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CHAPTER 2CHAPTER 2
FORECASTINGFORECASTING
LEARNING OBJECTIVESLEARNING OBJECTIVES
Define forecasting, forecasts approaches
Understand the three time horizons
Describe, Explain and Apply the naïve, moving average, exponential smoothing, and trend method
Compute the measures of forecast accuracy
Apply a tracking signal
Forecasting?Forecasting?Forecast
a statement about the future value of a variable of interest.
Forecasting
the art and science of predicting future events.
Forecasts
Forecasts affect decisions and activities throughout an organization Accounting, finance Human resources Marketing Operations Product / service design
Uses of ForecastsAccounting Cost/profit estimates
Finance Cash flow and funding
Human Resources Hiring/recruiting/training
Marketing Pricing, promotion, strategy
Operations Schedules, MRP, workloads
Product/service design
New products and services
I see that you willget an A this semester.
Elements of a Good Forecast
Timely
AccurateReliable
Mea
ningfu
lWritten
Easy
to u
se
Forecasting Time Horizons
Short-range forecastMedium-range forecastLong-range forecast
Distinguishing Differences
Medium/long range- more comprehensive issues and support management decisions regarding planning and products, plants and processes
Short-term- employs different methodologies than longer-term
Short-term- more accurate than longer-term forecasts
Influence of Product Life Cycle
Best period to Best period to increase market increase market shareshare
R&D engineering is R&D engineering is criticalcritical
Practical to change Practical to change price or quality price or quality imageimage
Strengthen nicheStrengthen niche
Poor time to Poor time to change image, change image, price, or qualityprice, or quality
Competitive costs Competitive costs become criticalbecome criticalDefend market Defend market positionposition
Cost control Cost control criticalcritical
Introduction Growth Maturity Decline
Co
mp
an
y S
tra
teg
y/Is
sue
sC
om
pa
ny
Str
ate
gy/
Issu
es
Internet search enginesInternet search engines
SalesSales
Xbox 360Xbox 360
Drive-through Drive-through restaurantsrestaurants
CD-ROMsCD-ROMs
3 1/2” 3 1/2” Floppy Floppy disksdisks
LCD & plasma TVsLCD & plasma TVsAnalog TVsAnalog TVs
iPodsiPods
Types of Forecasts
Economic forecasts Technological forecasts Demand forecasts
Seven Steps in Forecasting
Determine the use of the forecast Select the items to be forecasted Determine the time horizon of the
forecast Select the forecasting model(s) Gather the data Make the forecast Validate and implement results
Forecasting Approaches
Qualitative
Quantitative
Qualitative Approaches
Jury of executive opinionDelphi methodSales force compositeConsumer market survey
Quantitative Approaches
Naïve approach Moving average Exponential smoothing Trend projection Linear regression
Time-Series Time-Series ModelsModels
Time Series Forecasting
Set of evenly spaced numerical data Obtained by observing response variable
at regular time periods
Forecast based only on past values, no other variables important Assumes that factors influencing past and
present will continue influence in future
Time Series Components
Trend
Seasonal
Cycles
Random
Components of DemandD
eman
d f
or
pro
du
ct o
r se
rvic
e
| | | |1 2 3 4
Year
Average demand over four years
Seasonal peaks
Trend component
Actual demand
Random variation
Trend Component
Overall upward or downward patternChanges due to population, technology,
age, culture, etc.Typically several years duration
Seasonal Component
Regular pattern of up and down fluctuations
Due to weather, customs, etcOccurs within a single year
Number ofPeriod Length Seasons
Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52
Cycles Component
Repeating up and down movementsAffected by business cycle, political,
and economic factorsMultiple years duration
00 55 1010 1515 2020
Random Component
Erratic, unsystematic, Due to random variation or unforeseen
eventsShort duration and
non-repeating
MM TT WW TT FF
Naive Approach
Assumes demand in next period is the same as demand in most recent period
Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....
