Demand Planning

1
Demand Planning ForecastingSession 4

• Demand Forecasting Methods-2
• by
• K. Sashi Rao
• Management Teacher and Trainer

2
Exponential Smoothing(1)

• Based on idea that as time series data gets older
  it becomes less relevant and should be given
  lower weight
• Past data is weighted in an unequal fashion while
  estimating future periods forecast moreover,
  there is a smoothing effect as the weights of
  past data dies down in an exponential fashion
• For exponential forecasting the new forecast
  smoothing constant( alpha)x latest demand
  (1-alpha)x last forecast
• Or expressed as F(t1) F(t) alpha( D(t)- F(t))
  where
• F(t1) exponentially smoothened forecast for
  period t1
• F(t) exponentially smoothened forecast for
  period t
• D(t) actual demand during period t
• Alpha smoothening constant

3
Exponential Smoothing(2)

• Alpha- the chosen smoothening constant(or
  coefficient) plays an important role in
  determining how responsive is the forecast to the
  demand time series
• While chosen alpha can be as low as 0.10- 0.20 to
  even as high as 0.80- 0.90
• A low alpha value indicates that the forecast
  would not be as responsive to demand as case
  where a high alpha value is chosen, i.e. the more
  recent demand observations are given more weight
• This alpha value establishes the sensitivity of
  the forecast its ultimate choice is determined
  by the need to compromise between a responsive
  forecast that follows even random fluctuations
  and an unresponsive one that might not follow
  real patterns
• These differences are illustrated in the
  subsequent tabulated example

4
Exponential Smoothing(3)- example
ALPHA0.20
PERIOD FORECAST Actual Demand
Jan 100 90
Feb 98 95
Mar 97 105
Apr 99 110
May 101 100
June 101 130
July 107 90
Aug 103 110
Sep 105 100
Oct 104 140
Nov 111
ALPHA0.80
PERIOD FORECAST Actual Demand
Jan 100 90
Feb 92 95
Mar 94 105
Apr 103 110
May 109 100
June 102 130
July 124 90
Aug 97 110
Sep 107 100
Oct 101 140
Nov 132
5
Exponential Smoothing(4)

• Include all past observations
• Weight recent observations much more heavily than
  very old observations

weight
Decreasing weight given to older observations
today
6
Exponential Smoothing(5)

• Include all past observations
• Weight recent observations much more heavily than
  very old observations

weight
Decreasing weight given to older observations
today
7
Exponential Smoothing(6)

• Include all past observations
• Weight recent observations much more heavily than
  very old observations

weight
Decreasing weight given to older observations
today
8
Exponential Smoothing(7)

• Include all past observations
• Weight recent observations much more heavily than
  very old observations

weight
Decreasing weight given to older observations
today
9
Exponential Smoothing(8)

• Include all past observations
• Weight recent observations much more heavily than
  very old observations

weight
Decreasing weight given to older observations
today
10
Exponential Smoothing(9)

• Used when demand has no observable trend or
  seasonality
• Systematic component of demand level
• Initial estimate of level, L0, assumed to be the
  average of all historical data
• L0 Sum(i1 to n)Di/n
• Current forecast for all future periods is equal
  to the current estimate of the level and is given
  as follows
• Ft1 Lt and Ftn Lt
• After observing demand Dt1, revise the estimate
  of the level
• Lt1 aDt1 (1-a)Lt
• Lt1 Sum(n0 to t1)a(1-a)nDt1-n

11
Exponential Smoothing(10)
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Exponential Smoothing(11)
13
Exponential Smoothing(12)

• Thus, new forecast is weighted sum of old
  forecast and actual demand
• Notes
• Only 2 values (Dt and Ft-1 ) are required,
  compared with n for moving average
• Parameter a determined empirically (whatever
  works best)
• Rule of thumb ? lt 0.5
• Typically, ? 0.2 or ? 0.3 work well
• Forecast for k periods into future is

14
Exponential Smoothing(13)
a 0.2
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Time Series- complicating factors

• Exponential smoothing works well with data that
  is moving sideways (stationary) ( simple
  smoothing)
• Must be adapted for data series which exhibit a
  definite trend (double exponential smoothing)
• Must be further adapted for data series which
  exhibit trend and seasonal patterns (triple
  exponential smoothing)

16
Double Exponential Smoothing -trend corrected
(Holts Model)

• What happens when there is a definite trend?

