Study: Red Tomato Tools.Case Study: Red Tomato Tools.

Month Demand ForecastJanuary 1,600February 3,000March 3,200April 3,800May 2,200June 2,200

Time horizon: 6 months

Selling price:$40

Beginning inventory: 1,000 units

Ending inventory: at least 500 units

Workforce as on Jan 1st: 80 employees

20 working days each month- 8 hour day at $4 per hour regular time

No employee is allowed to work more than 10 hours of overtime per month

.

Case Study: Red Tomato Inc.Case Study: Red Tomato Inc. Cost ParametersCost Parameters

Item CostMaterials $10/unitInventory holding cost $2/unit/monthMarginal cost of a stockout $5/unit/monthHiring and training costs $300/workerLayoff cost $500/workerLabor hours required 4/unitRegular time cost $4/hourOver time cost $6/hourCost of subcontracting $30/unit

Following costs are evaluated.Following costs are evaluated. Regular time Labor costRegular time Labor cost Overtime Labor costOvertime Labor cost Cost of Hiring Cost of Hiring Cost of LayoffCost of Layoff Cost of Inventory Cost of Inventory Cost of Stock outCost of Stock out Cost of MaterialsCost of Materials Cost of SubcontractingCost of Subcontracting

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Case Study: Red Tomato Inc.Case Study: Red Tomato Inc. Decision VariablesDecision Variables

WWtt = Workforce size for month = Workforce size for month tt, , tt = 1, ..., 6 = 1, ..., 6

HHtt = Number of employees hired at the beginning of month = Number of employees hired at the beginning of month tt, , tt = 1, ..., 6 = 1, ..., 6

LLtt = Number of employees laid off at the beginning of month = Number of employees laid off at the beginning of month tt, , tt = 1, ..., 6 = 1, ..., 6

PPtt = Number of units produced in month = Number of units produced in month tt, , tt = 1, ..., 6 = 1, ..., 6

IItt = Inventory at the end of month = Inventory at the end of month tt, , tt = 1, ..., 6 = 1, ..., 6

SStt = Number of units stocked out/ backlogged at the end of = Number of units stocked out/ backlogged at the end of month month tt, , tt = 1, ..., 6 = 1, ..., 6

CCtt = Number of units subcontracted for month = Number of units subcontracted for month tt, , tt = 1, ..., 6 = 1, ..., 6

OOtt = Number of overtime hours worked in month = Number of overtime hours worked in month tt, , tt = 1, ..., 6 = 1, ..., 6

Objective FunctionObjective Function

6

1

6

1

6

1

6

1

6

1

6

1

6

1

6

1

30105

26500

300640

tt

tt

tt

tt

tt

tt

tt

tt

CPS

IOL

HWMin

Constraints:Constraints:

1.1. Workforce, hiring and layoff constraintWorkforce, hiring and layoff constraint

.80,6,...,1

0

,

0

1

1

WwheretforLHWW

orLHWW

tttt

tttt

Constraints ( Contd..)Constraints ( Contd..)

2.2. Capacity Constraint:Capacity Constraint:

Production for each month Production for each month cannot exceed capacitycannot exceed capacity

.6,...,1

,0440

,440

tforPOW

OWP

ttt

ttt


3.3. Inventory balance constraint:Inventory balance constraint:(Balances inventory at the end of each period)(Balances inventory at the end of each period)

.500,0

,000,1,6,...,1

,0

,

60

0

11

11

IandS

IwheretforSISDCPI

SISDCPI

ttttttt

ttttttt


4.4. Over time limit constraintOver time limit constraint

.6,...,1

,010

,10

tforOW

WO

tt

tt

Plus, add constraints such that

•Each variable must be non-negative

• Make number of employees, number of production units an Integer value

•There is no backlogs at the end of period ie, S6 =0

The LPP can be solved using Excel tool solver, LINGO, LINDO etc.

SummarySummary

Aggregate planning is an intermediate time frame Aggregate planning is an intermediate time frame planning process by which a company determines planning process by which a company determines optimum levels of capacity, production and optimum levels of capacity, production and inventory over a specified time horizon.inventory over a specified time horizon.

Aggregate planning problem aims to maximize Aggregate planning problem aims to maximize firm’s profit/ minimize costs over the planning firm’s profit/ minimize costs over the planning horizon.horizon.

There are 3 main kinds of aggregate planning There are 3 main kinds of aggregate planning strategies: Chase, Level and Mixed.strategies: Chase, Level and Mixed.

Aggregate planning problem can be solved as an Aggregate planning problem can be solved as an LPP, depending on the nature of parameters LPP, depending on the nature of parameters involved.involved.

Thank you !Thank you !

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Aggregate Planning