chapter 4 forecasting production planning overview what is forecasting? types of forecasts 7...
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Chapter 4 Forecasting
Production Planning
SalesForecast
AggregatePlanning
MasterProductionSchedule
MRP
ProductionScheduling
Purchasing
Production
Overview
What is forecasting?
Types of forecasts
7 steps of forecasting
Qualitative forecasting
Overview
Quantitative forecastingTime-series forecasting
NaïveMoving averageExponential smoothingSeasonal variations
Associative methods Monitoring and
Controlling Forecasts
What is forecasting?
Sales will be $200 Million!Could be a
prediction based on historical data and mathematical models
Could be a prediction based on expertise and intuition
Forecasting - Is the art and science of predicting the future
Could be a prediction based on both a model and a manager’s expertise
7 Steps to a Forecast
Determine the use of the forecast
Select the items to be forecast
Determine the time horizon of the forecast
Select the forecasting model(s)
Gather the data
Make the forecast
Validate and implement results
Realities of Forecasting
Forecasts never perfect and seldom correct.
Most forecasting methods assume that there is
some underlying stability in the system
Both product family and aggregated product
forecasts are more accurate than individual product
forecasts
Demand Forecasts OM manager is primarily interested in demand
forecasts (as opposed to economic forecasts and technological forecasts)
Underlying basis of all business decisionsProduction InventoryPersonnelFacilities
Demand Forecast ApplicationsDemand Forecast ApplicationsTime Horizon
Medium Term Long Term Short Term (3 months– (more than
Application (0–3 months) 3 years) 3 years)
Forecast quantity
Decision area
Forecastingtechnique
Demand Forecast ApplicationsDemand Forecast ApplicationsTime Horizon
Medium Term Long Term Short Term (3 months– (more than
Application (0–3 months) 2 years) 2 years)
Forecast quantity Individualproducts orservices
Decision area Inventorymanagement
Final assemblyscheduling
Workforcescheduling
Master productionscheduling
Forecasting Time seriestechnique Associative
Demand Forecast ApplicationsDemand Forecast ApplicationsTime Horizon
Medium Term Long Term Short Term (3 months– (more than
Application (0–3 months) 2 years) 2 years)
Forecast quantity Individual Total salesproducts or Groups or familiesservices of products or
servicesDecision area Inventory Staff planning
management ProductionFinal assembly planning
scheduling Master productionWorkforce scheduling
scheduling PurchasingMaster production Distribution
schedulingForecasting Time series Associative
technique Associative
Demand Forecast ApplicationsDemand Forecast ApplicationsTime Horizon
Medium Term Long Term Short Term (3 months– (more than
Application (0–3 months) 2 years) 2 years)
Forecast quantity Individual Total sales Total salesproducts or Groups or familiesservices of products or
servicesDecision area Inventory Staff planning Facility location
management Production CapacityFinal assembly planning planning
scheduling Master production ProcessWorkforce scheduling management
scheduling PurchasingMaster production Distribution
schedulingForecasting Time series Associative Associative
technique Associative
Overview of Qualitative MethodsOverview of Qualitative MethodsREAD in TEXT (p. 81-82)
Jury of executive opinion Pool opinions of high-level executives, sometimes augment by statistical
models
Sales force composite Estimates from individual salespersons are reviewed for reasonableness, then
aggregated
Delphi method Panel of experts, queried iteratively
Consumer Market Survey Ask the customer
Patterns of DemandPatterns of Demand
Patterns of DemandPatterns of DemandQ
ua
nti
ty
Time
Patterns of DemandPatterns of DemandQ
ua
nti
ty
Time
(a) Random: Data cluster about a horizontal line.
Patterns of DemandPatterns of DemandQ
ua
nti
ty
Time
(b) Trend: Data consistently increase or decrease over a period of time.
Patterns of DemandPatterns of DemandQ
ua
nti
ty
| | | | | | | | | | | |J F M A M J J A S O N D
Months
(c) Seasonal: Data consistently show peaks and valleys at the same time each year.
Year 1
Patterns of DemandPatterns of DemandQ
ua
nti
ty
| | | | | | | | | | | |J F M A M J J A S O N D
Months
Year 1
Year 2
(c) Seasonal: Data consistently show peaks and valleys at the same time each year.
Patterns of DemandPatterns of DemandQ
ua
nti
ty
| | | | | |1 2 3 4 5 6
Years
(c) Cyclical: Data reveal gradual increases and decreases over extended periods.
