lss black belt training forecasting. forecasting models forecasting techniques qualitative models...
TRANSCRIPT
LSS Black Belt Training
Forecasting
Forecasting Models
Forecasting Techniques
Qualitative Models
Time Series Methods
Causal Methods
Delphi Method
Jury of Executive Opinion
Sales Force Composite
Consumer MarketSurvey
Naive
MovingAverage
Weighted Moving Average
ExponentialSmoothing
Trend Analysis
Seasonality AnalysisSimple
RegressionAnalysis
Multiple Regression
Analysis
MultiplicativeDecomposition
Model Differences
Qualitative – incorporates judgmental & subjective factors into forecast.
Time-Series – attempts to predict the future by using historical data.
Causal – incorporates factors that may influence the quantity being forecasted into the model
Qualitative Forecasting Models
Delphi method Iterative group process allows experts to make
forecasts Participants:
decision makers: 5 -10 experts who make the forecast staff personnel: assist by preparing, distributing, collecting,
and summarizing a series of questionnaires and survey results
respondents: group with valued judgments who provide input to decision makers
Qualitative Forecasting Models (cont)
Jury of executive opinion Opinions of a small group of high level managers, often in
combination with statistical models. Result is a group estimate.
Sales force composite Each salesperson estimates sales in his region. Forecasts are reviewed to ensure realistic. Combined at higher levels to reach an overall forecast.
Consumer market survey. Solicits input from customers and potential customers
regarding future purchases. Used for forecasts and product design & planning
Forecast Error
Bias - The arithmetic sum of the errors
Mean Square Error - Similar to simple sample variance
Variance - Sample variance (adjusted for degrees of freedom)
Standard Error - Standard deviation of the sampling distribution
MAD - Mean Absolute Deviation
MAPE – Mean Absolute Percentage Error
tt FAErrorForecast
TFAMAD tt
T
t
/|| /T|errorforecast |1
T
1t
TAFAMAPE ttt
T
t
/]/|[|1001
TFA
MSE
tt
T
t
/)(
/T|errorforecast |
2
1
T
1t
2
Quantitative Forecasting Models
Time Series Method Naïve
Whatever happened recently will happen again this time (same time period)
The model is simple and flexible
Provides a baseline to measure other models
Attempts to capture seasonal factors at the expense of ignoring trend
dataMonthly:
dataQuarterly:
12
4
tt
tt
YF
YF
1 tt YF
Naïve Forecast
Wallace Garden SupplyForecasting
PeriodActual Value
Naïve Forecast Error
Absolute Error
Percent Error
Squared Error
January 10 N/AFebruary 12 10 2 2 16.67% 4.0March 16 12 4 4 25.00% 16.0April 13 16 -3 3 23.08% 9.0May 17 13 4 4 23.53% 16.0June 19 17 2 2 10.53% 4.0July 15 19 -4 4 26.67% 16.0August 20 15 5 5 25.00% 25.0September 22 20 2 2 9.09% 4.0October 19 22 -3 3 15.79% 9.0November 21 19 2 2 9.52% 4.0December 19 21 -2 2 10.53% 4.0
0.818 3 17.76% 10.091BIAS MAD MAPE MSE
Standard Error (Square Root of MSE) = 3.176619
Storage Shed Sales
Naïve Forecast Graph
Wallace Garden - Naive Forecast
0
5
10
15
20
25
February March April May June July August September October November December
Period
Shed
s
Actual Value
Naïve Forecast
Quantitative Forecasting Models
Time Series Method Moving Averages
Assumes item forecasted will stay steady over time.
Technique will smooth out short-term irregularities in the time series.
/k periods)k previousin value(Actual average moving period-kk
1
k
Moving Averages
Wallace Garden SupplyForecasting
PeriodActual Value Three-Month Moving Averages
January 10February 12March 16April 13 10 + 12 + 16 / 3 = 12.67May 17 12 + 16 + 13 / 3 = 13.67June 19 16 + 13 + 17 / 3 = 15.33July 15 13 + 17 + 19 / 3 = 16.33August 20 17 + 19 + 15 / 3 = 17.00September 22 19 + 15 + 20 / 3 = 18.00October 19 15 + 20 + 22 / 3 = 19.00November 21 20 + 22 + 19 / 3 = 20.33December 19 22 + 19 + 21 / 3 = 20.67
Storage Shed Sales
Moving Averages Forecast
Wallace Garden SupplyForecasting 3 period moving average
Input Data Forecast Error Analysis
Period Actual Value Forecast ErrorAbsolute
errorSquared
errorAbsolute % error
Month 1 10Month 2 12Month 3 16Month 4 13 12.667 0.333 0.333 0.111 2.56%Month 5 17 13.667 3.333 3.333 11.111 19.61%Month 6 19 15.333 3.667 3.667 13.444 19.30%Month 7 15 16.333 -1.333 1.333 1.778 8.89%Month 8 20 17.000 3.000 3.000 9.000 15.00%Month 9 22 18.000 4.000 4.000 16.000 18.18%Month 10 19 19.000 0.000 0.000 0.000 0.00%Month 11 21 20.333 0.667 0.667 0.444 3.17%Month 12 19 20.667 -1.667 1.667 2.778 8.77%
Average 12.000 2.000 6.074 10.61%Next period 19.667 BIAS MAD MSE MAPE
Actual Value - Forecast
Moving Averages Graph
Three Period Moving Average
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12
Time
Valu
e Actual Value
Forecast
Quantitative Forecasting Models
Time Series Method Weighted Moving Averages
Assumes data from some periods are more important than data from other periods (e.g. earlier periods).
