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Tracking SignalTracking SignalA Measure of Forecast AccuracyA Measure of Forecast Accuracy
Prepared by:
Tyler Hedin
• Tracking Signal Defined– Tracking Signal and Forecasting
• Application, Advantages & Disadvantages• How it works
– Step by step formula• Company XYZ Example• Exercise• Summary• Readings list• Useful websites• Appendix A
AgendaAgenda
• A measure that indicates whether the forecast average is keeping pace with any genuine upward or downward changes in demand*
What is Tracking Signal?What is Tracking Signal?
Tracking Signal and ForecastingTracking Signal and Forecasting
• Continuous control indicator
• Monitor effectiveness of forecasting method
• Provide control limits
ApplicationApplication
• Evaluates forecasting method
• Indicator of change in demand patterns
• Used in conjunction with anything dependent on future demand – Sales– Inventory
AdvantagesAdvantages
• Unbiased
• Versatile– Can be used with any type of forecasting
method (time series, regression line, etc.)
• Could wrongfully flag perfect forecasts– Unlikely
• Small differences in the same direction could cause signal to go outside of control limits
DisadvantagesDisadvantages
How it Works – Forecast ErrorHow it Works – Forecast Error
• Difference between actual demand and forecast
Week Actual Demand
Forecasted Demand
Forecast Error
1 21 19 2
2 25 22 3
3 22 24 -2
How it Works – Absolute ValuesHow it Works – Absolute Values
• Express the forecast errors as absolute values
WeekActual
DemandForecasted
DemandForecast
ErrorAbsolute
Value
1 21 19 2 2
2 25 22 3 3
3 22 24 -2 2
How it Works – Running SumHow it Works – Running Sum
• Keep a continuous running sum of the forecast errors
• Do not add absolute values
WeekActual
DemandForecasted
DemandForecast
ErrorAbsolute
ValueRunning
Sum
1 21 19 2 2 2
2 25 22 3 3 5
3 22 24 -2 2 3
How it Works - MADHow it Works - MAD
• Divide the summed absolute values by the number of periods to calculate MAD.
WeekActual
DemandForecasted
DemandForecast
ErrorAbsolute
ValueRunning
SumMAD
1 21 19 2 2 2 2.00
2 25 22 3 3 5 2.50
3 22 24 -2 2 3 2.33
The EquationThe Equation
• Tracking signal is mathematically defined as the sum of the forecast errors divided by the mean absolute deviation
Tracking signalTracking signal == (Dt – Ft)
MAD
How it Works – Tracking SignalHow it Works – Tracking Signal
• Divide the running sum of forecast errors by the corresponding MAD value
WeekActual
DemandForecasted
DemandForecast
ErrorAbsolute
ValueRunning
SumMAD Tracking
Signal
1 21 19 2 2 2 2.00 1.00
2 25 22 3 3 5 2.50 2.00
3 22 24 -2 -2 3 2.33 1.29
What Do These Values Mean?What Do These Values Mean?
• Ratio of cumulative error to average deviation
• 0.8 σ ~ 1.25 MAD
• Limits are usually between 2 to 5 standard deviations
Example 1Example 1
• Company XYZ has implemented a linear regression method to forecast sales. Actual sales for the months of January 2005 through January 2006 are given in Table 1 along with their corresponding forecasts.
SALES (in thousands)
MONTH PERIOD DEMAND FORECAST
January-05 1 $37 37.35
February-05 2 $40 38.97
March-05 3 $41 40.60
April-05 4 $37 42.23
May-05 5 $45 43.85
June-05 6 $50 45.48
July-05 7 $43 47.10
August-05 8 $47 48.73
September-05 9 $56 50.36
October-05 10 $52 51.98
November-05 11 $55 53.61
December-05 12 $54 55.23
January-06 13 $55 56.86
Table 1Table 1
Example 1Example 1
• Company XYZ would like to employ a tracking signal to measure the performance of its forecasting method.