Moving Average Method
Use a number of historical actual data values to generate a forecast
An average of the n most recent periods
Useful if can assume that market demand will stay fairly steady over time
∑∑ demand in previous n demand in previous n periodsperiods
nn
Moving average =Moving average =
Moving Average Example
JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626
ActualActual 3-Month3-MonthMonthMonth Shed SalesShed Sales Moving AverageMoving Average
(12 + 13 + 16)/3 = 13 (12 + 13 + 16)/3 = 13 22//33
(13 + 16 + 19)/3 = 16(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 (16 + 19 + 23)/3 = 19 11//33
101012121313
((1010 + + 1212 + + 1313)/3 = 11 )/3 = 11 22//33
Graph of Moving Average
| | | | | | | | | | | |
JJ FF MM AA MM JJ JJ AA SS OO NN DD
Sh
ed S
ales
Sh
ed S
ales
30 30 –28 28 –26 26 –24 24 –22 22 –20 20 –18 18 –16 16 –14 14 –12 12 –10 10 –
Actual Actual SalesSales
Moving Moving Average Average ForecastForecast
Weighted Moving Average
Used when trend or pattern is presentWeights based on experience and intuition
WeightedWeightedmoving averagemoving average ==
∑∑ ((weight for period nweight for period n)) x x ((demand in period ndemand in period n))
∑∑ weightsweights
Weighted Moving Average Example
JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626
ActualActual 3-Month Weighted3-Month WeightedMonthMonth Shed SalesShed Sales Moving AverageMoving Average
[(3 x 16) + (2 x 13) + (12)]/6 = 14[(3 x 16) + (2 x 13) + (12)]/6 = 1411//33
[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 20[(3 x 23) + (2 x 19) + (16)]/6 = 2011//22
101012121313
[(3 x [(3 x 1313) + (2 x ) + (2 x 1212) + () + (1010)]/6 = 12)]/6 = 1211//66
Weights Applied Period
3 Last month2 Two months ago1 Three months ago
6 Sum of weights
Potential Problems With Moving Average
Increasing n smooths the forecast but makes it less sensitive to changes
Do not forecast trends wellRequire extensive historical data
Moving Average And Weighted Moving Average
30 30 –
25 25 –
20 20 –
15 15 –
10 10 –
5 5 –
Sa
les
de
man
dS
ale
s d
em
and
| | | | | | | | | | | |
JJ FF MM AA MM JJ JJ AA SS OO NN DD
Actual Actual salessales
Moving Moving averageaverage
Weighted Weighted moving moving averageaverage
Exponential Smoothing Weighted averaging method based on
previous forecast plus a percentage of the forecast error
A-F is the error term, is the % feedbackWeights decline exponentially Most recent data weighted most
Involves little record keeping of past data Requires smoothing constant ()
Ranges from 0 to 1Subjectively chosen
Exponential Smoothing
New forecast =New forecast = Last period’s forecastLast period’s forecast+ + ((Last period’s actual demand Last period’s actual demand
– – Last period’s forecastLast period’s forecast))
FFtt = F = Ft t – 1– 1 + + ((AAt t – 1– 1 - - F Ft t – 1– 1))
wherewhere FFtt == new forecastnew forecast
FFt t – 1– 1 == previous forecastprevious forecast
== smoothing (or weighting) smoothing (or weighting) constant constant (0 ≤ (0 ≤ ≤ 1) ≤ 1)
Exponential Smoothing Example
Predicted demand Predicted demand = 142= 142 Ford Mustangs Ford MustangsActual demand Actual demand = 153= 153Smoothing constant Smoothing constant = .20 = .20
New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)
= 142 + 2.2= 142 + 2.2
= 144.2 ≈ 144 cars= 144.2 ≈ 144 cars
Selecting of Smoothing Constant
Chose high values of Chose high values of when actual when actual demand display an increasing (or demand display an increasing (or decreasing) trenddecreasing) trend
Chose low values of Chose low values of when demand is when demand is relatively stable without any trendrelatively stable without any trend
Exponential Smoothing with Trend Adjustment