Overview of Quantitative Methods
Naïve approach
Moving averages
Exponential smoothing
Linear regression
Time-series Models – no trend, seasonal, or cyclical fluctuations
Associative models
Set of evenly spaced numerical data Obtained by observing response variable at regular time
periods
Forecast based only on past values Assumes that factors influencing past and present will
continue influence in future
ExampleYear: 1993 1994 1995 1996 1997
Sales: 78.7 63.5 89.7 93.2 92.1
What is a Time Series?
Naïve Approach
Assumes demand in next period is the same
as demand in most recent periode.g., If May sales were 48, then June sales will
be 48
Sometimes cost effective & efficient
Moving Average Approach
MA is a series of arithmetic means
Used if little or no trend
Used often for smoothingProvides overall impression of data over time
MAMAnn
nn Demand inDemand in PreviousPrevious PeriodsPeriods
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Patient arrivals have been recorded at a medical clinic over the past 28 weeks.
Want to predict the number of patient arrivals for the 29th week.
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Week
450 —
430 —
410 —
390 —
370 —Pat
ien
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| | | | | |0 5 10 15 20 25 30
Pat
ien
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ls
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Week
450 —
430 —
410 —
390 —
370 —
| | | | | |0 5 10 15 20 25 30
Actual patientarrivals
Pat
ien
t ar
riva
ls
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Week
450 —
430 —
410 —
390 —
370 —
| | | | | |0 5 10 15 20 25 30
Actual patientarrivals
Pat
ien
t ar
riva
ls-No trend
-No seasonal variation
-No cycle
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientarrivals
450 —
430 —
410 —
390 —
370 —
Week
| | | | | |0 5 10 15 20 25 30
Pat
ien
t ar
riva
ls
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientarrivals
Actual patientarrivals
450 —
430 —
410 —
390 —
370 —
Week
| | | | | |0 5 10 15 20 25 30
PatientWeek Arrivals
1 4002 3803 411
Pat
ien
t ar
riva
ls
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientarrivals
Actual patientarrivals
450 —
430 —
410 —
390 —
370 —
Week
| | | | | |0 5 10 15 20 25 30
PatientWeek Arrivals
1 4002 3803 411
Pat
ien
t ar
riva
ls
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientarrivals
Week
450 —
430 —
410 —
390 —
370 —
| | | | | |0 5 10 15 20 25 30
PatientWeek Arrivals
1 4002 3803 411
F4 = 411 + 380 + 4003
Pat
ien
t ar
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ls
F4 = 397.0
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientarrivals
450 —
430 —
410 —
390 —
370 —
Week
| | | | | |0 5 10 15 20 25 30
PatientWeek Arrivals
1 4002 3803 411
F4 = 397.0
Pat
ien
t ar
riva
ls
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientarrivals
Week
450 —
430 —
410 —
390 —
370 —
| | | | | |0 5 10 15 20 25 30
PatientWeek Arrivals
2 3803 4114 415
F5 = 415 + 411 + 380
3
Pat
ien
t ar
riva
ls
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientarrivals
450 —
430 —
410 —
390 —
370 —
Week
| | | | | |0 5 10 15 20 25 30
PatientWeek Arrivals
2 3803 4114 415
F5 = 402.0
Pat
ien
t ar
riva
ls
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
450 —
430 —
410 —
390 —
370 —
Week
| | | | | |0 5 10 15 20 25 30
Actual patientarrivals
Pat
ien
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ls
Go To Excel
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
450 —
430 —
410 —
390 —
370 —
Week
| | | | | |0 5 10 15 20 25 30
Actual patientarrivals
3-week MAforecast
Pat
ien
t ar
riva
ls
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Week
450 —
430 —
410 —
390 —
370 —
| | | | | |0 5 10 15 20 25 30
Actual patientarrivals
3-week MAforecast
6-week MAforecast
Pat
ien
t ar
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ls
WEIGHTED Moving Averages
SKIP
Increasing n makes forecast less sensitive to changes
Do not forecast trend well Require much historical data
© 1984-1994 T/Maker Co.