Table 2Table 2
MONTH PERIOD DEMAND FORECAST ERROR ABS DVN RUNNING SUM MADTRACKING
SIGNAL
January-05 1 37 37.35 -0.35 0.35 -0.35 0.35 -1.00
February-05 2 40 38.97 1.03 1.03 0.68 0.69 0.99
March-05 3 41 40.60 0.40 0.40 1.08 0.59 1.82
April-05 4 37 42.23 -5.23 5.23 -4.15 1.75 -2.37
May-05 5 45 43.85 1.15 1.15 -3.00 1.63 -1.84
June-05 6 50 45.48 4.52 4.52 1.52 2.11 0.72
July-05 7 43 47.10 -4.10 4.10 -2.58 2.40 -1.08
August-05 8 47 48.73 -1.73 1.73 -4.31 2.31 -1.86
September-05 9 56 50.36 5.64 5.64 1.33 2.68 0.50
October-05 10 52 51.98 0.02 0.02 1.35 2.42 0.56
November-05 11 55 53.61 1.39 1.39 2.74 2.32 1.18
December-05 12 54 55.23 -1.23 1.23 1.51 2.23 0.68
January-06 13 55 56.86 -1.86 1.86 -0.35 2.20 -0.16
TRACKING SIGNAL
-1.00
0.99
1.82
-2.37
-1.84
0.72
-1.08
-1.86
0.50
0.56
1.18
0.68
-0.16
ExerciseExercise
• Your employer, Jones & Associates, has been using a linear regression method to forecast sales for 2006. After nine months have passed and actual sales data have been collected, your boss asks you to develop a tracking signal to measure the accuracy of the forecasts. The data for actual sales and forecasted sales is in Table 3.
Table 3Table 3
SALES
MONTH PERIOD DEMAND FORECAST
January-06 1 $3,769 3664.18
February-06 2 $3,912 3953.92
March-06 3 $4,212 4243.65
April-06 4 $4,861 4533.39
May-06 5 $4,672 4823.13
June-06 6 $4,937 5112.87
July-06 7 $5,346 5402.61
August-06 8 $5,783 5692.35
September-06 9 $6,021 5982.08
SummarySummary
• A tracking signal statistically determines if a forecasting method is out-of-control.– As long as tracking signal stays within 3 standard deviations,
probability of forecast error caused by random variation is high
• Used by companies to track changes in demand patterns• Calculated by dividing the most recent sum of forecast
errors by the most recent estimate of MAD• A tracking signal outside of established limits indicates
that a forecasting method should be modified.• Compatible with any forecasting method
Readings ListReadings List
• Chase, R. B. et al. (2004). Operations Management for Competitive Advantage 10th edition. McGraw-Hill Higher Education.
• Duncan, Robert M. (1992). Quality Forecasting Drives Quality Inventory at GE. Industrial Engineer, January edition.
• Hanke, J.E. & Wichern, D. W. (2004). Business Forecasting. Prentice Hall.
• Lawrence, F. B. (1999). Closing the logistics loop: A tutorial. Production & Inventory Management Journal, 40(1).
Useful WebsitesUseful Websites
• http://www.bestforecastingsoftware.com• http://www.IdeaWins.com• http://www.lehigh.edu/~rhs2/IBE098/forecating.ppt• http://is.ba.ttu.edu/faculty/ch11.ppt• http://www.microsoft.com/dynamics/intro/default.mspx
Appendix A – Solution to ExerciseAppendix A – Solution to ExerciseMONTH PERIOD DEMAND FORECAST ERROR ABS DVN RUNNING SUM MAD
TRACKING SIGNAL
January-05 1 37 37.35 -0.35 0.35 -0.35 0.35 -1.00
February-05 2 40 38.97 1.03 1.03 0.68 0.69 0.99
March-05 3 41 40.60 0.40 0.40 1.08 0.59 1.82
April-05 4 37 42.23 -5.23 5.23 -4.15 1.75 -2.37
May-05 5 45 43.85 1.15 1.15 -3.00 1.63 -1.84
June-05 6 50 45.48 4.52 4.52 1.52 2.11 0.72
July-05 7 43 47.10 -4.10 4.10 -2.58 2.40 -1.08
August-05 8 47 48.73 -1.73 1.73 -4.31 2.31 -1.86
September-05 9 56 50.36 5.64 5.64 1.33 2.68 0.50
October-05 10 52 51.98 0.02 0.02 1.35 2.42 0.56
November-05 11 55 53.61 1.39 1.39 2.74 2.32 1.18
December-05 12 54 55.23 -1.23 1.23 1.51 2.23 0.68
January-06 13 55 56.86 -1.86 1.86 -0.35 2.20 -0.16