When a trend is present, exponential When a trend is present, exponential smoothing must be modifiedsmoothing must be modified
Forecast Forecast including including ((FITFITtt)) = = trendtrend
ExponentiallyExponentially ExponentiallyExponentiallysmoothed smoothed ((FFtt)) + + ((TTtt)) smoothedsmoothedforecastforecast trendtrend
FFtt = = ((AAtt - 1 - 1) + (1 - ) + (1 - )()(FFtt - 1 - 1 + + TTtt - 1 - 1))
TTtt = = ((FFtt - - FFtt - 1 - 1) + (1 - ) + (1 - ))TTtt - 1 - 1
Exponential Smoothing with Trend Adjustment Example
ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding
MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt
11 1212 1111 22 13.0013.0022 171733 202044 191955 242466 212177 313188 282899 3636
1010
Exponential Smoothing with Trend Adjustment Example
ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding
MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt
11 1212 1111 22 13.0013.0022 171733 202044 191955 242466 212177 313188 282899 3636
1010
F2 = A1 + (1 - )(F1 + T1)
F2 = (.2)(12) + (1 - .2)(11 + 2)
= 2.4 + 10.4 = 12.8 units
Step 1: Forecast for Month 2
Exponential Smoothing with Trend Adjustment Example
ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding
MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt
11 1212 1111 22 13.0013.0022 1717 12.8012.8033 202044 191955 242466 212177 313188 282899 3636
1010
T2 = (F2 - F1) + (1 - )T1
T2 = (.4)(12.8 - 11) + (1 - .4)(2)
= .72 + 1.2 = 1.92 units
Step 2: Trend for Month 2
Exponential Smoothing with Trend Adjustment Example
ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding
MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt
11 1212 1111 22 13.0013.0022 1717 12.8012.80 1.921.9233 202044 191955 242466 212177 313188 282899 3636
1010
FIT2 = F2 + T1
FIT2 = 12.8 + 1.92
= 14.72 units
Step 3: Calculate FIT for Month 2
Exponential Smoothing with Trend Adjustment Example
ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding
MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt
11 1212 1111 22 13.0013.0022 1717 12.8012.80 1.921.92 14.7214.7233 202044 191955 242466 212177 313188 282899 3636
1010
15.1815.18 2.102.10 17.2817.2817.8217.82 2.322.32 20.1420.1419.9119.91 2.232.23 22.1422.1422.5122.51 2.382.38 24.8924.8924.1124.11 2.072.07 26.1826.1827.1427.14 2.452.45 29.5929.5929.2829.28 2.322.32 31.6031.6032.4832.48 2.682.68 35.1635.16
Exponential Smoothing with Trend Adjustment Example
| | | | | | | | |
11 22 33 44 55 66 77 88 99
Time (month)Time (month)
Pro
du
ct d
eman
dP
rod
uct
dem
and
35 35 –
30 30 –
25 25 –
20 20 –
15 15 –
10 10 –
5 5 –
0 0 –
Actual demand Actual demand ((AAtt))
Forecast including trend Forecast including trend ((FITFITtt))
withwith = .2 = .2 andand = .4 = .4
Seasonal Variations In DataRegularly repeating movements (upward or
downward) in a time series that can be tie to recurring events. Multiplicative seasonal method a method whereby
seasonal factors are multiplied by an estimate of average demand to arrive at a seasonal forecast.
Seasonal Variations In Data
1.1. Find average historical demand for each Find average historical demand for each season season
2.2. Compute the average demand over all Compute the average demand over all seasons seasons
3.3. Compute a seasonal index for each season Compute a seasonal index for each season
4.4. Estimate next year’s total demandEstimate next year’s total demand
5.5. Divide this estimate of total demand by the Divide this estimate of total demand by the number of seasons, then multiply it by the number of seasons, then multiply it by the seasonal index for that seasonseasonal index for that season
Steps in the process:Steps in the process:
Seasonal Index Example
JanJan 8080 8585 105105 9090 9494
FebFeb 7070 8585 8585 8080 9494
MarMar 8080 9393 8282 8585 9494