Use weights to place more emphasis on some periods and less on others.
(weights) /periods)k previousin valuei)(Actual periodeach for (Weight
average moving weightedperiod-kk
1i
k
1
i
Weighted Moving Average
Wallace Garden SupplyForecasting
PeriodActual Value Weights Three-Month Weighted Moving Averages
January 10 0.222February 12 0.593March 16 0.185April 13 2.2 + 7.1 + 3 / 1 = 12.298May 17 2.7 + 9.5 + 2.4 / 1 = 14.556June 19 3.5 + 7.7 + 3.2 / 1 = 14.407July 15 2.9 + 10 + 3.5 / 1 = 16.484August 20 3.8 + 11 + 2.8 / 1 = 17.814September 22 4.2 + 8.9 + 3.7 / 1 = 16.815October 19 3.3 + 12 + 4.1 / 1 = 19.262November 21 4.4 + 13 + 3.5 / 1 = 21.000December 19 4.9 + 11 + 3.9 / 1 = 20.036
Next period 20.185
Sum of weights = 1.000
Storage Shed Sales
Weighted Moving Average
Wallace Garden Supply Forecasting 3 period weighted moving average
Input Data Forecast Error Analysis
Period Actual value Weights Forecast ErrorAbsolute
errorSquared
errorAbsolute % error
Month 1 10 0.222Month 2 12 0.593Month 3 16 0.185Month 4 13 12.298 0.702 0.702 0.492 5.40%Month 5 17 14.556 2.444 2.444 5.971 14.37%Month 6 19 14.407 4.593 4.593 21.093 24.17%Month 7 15 16.484 -1.484 1.484 2.202 9.89%Month 8 20 17.814 2.186 2.186 4.776 10.93%Month 9 22 16.815 5.185 5.185 26.889 23.57%Month 10 19 19.262 -0.262 0.262 0.069 1.38%Month 11 21 21.000 0.000 0.000 0.000 0.00%Month 12 19 20.036 -1.036 1.036 1.074 5.45%
Average 1.988 6.952 6.952 10.57%Next period 20.185 BIAS MAD MSE MAPE
Sum of weights = 1.000
Quantitative Forecasting Models
Time Series Method Exponential Smoothing
Moving average technique that requires little record keeping of past data.
Uses a smoothing constant α with a value between 0 and 1. (Usual range 0.1 to 0.3)
)- tperiodfor forecast - - tperiodin value(actual - tperiodfor forecast
t periodfor Forecast
111
Exponential Smoothing Data
Wallace Garden SupplyForecasting
Exponential Smoothing
PeriodActual Value Ft α At Ft Ft+1
January 10 10 0.1February 12 10 + 0.1 *( 10 - 10 ) = 10.000March 16 10 + 0.1 *( 12 - 10 ) = 10.200April 13 10 + 0.1 *( 16 - 10 ) = 10.780May 17 11 + 0.1 *( 13 - 11 ) = 11.002June 19 11 + 0.1 *( 17 - 11 ) = 11.602July 15 12 + 0.1 *( 19 - 12 ) = 12.342August 20 12 + 0.1 *( 15 - 12 ) = 12.607September 22 13 + 0.1 *( 20 - 13 ) = 13.347October 19 13 + 0.1 *( 22 - 13 ) = 14.212November 21 14 + 0.1 *( 19 - 14 ) = 14.691December 19 15 + 0.1 *( 21 - 15 ) = 15.322
Storage Shed Sales
Exponential Smoothing
Wallace Garden SupplyForecasting Exponential smoothing
Input Data Forecast Error Analysis
Period Actual value Forecast ErrorAbsolute
errorSquared
errorAbsolute % error
Month 1 10 10.000Month 2 12 10.000 2.000 2.000 4.000 16.67%Month 3 16 10.838 5.162 5.162 26.649 32.26%Month 4 13 13.000 0.000 0.000 0.000 0.00%Month 5 17 13.000 4.000 4.000 16.000 23.53%Month 6 19 14.675 4.325 4.325 18.702 22.76%Month 7 15 16.487 -1.487 1.487 2.211 9.91%Month 8 20 15.864 4.136 4.136 17.106 20.68%Month 9 22 17.596 4.404 4.404 19.391 20.02%Month 10 19 19.441 -0.441 0.441 0.194 2.32%Month 11 21 19.256 1.744 1.744 3.041 8.30%Month 12 19 19.987 -0.987 0.987 0.973 5.19%
Average 2.608 9.842 14.70%Alpha 0.419 MAD MSE MAPE
Next period 19.573
Exponential Smoothing
Exponential Smoothing
0
5
10
15
20
25
January April July October
Sh
ed
s Actual value
Forecast
Trend & Seasonality
Trend analysis technique that fits a trend equation (or curve) to a
series of historical data points. projects the curve into the future for medium and long
term forecasts.Seasonality analysis
adjustment to time series data due to variations at certain periods.