Actual
Demand
Forecast
Month
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Double Exponential Smoothing -trend corrected
(Holts Model)

• Ideas behind smoothing with trend
• De-trend'' time-series by separating base from
  trend effects
• Smooth base in usual manner using ?
• Smooth trend forecasts in usual manner using ?
• Smooth the base forecast Bt
• Smooth the trend forecast Tt
• Forecast k periods into future Ftk with base and
  trend

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Double Exponential Smoothing -trend corrected
(Holts Model)

• Appropriate when the demand is assumed to have a
  level and trend in the systematic component of
  demand but no seasonality
• Obtain initial estimate of level and trend by
  running a linear regression of the following
  form
• Dt at b
• T0 a
• L0 b
• In period t, the forecast for future periods is
  expressed as follows
• Ft1 Lt Tt
• Ftn Lt nTt

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Double Exponential Smoothing -trend corrected
(Holts Model)

• After observing demand for period t, revise the
  estimates for level and trend as follows
• Lt1 aDt1 (1-a)(Lt Tt)
• Tt1 b(Lt1 - Lt) (1-b)Tt
• a smoothing constant for level( chosen as 0.20
  in next slide)
• b smoothing constant for trend(chosen as 0.40
  in next slide)

20
DES with Trend (Holts Model)
a 0.2, b 0.4
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Triple Exponential Smoothing-trend and
seasonality corrected(Winters Model)

• Appropriate when the systematic component of
  demand is assumed to have a level, trend, and
  seasonal factor
• Systematic component (leveltrend)(seasonal
  factor)
• Assume periodicity p
• Obtain initial estimates of level (L0), trend
  (T0), seasonal factors (S1,,Sp) using procedure
  for static forecasting
• In period t, the forecast for future periods is
  given by
• Ft1 (LtTt)(St1) and Ftn (Lt nTt)Stn

22
Triple Exponential Smoothing-trend and
seasonality corrected(Winters Model)

• After observing demand for period t1, revise
  estimates for level, trend, and seasonal factors
  as follows
• Lt1 a(Dt1/St1) (1-a)(LtTt)
• Tt1 b(Lt1 - Lt) (1-b)Tt
• Stp1 g(Dt1/Lt1) (1-g)St1
• a smoothing constant for level
• b smoothing constant for trend
• g smoothing constant for seasonal factor
• Example Tahoe Salt data. Forecast demand for
  period 1 using Winters model.
• Initial estimates of level, trend, and seasonal
  factors are obtained as in the static forecasting
  case

23
Triple Exponential Smoothing-trend and
seasonality corrected(Winters Model)

• After observing demand for period t1, revise
  estimates for level, trend, and seasonal factors
  as follows
• Lt1 a(Dt1/St1) (1-a)(LtTt)
• Tt1 b(Lt1 - Lt) (1-b)Tt
• Stp1 g(Dt1/Lt1) (1-g)St1
• a smoothing constant for level
• b smoothing constant for trend
• g smoothing constant for seasonal factor

24
Triple Exponential Smoothing-trend and
seasonality corrected(Winters Model)

• Ideas behind smoothing with trend and
  seasonality
• De-trend and de-seasonalizetime-series by
  separating base from trend and seasonality
  effects
• Smooth base in usual manner using ?
• Smooth trend forecasts in usual manner using ?
• Smooth seasonality forecasts using g
• Assume m seasons in a cycle
• 12 months in a year
• 4 quarters in a month
• 3 months in a quarter
• et cetera

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Triple Exponential Smoothing-trend and
seasonality corrected(Winters Model)

• Smooth the base forecast Bt
• Smooth the trend forecast Tt
• Smooth the seasonality forecast St

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Triple Exponential Smoothing-trend and
seasonality corrected(Winters Model)

• Forecast Ft with trend and seasonality
  
• Smooth the trend forecast Tt
• Smooth the seasonality forecast St

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TES with Trend and Seasonality(Winters Model)
a 0.2, b 0.4, g 0.6
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Adaptive Forecasting