AprApr 9090 9595 115115 100100 9494
MayMay 113113 125125 131131 123123 9494
JunJun 110110 115115 120120 115115 9494
JulJul 100100 102102 113113 105105 9494
AugAug 8888 102102 110110 100100 9494
SeptSept 8585 9090 9595 9090 9494
OctOct 7777 7878 8585 8080 9494
NovNov 7575 7272 8383 8080 9494
DecDec 8282 7878 8080 8080 9494
DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20052005 20062006 20072007 2005-20072005-2007 MonthlyMonthly IndexIndex
Seasonal Index Example
JanJan 8080 8585 105105 9090 9494
FebFeb 7070 8585 8585 8080 9494
MarMar 8080 9393 8282 8585 9494
AprApr 9090 9595 115115 100100 9494
MayMay 113113 125125 131131 123123 9494
JunJun 110110 115115 120120 115115 9494
JulJul 100100 102102 113113 105105 9494
AugAug 8888 102102 110110 100100 9494
SeptSept 8585 9090 9595 9090 9494
OctOct 7777 7878 8585 8080 9494
NovNov 7575 7272 8383 8080 9494
DecDec 8282 7878 8080 8080 9494
DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20052005 20062006 20072007 2005-20072005-2007 MonthlyMonthly IndexIndex
0.9570.957
Seasonal index = average 2005-2007 monthly demand
average monthly demand
= 90/94 = .957
JanJan 8080 8585 105105 9090 9494 0.9570.957
FebFeb 7070 8585 8585 8080 9494 0.8510.851
MarMar 8080 9393 8282 8585 9494 0.9040.904
AprApr 9090 9595 115115 100100 9494 1.0641.064
MayMay 113113 125125 131131 123123 9494 1.3091.309
JunJun 110110 115115 120120 115115 9494 1.2231.223
JulJul 100100 102102 113113 105105 9494 1.1171.117
AugAug 8888 102102 110110 100100 9494 1.0641.064
SeptSept 8585 9090 9595 9090 9494 0.9570.957
OctOct 7777 7878 8585 8080 9494 0.8510.851
NovNov 7575 7272 8383 8080 9494 0.8510.851
DecDec 8282 7878 8080 8080 9494 0.8510.851
DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20052005 20062006 20072007 2005-20072005-2007 MonthlyMonthly IndexIndex
Seasonal Index Example
JanJan 8080 8585 105105 9090 9494 0.9570.957
FebFeb 7070 8585 8585 8080 9494 0.8510.851
MarMar 8080 9393 8282 8585 9494 0.9040.904
AprApr 9090 9595 115115 100100 9494 1.0641.064
MayMay 113113 125125 131131 123123 9494 1.3091.309
JunJun 110110 115115 120120 115115 9494 1.2231.223
JulJul 100100 102102 113113 105105 9494 1.1171.117
AugAug 8888 102102 110110 100100 9494 1.0641.064
SeptSept 8585 9090 9595 9090 9494 0.9570.957
OctOct 7777 7878 8585 8080 9494 0.8510.851
NovNov 7575 7272 8383 8080 9494 0.8510.851
DecDec 8282 7878 8080 8080 9494 0.8510.851
DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20052005 20062006 20072007 2005-20072005-2007 MonthlyMonthly IndexIndex
Expected annual demand = 1,200
Jan x .957 = 961,200
12
Feb x .851 = 851,200
12
Forecast for 2008
Seasonal Index Example
140 140 –
130 130 –
120 120 –
110 110 –
100 100 –
90 90 –
80 80 –
70 70 –| | | | | | | | | | | |
JJ FF MM AA MM JJ JJ AA SS OO NN DD
TimeTime
Dem
and
Dem
and
2008 Forecast2008 Forecast
2007 Demand 2007 Demand
2006 Demand2006 Demand
2005 Demand2005 Demand
Seasonal Index Example
Associative Forecasting
Used when changes in one or more Used when changes in one or more independent variables can be used to independent variables can be used to predict the changes in the dependent predict the changes in the dependent variablevariable
Most common technique is linear Most common technique is linear regression analysisregression analysis
Regression Analysis
Forecasting an outcome based on Forecasting an outcome based on predictor variables using the least predictor variables using the least squares techniquesquares technique
y y = = a a + + bxbx^̂
where ywhere y= computed value of the = computed value of the variable to be predicted (dependent variable to be predicted (dependent variable)variable)aa= y-axis intercept= y-axis interceptbb= slope of the regression line= slope of the regression linexx= the independent variable though = the independent variable though to predict the value of the to predict the value of the dependent variabledependent variable