adjust with seasonal index – ratio of average value of the item in a season to the overall annual average value.
example: demand for coal & fuel oil in winter months.
Linear Trend AnalysisMidwestern Manufacturing Sales
Scatter Diagram
Actual value (or)
Y
Period number (or) X
74 199579 199680 199790 1998
105 1999142 2000122 2001
Sales(in units) vs. Time
0
20
40
60
80
100
120
140
160
1994 1996 1998 2000 2002
Period number (or) X
Least Squares for Linear RegressionMidwestern Manufacturing
Least Squares Method
Time
Va
lue
s o
f D
ep
en
de
nt
Va
ria
ble
s
Least Squares Method
bX a Y^
Where
Y^
= predicted value of the dependent variable (demand)
X = value of the independent variable (time)
a = Y-axis intercept
b = slope of the regression line
]Xn - XY[ __
Y
_
22 Xn -X
b =
Linear Trend Data & Error Analysis
Midwestern Manufacturing CompanyForecasting Linear trend analysis
Input Data Forecast Error Analysis
PeriodActual value
(or) YPeriod number
(or) X Forecast ErrorAbsolute
errorSquared
errorAbsolute % error
Year 1 74 1 67.250 6.750 6.750 45.563 9.12%Year 2 79 2 77.786 1.214 1.214 1.474 1.54%Year 3 80 3 88.321 -8.321 8.321 69.246 10.40%Year 4 90 4 98.857 -8.857 8.857 78.449 9.84%Year 5 105 5 109.393 -4.393 4.393 19.297 4.18%Year 6 142 6 119.929 22.071 22.071 487.148 15.54%Year 7 122 7 130.464 -8.464 8.464 71.644 6.94%
Average 8.582 110.403 8.22%Intercept 56.714 MAD MSE MAPESlope 10.536
Next period 141.000 8
Least Squares Graph
Trend Analysis
y = 10.536x + 56.714
0
20
40
60
80
100
120
140
160
1 2 3 4 5 6 7Time
Va
lue
Actual values Linear (Actual values)
Seasonality Analysis
Eichler Supplies
Year Month DemandAverage Demand Ratio
Seasonal Index
1 January 80 94 0.851 0.957February 75 94 0.798 0.851
March 80 94 0.851 0.904April 90 94 0.957 1.064May 115 94 1.223 1.309June 110 94 1.170 1.223July 100 94 1.064 1.117
August 90 94 0.957 1.064September 85 94 0.904 0.957
October 75 94 0.798 0.851November 75 94 0.798 0.851December 80 94 0.851 0.851
2 January 100 94 1.064February 85 94 0.904
March 90 94 0.957April 110 94 1.170May 131 94 1.394June 120 94 1.277July 110 94 1.170
August 110 94 1.170September 95 94 1.011
October 85 94 0.904November 85 94 0.904December 80 94 0.851
Seasonal Index – ratio of the average value of the item in a season to the overall average annual value.
Example: average of year 1 January ratio to year 2 January ratio. (0.851 + 1.064)/2 = 0.957
Ratio = demand / average demand
If Year 3 average monthly demand is expected to be 100 units.Forecast demand Year 3 January: 100 X 0.957 = 96 unitsForecast demand Year 3 May: 100 X 1.309 = 131 units
Deseasonalized Data
Going back to the conceptual model, solve for trend: Trend = Y / Season
(96 units/ 0.957 = 100.31) This eliminates seasonal variation and isolates
the trend Now use the Least Squares method to
compute the Trend
Forecast
Now that we have the Seasonal Indices and Trend, we can reseasonalize the data and generate the forecast.
Y = Trend x Seasonal Index