• The estimates of level, trend, and seasonality
  are adjusted after each demand observation
• General steps in adaptive forecasting
• Moving average
• Exponential smoothing( simple)
• Trend-corrected exponential smoothing (Holts
  model)
• Trend- and seasonality-corrected exponential
  smoothing (Winters model)

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Basic Formula forAdaptive Forecasting

• Ft1 (Lt lT)St1 forecast for period tl in
  period t
• Lt Estimate of level at the end of period t
• Tt Estimate of trend at the end of period t
• St Estimate of seasonal factor for period t
• Ft Forecast of demand for period t (made period
  t-1 or earlier)
• Dt Actual demand observed in period t
• Et Forecast error in period t
• At Absolute deviation for period t Et
• MAD Mean Absolute Deviation average value of
  At

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General Steps inAdaptive Forecasting

• Initialize Compute initial estimates of level
  (L0), trend (T0), and seasonal factors (S1,,Sp).
  This is done as in static forecasting.
• Forecast Forecast demand for period t1 using
  the general equation
• Estimate error Compute error Et1 Ft1- Dt1
• Modify estimates Modify the estimates of level
  (Lt1), trend (Tt1), and seasonal factor
  (Stp1), given the error Et1 in the forecast
• Repeat steps 2, 3, and 4 for each subsequent
  period

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Forecasting Accuracy

• Any of the chosen forecasting models are useful
  only as long as their predictions are close to
  reality
• Inevitably, forecast errors arise when there is a
  difference between the forecast and the actual
  demand
• Implications of incorrect or wrong forecasts can
  be very serious to business operations
• For instance, if projected demand is 250, 000
  units and actual demand is 100,000 units leads
  to serious inventory buildup problems of both
  inputs and finished goods alternatively, if
  actual demand is 350,000 units, then severe
  shortages, rush purchasing at higher costs,
  production rescheduling, quality compromises- all
  pose serious operational strains and problems
• Therefore, obtaining reliable and accurate ( as
  far as possible !) forecasts vital
• Hence, knowledge of forecasting errors important
  

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Forecasting Performance Measures

• Mean Forecast Error (MFE or Bias) Measures
  average deviation of forecast from actual.
• Mean Absolute Deviation (MAD) Measures average
  absolute deviation of forecast from
  actual.
• Mean Absolute Percentage Error (MAPE) Measures
  absolute error as a percentage of the
  forecast.
• Standard Squared Error (MSE) Measures variance
  of forecast error
• Tracking Signal (TS) Measures the shift/drift of
  the forecasting model to consistently
  overestimate or underestimate demand

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Forecasting Performance Measures
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Mean Forecast Error (MFE or Bias)

• Want MFE to be as close to zero as possible --
  minimum bias
• A large positive (negative) MFE means that the
  forecast is undershooting (overshooting) the
  actual observations
• Note that zero MFE does not imply that forecasts
  are perfect (no error) -- only that mean is on
  target and model is consistently undershooting
  and overshooting !
• Also called forecast BIAS

35
Mean Absolute Deviation (MAD)

• Measures absolute error- adding both the pluses
  and minuses
• Positive and negative errors thus do not cancel
  out (as with MFE)
• Want MAD to be as small as possible
• No way to know if MAD error is large or small in
  relation to the actual data

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Mean Absolute Percentage Error (MAPE)

• Same as MAD, except ...
• Measures deviation as a percentage of actual data

37
Mean Squared Error (MSE)

• Measures squared forecast error -- error variance
• Recognizes that large errors are
  disproportionately more expensive than small
  errors
• Must be used where low tolerance of errors is
  critical
• But is not as easily interpreted as MAD, MAPE --
  not as intuitive

38
Tracking Signal

• Measures extent of deviation from the forecasting
  system/model
• Need to know if system/model is shifting/drifting
  away consistently
• Tracking signal (TS)is ratio of MFE and MAD
• TS MFE/MAD
• In above equation, MAD is always positive and a
  fraction of numerator value if demand is more
  than forecast, then the numerator is positive or
  negative if demand is less than the forecast so
  the sign and magnitude of TS will indicate if and
  by how much the forecasting system is drifting
  away from actual demand