Disadvantages of Moving Average Methods
Form of weighted moving averageWeights decline exponentiallyMost recent data weighted most
Requires smoothing constant ()Ranges from 0 to 1Subjectively chosen
Involves little record keeping of past data
Exponential Smoothing Method
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
450 —
430 —
410 —
390 —
370 —
Week
| | | | | |0 5 10 15 20 25 30
Exponential Smoothing = 0.10
Ft +1 = Ft + (Dt – Ft )
Pat
ien
t ar
riva
ls
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
450 —
430 —
410 —
390 —
370 —
Week
| | | | | |0 5 10 15 20 25 30
Exponential Smoothing = 0.10
F3 = 390 (Given)D3 = 411
Ft +1 = Ft + (Dt – Ft )
Pat
ien
t ar
riva
ls
F4 = 390 + 0.10(411-390)
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
450 —
430 —
410 —
390 —
370 —
Week
| | | | | |0 5 10 15 20 25 30
F4 = 392.1
Exponential Smoothing = 0.10
F3 = 390 (Given)D3 = 411
Ft +1 = Ft + (Dt – Ft )
Pat
ien
t ar
riva
ls
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
Week
450 —
430 —
410 —
390 —
370 —
| | | | | |0 5 10 15 20 25 30
F4 = 392.1D4 = 415
Exponential Smoothing = 0.10
F4 = 392.1 F5 = 394.4
Ft +1 = Ft + (Dt – Ft )
Pat
ien
t ar
riva
ls
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
Week
450 —
430 —
410 —
390 —
370 —
| | | | | |0 5 10 15 20 25 30
Pat
ien
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ls
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
450 —
430 —
410 —
390 —
370 —Pat
ien
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ls
Week
| | | | | |0 5 10 15 20 25 30
Exponential smoothing = 0.10
Go To Excel
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
450 —
430 —
410 —
390 —
370 —Pat
ien
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ls
Week
| | | | | |0 5 10 15 20 25 30
3-week MAforecast
Exponential smoothing = 0.10
Exponential smoothing with trend adjustmentSKIP
Trend projection (p. 93-96)Regression analysis
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
1 45 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215
Total 1000 1200 1800 2200 Average 250 300 450 550
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Stanley Steamer Carpet Cleaners
0200400600800
100012001400
0 1 2 3 4 5
Quarter
Num
ber o
f cus
tom
ers
Year 1
Year 2
Year 3
Year 4
Quarter Year 1 Year 2 Year 3 Year 4
1 45 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215
Total 1000 1200 1800 2200 Average 250 300 450 550
Seasonal Index = Actual Demand
Average Demand
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Projected Annual Demand = 2600Average Quarterly Demand = 2600/4 = 650
Quarter Year 1 Year 2 Year 3 Year 4
1 45 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215
Total 1000 1200 1800 2200 Average 250 300 450 550
Seasonal Index = Actual Demand
Average Demand
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
1 45 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215
Total 1000 1200 1800 2200 Average 250 300 450 550
Seasonal Index = = 0.1845
250
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.323 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.323 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39
Quarter Average Seasonal Index
1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20234
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.323 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39
Quarter Average Seasonal Index
1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.202 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.303 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.004 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.323 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39
Quarter Average Seasonal Index Forecast
1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.202 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.303 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.004 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50
Projected Annual Demand = 2600Average Quarterly Demand = 2600/4 = 650
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.323 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39
Quarter Average Seasonal Index Forecast
1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20 650(0.20) = 1302 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.303 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.004 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50
Projected Annual Demand = 2600Average Quarterly Demand = 2600/4 = 650
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.323 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39
Quarter Average Seasonal Index Forecast
1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20 650(0.20) = 1302 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.30 650(1.30) = 8453 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.00 650(2.00) = 13004 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50 650(0.50) = 325
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Remember Regression Remember Regression Analysis?Analysis?
Remember Regression Remember Regression Analysis?Analysis?
Dep
end
ent
vari
able
Independent variableX
Y
Remember Regression Remember Regression Analysis?Analysis?
Dep
end
ent
vari
able
Independent variableX
Y
Remember Regression Remember Regression Analysis?Analysis?
Dep
end
ent
vari
able
Independent variableX
Y Regressionequation:Y = a + bX
Remember Regression Remember Regression Analysis?Analysis?
Dep
end
ent
vari
able
Independent variableX
Y
Actualvalueof Y
Value of X usedto estimate Y
Regressionequation:Y = a + bX
Remember Regression Remember Regression Analysis?Analysis?
Dep
end
ent
vari
able
Independent variableX
Y
Actualvalueof Y
Estimate ofY from regressionequation
Value of X usedto estimate Y
Regressionequation:Y = a + bX
Remember Regression Remember Regression Analysis?Analysis?
