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Transcript of 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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Capacity OptionsCapacity Options
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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Capacity OptionsCapacity Options
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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Capacity OptionsCapacity Options
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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Capacity OptionsCapacity Options
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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Aggregate Planning Aggregate Planning OptionsOptions
OptionOption AdvantagesAdvantages DisadvantagesDisadvantages Some Some CommentsComments
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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Aggregate Planning Aggregate Planning OptionsOptions
OptionOption AdvantagesAdvantages DisadvantagesDisadvantages Some Some CommentsComments
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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Aggregate Planning Aggregate Planning OptionsOptions
OptionOption AdvantagesAdvantages DisadvantagesDisadvantages Some Some CommentsComments
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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ayP
rod
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ion
rat
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ork
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day
Level production using average Level production using average monthly forecast demandmonthly forecast demand
Forecast demandForecast demand
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Roofing Supplier Example Roofing Supplier Example 22
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)
$600$600 per unit per unit
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Roofing Supplier Example Roofing Supplier Example 22
Table 13.3Table 13.3
Cost InformationCost Information
Inventory carry costInventory carry 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)
$600$600 per unit per unit
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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Roofing Supplier Example Roofing Supplier Example 22
Table 13.3Table 13.3
Cost InformationCost Information
Inventory carry costInventory carry 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)
$600$600 per unit per unit
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
31
Roofing Supplier Example Roofing Supplier Example 22
Figure 13.4Figure 13.4
Cu
mu
lati
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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
32
Roofing Supplier Example Roofing Supplier Example 33
Table 13.2Table 13.2
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
Minimum requirementMinimum requirement = 38 = 38 units per day units per day
Plan 2 – subcontracting
Plan 2 – subcontracting
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Roofing Supplier Example Roofing Supplier Example 33
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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per
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ion
rat
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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
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Roofing Supplier Example Roofing Supplier Example 33
Table 13.3Table 13.3
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)
$600$600 per unit per unit
35
Roofing Supplier Example Roofing Supplier Example 33
Table 13.3Table 13.3
Cost InformationCost Information
Inventory carry costInventory carry 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)
$600$600 per unit per unit
In-house production = 38 units per day x 124 days
= 4,712 units
Subcontract units = 6,200 - 4,712= 1,488 units
36
Table 13.3Table 13.3
Cost InformationCost Information
Inventory carry costInventory carry 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)
$600$600 per unit per unit
Roofing Supplier Example Roofing Supplier Example 33
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
37
Roofing Supplier Example Roofing Supplier Example 44
Table 13.2Table 13.2
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
Production = Expected DemandProduction = Expected DemandPlan 3 – hiring and firing
Plan 3 – hiring and firing
38
Roofing Supplier Example Roofing Supplier Example 44
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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day Forecast demand and Forecast demand and
monthly productionmonthly production
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Roofing Supplier Example Roofing Supplier Example 44
Table 13.3Table 13.3
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)
$600$600 per unit per unit
40
Roofing Supplier Example Roofing Supplier Example 44
Table 13.3Table 13.3
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)
$600$600 per unit per unit
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
Table 13.4Table 13.4
41
Comparison of Three Comparison of Three PlansPlans
Table 13.5Table 13.5
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
Constraints ( Contd..)Constraints ( Contd..)
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
Constraints ( Contd..)Constraints ( Contd..)
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 !