^̂
Least Squares Method
Time periodTime period
Va
lue
s o
f D
ep
end
en
t V
ari
able
Figure 4.4Figure 4.4
DeviationDeviation11
(error)(error)
DeviationDeviation55
DeviationDeviation77
DeviationDeviation22
DeviationDeviation66
DeviationDeviation44
DeviationDeviation33
Actual observation Actual observation (y value)(y value)
Trend line, y = a + bxTrend line, y = a + bx^̂
Time periodTime period
Va
lue
s o
f D
ep
end
en
t V
ari
able
Figure 4.4Figure 4.4
DeviationDeviation11
DeviationDeviation55
DeviationDeviation77
DeviationDeviation22
DeviationDeviation66
DeviationDeviation44
DeviationDeviation33
Actual observation Actual observation (y value)(y value)
Trend line, y = a + bxTrend line, y = a + bx^̂
Least squares method minimizes the sum of the
squared errors (deviations)
Least Squares Method
Equations to calculate the regression variablesEquations to calculate the regression variables
b =b =xy - nxyxy - nxy
xx22 - nx - nx22
y y = = a a + + bxbx^̂
a = y - bxa = y - bx
Least Squares Method
Associative Forecasting Example
SalesSales Local PayrollLocal Payroll($ millions), y($ millions), y ($ billions), x($ billions), x
2.02.0 113.03.0 332.52.5 442.02.0 222.02.0 113.53.5 77
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
Sal
es
Area payroll
Sales, y Payroll, x x2 xy
2.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5
∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5
xx = ∑ = ∑xx/6 = 18/6 = 3/6 = 18/6 = 3
yy = ∑ = ∑yy/6 = 15/6 = 2.5/6 = 15/6 = 2.5
bb = = = .25 = = = .25∑∑xy - nxyxy - nxy
∑∑xx22 - nx - nx22
51.5 - (6)(3)(2.5)51.5 - (6)(3)(2.5)
80 - (6)(380 - (6)(322))
aa = = yy - - bbx = 2.5 - (.25)(3) = 1.75x = 2.5 - (.25)(3) = 1.75
Associative Forecasting Example
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
Sal
es
Area payroll
y y = 1.75 + .25= 1.75 + .25xx^̂ Sales Sales = 1.75 + .25(= 1.75 + .25(payrollpayroll))
If payroll next year If payroll next year is estimated to be is estimated to be $6$6 billion, then: billion, then:
Sales Sales = 1.75 + .25(6)= 1.75 + .25(6)SalesSales = $3,250,000 = $3,250,000
3.25
Associative Forecasting Example
Standard Error of the Estimate
A forecast is just a point estimate of a A forecast is just a point estimate of a future valuefuture value
This point is This point is actually the actually the mean of a mean of a probability probability distributiondistribution
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
Sal
es
Area payroll
3.25
wherewhere yy == y-value of each data y-value of each data pointpoint
yycc == computed value of the computed value of the dependent variable, from the dependent variable, from the regression equationregression equation
nn == number of data pointsnumber of data points
SSy,xy,x = =∑∑((y - yy - ycc))22
n n - 2- 2
Standard Error of the Estimate
Computationally, this equation is Computationally, this equation is considerably easier to useconsiderably easier to use
We use the standard error to set up We use the standard error to set up prediction intervals around the prediction intervals around the
point estimatepoint estimate
SSy,xy,x = =∑∑yy22 - a - a∑∑y - by - b∑∑xyxy
n n - 2- 2
Standard Error of the Estimate
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
Sal
es
Area payroll
3.25
SSy,xy,x = = = =∑∑yy22 - a - a∑∑y - by - b∑∑xyxyn n - 2- 2
39.5 - 1.75(15) - .25(51.5)39.5 - 1.75(15) - .25(51.5)6 - 26 - 2
SSy,xy,x = = .306.306
The standard error The standard error of the estimate is of the estimate is $306,000$306,000 in sales in sales
Standard Error of the Estimate
How strong is the linear relationship between the variables?