Dep
end
ent
vari
able
Independent variableX
Y
Actualvalueof Y
Estimate ofY from regressionequation
Value of X usedto estimate Y
Deviation,or error
{
Regressionequation:Y = a + bX
Regression analysis in forecasting
Two applications of regressions analysis in forecasting Time-series data
Independent variable is time Dependent variable is the variable that you want to forecast (i.e. demand)
Data is not time-series Independent variable is a known variable that can be used to predict (i.e.
advertising dollars, customer population) Dependent variable is the variable that you want to forecast (i.e. demand)
Regression analysis is the same in both applications
Armand, Inc.: Regression Analysis
Armand, Inc. is a chain of Italian restaurants located in a five-state area.
The most successful locations have been near college campuses.
Prior to opening a new restaurant, management requires a forecast of the yearly sales revenues.Such an estimate is used
in planning the restaurant capacity, personnel requirements, and to see if the operations costs are smaller than the predicted
revenue.
Armand, Inc.Student population Annual sales
Restaurant (1000s) ($1000s)1 2 582 6 1053 8 884 8 1185 12 1176 16 1377 20 1578 20 1699 22 149
10 26 202
Armand, Inc.
Annual sales and Student Population
0
50
100
150
200
250
0 5 10 15 20 25 30
Student Population (1000s)
An
nu
al S
ales
($10
00s)
Armand, Inc.
Annual sales and Student Population
0
50
100
150
200
250
0 5 10 15 20 25 30
Student Population (1000s)
An
nu
al S
ales
($10
00s)
Go To Excel
Armand, Inc.
bXaY Intercept
Coefficient for Student Population
XY 560
Armand, Inc.
Forecast the Annual Sales if the student population is 20,000.
XY 560
Armand, Inc.
Forecast the Annual Sales if the student population is 20,000.
160
)20(560
560
Y
Y
XY Forecast is :
$160,000
Forecasting accuracy
“I think there is a world market for about FIVE computers.”
— Thomas J. Watson, chairman of IBM, 1943
Forecast accuracy
IBM 1994
$700 million inventory of OBSOLETE PCs that took 6
months to unload.
Reaction: too conservative when releasing the new
Aptiva home PCs. New models sold out before the
holiday season had begun.
Measuring the quality of forecasting
MAD – mean absolute deviation
MSE – mean square error
n
rorsForecastErMAD n
n
rorForecastErMSE n
2
Your Turn Demand for April-September is given. Determine the exponential smoothing forecasts for those
April. Forecast for Mar was 58 Demand for Mar was 60.
Determine the regression equation forecasts for those April. X is the number of months in the future (for April, X = 1)
Your TurnDemand Exponential
Smoothing alpha = 0.2
Regression Y = 54 + 3.9X
April 60
May 55
June 75
July 60
August 80
September 75
Calculate for APRIL:
Exponential smoothing forecast
Regression forecast
Forecast for Mar was 58Demand for Mar was 60.X is the number of months in the future (for April, X = 1)
Your Turn
Demand
Exponential Smoothing alpha = 0.20
Regression Y = 54 + 3.9X
April 60 58.4 1.6 57.9 2.1
May
June
July
August
September
Your Turn
Demand
Exponential Smoothing
alpha = 0.20Exp Smooth
abs(forecast error) Regression Y = 54 + 3.9X
Regressionabs(forecast error)
April 60 58.4 57.9
May 55 58.7 61.8
June 75 58.0 65.7
July 60 61.4 69.6
August 80 61.1 73.5
September 75 64.9 77.4
MAD = MAD =
Calculate abs(forecast error) for April
Your Turn
Demand
Exponential Smoothing alpha = 0.20
Regression Y = 54 + 3.9X
April 60 58.4 1.6 57.9 2.1
May 55 58.7 61.8
June 75 58.0 65.7
July 60 61.4 69.6
August 80 61.1 73.5
September 75 64.9 77.4
MAD = MAD =
Your Turn
Demand
Exponential Smoothing alpha = 0.20
Regression Y = 54 + 3.9X
April 60 58.4 1.6 57.9 2.1
May 55 58.7 3.7 61.8 6.8
June 75 58.0 17.0 65.7 9.3
July 60 61.4 1.4 69.6 9.6
August 80 61.1 18.9 73.5 6.5
September 75 64.9 10.1 77.4 2.4
MAD = MAD =
Calculate MAD for each.
Your Turn
Demand
Exponential Smoothing alpha = 0.20
Regression Y = 54 + 3.9X
April 60 58.4 1.6 57.9 2.1
May 55 58.7 3.7 61.8 6.8
June 75 58.0 17.0 65.7 9.3
July 60 61.4 1.4 69.6 9.6
August 80 61.1 18.9 73.5 6.5
September 75 64.9 10.1 77.4 2.4
MAD = 8.8 MAD = 6.12
Third Wave Research Group
- offers marketing software and databases
- Forecasts sales for specific
-Market areas
-Products
-segments
Tracking SignalsTracking Signals
Tracking SignalsTracking SignalsTracking signal =
RSFE
MAD
+2.0 —
+1.5 —
+1.0 —
+0.5 —
0 —
–0.5 —
–1.0 —
–1.5 —| | | | |
0 5 10 15 20 25 Observation number
Tra
ckin
g s
ign
al
Control limit
Control limit
Tracking SignalsTracking SignalsTracking signal =
RSFE
MAD
+2.0 —
+1.5 —
+1.0 —
+0.5 —
0 —
–0.5 —
–1.0 —
–1.5 —| | | | |
0 5 10 15 20 25 Observation number
Tra
ckin
g s
ign
al
Control limit
Control limit
Out of control
MoMo FcstFcst ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
|Error||Error|
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
-10-10
Error = Actual - Forecast = 90 - 100 = -10
Error = Actual - Forecast = 90 - 100 = -10
|Error||Error|
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
6 100 140
-10-10 -10-10
RSFE = Errors = NA + (-10) = -10
RSFE = Errors = NA + (-10) = -10
|Error||Error|
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
-10-10 -10-10 1010
Abs Error = |Error| = |-10| = 10
Abs Error = |Error| = |-10| = 10
|Error||Error|
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
-10-10 -10-10 1010 1010
Cum |Error| = |Errors| = NA + 10 = 10
Cum |Error| = |Errors| = NA + 10 = 10
|Error||Error|
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum|Error||Error|
MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
-10-10 -10-10 1010 1010 10.010.0
MAD = |Errors|/n = 10/1 = 10
MAD = |Errors|/n = 10/1 = 10
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
-10-10 -10-10 1010 1010 10.010.0 -1-1
TS = RSFE/MAD = -10/10 = -1
TS = RSFE/MAD = -10/10 = -1
|Error||Error|
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
-10-10 -10-10 1010 1010 10.010.0 -1-1
-5-5
Error = Actual - Forecast = 95 - 100 = -5
Error = Actual - Forecast = 95 - 100 = -5
|Error||Error|
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
-10-10 -10-10 1010 1010 10.010.0 -1-1
-5-5 -15-15
RSFE = Errors = (-10) + (-5) = -15
RSFE = Errors = (-10) + (-5) = -15
|Error||Error|
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
-10-10 -10-10 1010 1010 10.010.0 -1-1
-5-5 -15-15 55
Abs Error = |Error| = |-5| = 5
Abs Error = |Error| = |-5| = 5
|Error||Error|
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
-10-10 -10-10 1010 1010 10.010.0 -1-1
-5-5 -15-15 55 1515
Cum Error = |Errors| = 10 + 5 = 15
Cum Error = |Errors| = 10 + 5 = 15
|Error||Error|
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
-10-10 -10-10 1010 1010 10.010.0 -1-1
-5-5 -15-15 55 1515 7.57.5
MAD = |Errors|/n = 15/2 = 7.5
MAD = |Errors|/n = 15/2 = 7.5
|Error||Error|
Tracking Signal Computation
MoMo ForcForc ActAct ErrorError RSFERSFE AbsAbsErrorError
CumCum MADMAD TSTS
11 100100 9090
22 100100 9595
33 100100 115115
44 100100 100100
55 100100 125125
66 100100 140140
-10-10 -10-10 1010 1010 10.010.0 -1-1
-5-5 -15-15 55 1515 7.57.5 -2-2
|Error||Error|
TS = RSFE/MAD = -15/7.5 = -2
TS = RSFE/MAD = -15/7.5 = -2
Tracking Signal Computation
Tracking SignalsTracking SignalsTracking signal =
RSFE
MAD
+2.0 —
+1.5 —
+1.0 —
+0.5 —
0 —
–0.5 —
–1.0 —
–1.5 —| | | | |
0 5 10 15 20 25 Observation number
Tra
ckin
g s
ign
al
Control limit
Control limit
Out of control