Coefficient of correlation, r, measures degree of association
Values range from -1 to +1
Correlation
r = r = nnxyxy - - xxy y
[[nnxx22 - ( - (xx))22][][nnyy22 - ( - (yy))22]]
y
x(a) Perfect positive correlation: r = +1
y
x(b) Positive correlation: 0 < r < 1
y
x(c) No correlation: r = 0
y
x(d) Perfect negative correlation: r = -1
Measuring Forecast Error
Mean Absolute Deviation Mean Absolute Deviation ((MADMAD))
MAD =MAD =∑∑ |Actual - Forecast||Actual - Forecast|
nn
Mean Squared Error Mean Squared Error ((MSEMSE))
MSE =MSE =∑∑ ((Forecast ErrorsForecast Errors))22
nn
Mean Absolute Percent Error Mean Absolute Percent Error ((MAPEMAPE))
MAPE =MAPE =∑∑100100|Actual|Actualii - Forecast - Forecastii|/Actual|/Actualii
nn
nn
i i = 1= 1
Measuring Forecast Error
Comparison of Forecast Error
RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation
TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50
11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30
82.4582.45 98.6298.62
RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation
TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50
11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30
82.4582.45 98.6298.62
MAD =∑ |deviations|
n
= 82.45/8 = 10.31
For = .10
= 98.62/8 = 12.33
For = .50
Comparison of Forecast Error
RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation
TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50
11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30
82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33
= 1,526.54/8 = 190.82
For = .10
= 1,561.91/8 = 195.24
For = .50
MSE =∑ (forecast errors)2
n
Comparison of Forecast Error
RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation
TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50
11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30
82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33MSEMSE 190.82190.82 195.24195.24
= 44.75/8 = 5.59%
For = .10
= 54.05/8 = 6.76%
For = .50
MAPE =∑100|deviationi|/actuali
n
n
i = 1
Comparison of Forecast Error
RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation
TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50
11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30
82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33MSEMSE 190.82190.82 195.24195.24MAPEMAPE 5.59%5.59% 6.76%6.76%
Comparison of Forecast Error
Measures how well the forecast is predicting actual values
Good tracking signal has low values If forecasts are continually high or low, the
forecast has a bias error +ve signal : demand greater then forecast
Monitoring and Controlling Forecasts
Tracking SignalTracking Signal
Tracking Tracking signalsignal
RSFERSFEMADMAD==
Tracking Tracking signalsignal ==
∑∑(Actual demand in (Actual demand in period i - period i -
Forecast demand Forecast demand in period i)in period i)
∑∑|Actual - Forecast|/n|Actual - Forecast|/n))
Monitoring and Controlling Forecasts
Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD)
Tracking Signal
Tracking signalTracking signal
++
00 MADs MADs
––
Upper control limitUpper control limit
Lower control limitLower control limit
TimeTime
Signal exceeding limitSignal exceeding limit
Acceptable Acceptable rangerange
Tracking Signal Example
CumulativeCumulativeAbsoluteAbsolute AbsoluteAbsolute
ActualActual ForecastForecast ForecastForecast ForecastForecastQtrQtr DemandDemand DemandDemand ErrorError RSFERSFE ErrorError ErrorError MADMAD
11 9090 100100 -10-10 -10-10 1010 1010 10.010.022 9595 100100 -5-5 -15-15 55 1515 7.57.533 115115 100100 +15+15 00 1515 3030 10.010.044 100100 110110 -10-10 -10-10 1010 4040 10.010.055 125125 110110 +15+15 +5+5 1515 5555 11.011.066 140140 110110 +30+30 +35+35 3030 8585 14.214.2
CumulativeCumulativeAbsoluteAbsolute AbsoluteAbsolute
ActualActual ForecastForecast ForecastForecast ForecastForecastQtrQtr DemandDemand DemandDemand ErrorError RSFERSFE ErrorError ErrorError MADMAD
11 9090 100100 -10-10 -10-10 1010 1010 10.010.022 9595 100100 -5-5 -15-15 55 1515 7.57.533 115115 100100 +15+15 00 1515 3030 10.010.044 100100 110110 -10-10 -10-10 1010 4040 10.010.055 125125 110110 +15+15 +5+5 1515 5555 11.011.066 140140 110110 +30+30 +35+35 3030 8585 14.214.2
TrackingSignal
(RSFE/MAD)
-10/10 = -1-15/7.5 = -2
0/10 = 0-10/10 = -1
+5/11 = +0.5+35/14.2 = +2.5
The variation of the tracking signal The variation of the tracking signal between between -2.0-2.0 and and +2.5+2.5 is within acceptable is within acceptable limitslimits
Tracking Signal Example
Forecasting in the Service Sector
Presents unusual challenges Special need for short term records Holidays and other calendar events Unusual events
Fast Food Restaurant Forecast
20% 20% –
15% 15% –
10% 10% –
5% 5% –
11-1211-12 1-21-2 3-43-4 5-65-6 7-87-8 9-109-1012-112-1 2-32-3 4-54-5 6-76-7 8-98-9 10-1110-11
(Lunchtime)(Lunchtime) (Dinnertime)(Dinnertime)
Hour of dayHour of day
Per
cen
tag
e o
f sa
les
Per
cen
tag
e o
f sa
les
Figure 4.12Figure 4.12
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