2. Forecasting in Operations Function
Forecasting allows predicting future values of a
series based on past observations;
In supply chain the primarily interest is in
forecasting product demand;
Trends, cycles and seasonal variation may be present
in past observations that help us to predict future
demand more closely.
3. Forecasting Horizon in Supply Chain Planning
Long (Months / Years)
Capacity needs, Long-term sales patterns, Growth trends
Intermediate (Weeks / Months)
Product family sales, Labor needs, Resource requirements
Short (Days / Weeks)
Short-term sales, Shift schedule, Resource requirements
4. Characteristics of Forecasts
They are usually wrong.
A good forecast is more than a single number.
Aggregate forecasts are more accurate.
The longer the forecast horizon, the less accurate the
forecast will be.
Forecasts should not be used to the exclusion of
known information.
5. Benefits of Forecasting
Lower inventories
Reduced Stock-outs
Smoother production and supply-chain plans
Reduced production costs
Improved customer service
Etc.
6. Forecasting Methods
Qualitative (or Subjective) Methods:
Forecasts based on subjective judgment or opinion
Sales Force Composites
Customer Surveys
Jury of Executive Opinion
Delphi Method
Quantitative (or Objective) Methods:
Forecasts are derived based on an analysis of data.
Time Series Forecasting Models
Causal or Associative Models
7. Time Series Forecasting Models
Information can be inferred from the pattern of past
observations and can be used to forecast future values of
the series.
Observations about past values are drawn at discrete points
in time, usually equally spaced.
Time series include various patterns of data:
Trend
Seasonality
Cycles
Randomness
8. Simple Moving Average Forecasting Model
A moving average of order N is simply the arithmetic
average of the most recent N observations.
For one step ahead forecasts for most recent N
observations:
t −1
Ft = (1 / N ) ∑ Ai = (1 / N )( At −1 + At − 2 + ... + At − N )
i =t − N
or
t
t −1
Ft +1 = (1 / N ) ∑ Ai = (1 / N ) At + ∑ Ai − At − N
i = t − N +1 i =t − N
Ft +1 = Ft + (1 / N )[ At − At − N ]
9. Example: Simple Moving Average
Consider a demand Period Demand MA(3) MA(6)
process 2, 4, 6, 8,
10, 12, 14, 16, 18, 20, 1 2
22, 24 in which 2 4
there is a definite 3 6
4 8 4
trend. 5 10 6
6 12 8
Consider the MA(3) 7 14 10 7
8 16 12 9
and MA(6) 9 18 14 11
10 20 16 13
11 22 18 15
12 24 20 17
10. Simple Moving Average Forecasting Model (Excel)
Period Demand Forecast MA(3) Forecast MA(6) Moving Average MA(3)
1 2 #N/A #N/A 30
25
2 3 #N/A #N/A 20
Value
15
3 10 5 #N/A 10 Actual
5 Forecast
4 8 7 #N/A 0
1 2 3 4 5 6 7 8 9 10 11 12
5 12 10 #N/A
Data Point
6 18 12.66666667 8.833333333
7 24 18 12.5
Moving Average MA(6)
8 26 22.66666667 16.33333333
30
9 20 23.33333333 18
Value
20
10 16 20.66666667 19.33333333 10 Actual
0 Forecast
11 22 19.33333333 21
1 2 3 4 5 6 7 8 9 10 11 12
12 24 20.66666667 22 Data Point
Con: Less responsive to changes
in demand.
11. Weighted Moving Average Forecasting Model
t
Ft +1 = ∑w A
i =t − N +1
i i
Allows more emphasis to be placed on recent or past
data.
Weights can be determined by experience of the
forecaster.
Still not responsive enough to track changes in
demand.
13. Exponential Smoothing Forecasting Model
Is a sophisticated weighted moving average technique.
Forecast for next period’s demand is the current period’s forecast
adjusted by a fraction of the difference between the current
period’s actual demand and its forecast.
Requires less data to be implemented, thus is more widely
practiced technique.
Suitable for data that show little trend or seasonal patterns.
Ft = α At −1 + (1 − α ) Ft −1
where 0 < α ≤ 1 is the smoothing constant, determines relative weight placed on demand
Ft = Ft −1 − α ( Ft −1 − At −1 )
Ft = Ft −1 − α et −1
14. Exponential Smoothing Forecasting Model
If we forecast high in period t-1, et-1 is positive and the
adjustment is to decrease the forecast. And vice versa.
If α is large, more weight is given to the current
observation and less weight on past observations,
which results into a forecast that will react quickly to
changes in the demand pattern but may have much
greater variation from period to period.
16. Trend Based Exponential Smoothing
Forecasting Model
Ft = α At −1 + (1 − α )( Ft −1 + Tt −1 )
Tt = β ( Ft − Ft −1 ) + (1 − β )Tt −1
and the trend - adjusted forecast is
TAFt + m = Ft + mTt
Higher the β higher the emphasis on recent trend
changes.
α & β are determined by trial and error approach.
17. Linear Trend Forecasting Model
Simple linear regression can be used to fit a line to the time
series historical data.
Linear trend method minimizes the sum of squared deviations
to determine the characteristics of the linear equation:
( x1 , y1 ), ( x2 , y2 ),..., ( xn , yn ) be n paired data points for X & Y
X = Independent Variable
Y = Dependent Variable
Suppose a linear relationship exists between X and Y, then
∧
Y = b +b X
0 1
18. Linear Trend Forecasting Model
∧
where, Y = predicted value of Y
x = time variable
b 0 = intercept of the line, and
b1 = slope of the line
n∑ ( xy ) − ∑ x ∑ y
b1 =
n∑ x 2 − (∑ x ) 2
b0 =
∑ y −b ∑ x1
n
19. Linear Trend Forecasting Model (Example)
What is the trend line and forecast for Period-13 for
the following data?
Period Demand Period Demand Period Demand
1 1600 5 2500 9 3900
2 2200 6 3500 10 4700
3 2000 7 3300 11 4300
4 1600 8 3200 12 4400
22. Associative Models
One or several external variables are identified that are
related to demand, which are easier to determine than
demand.
Once the relationship between the external variable and
demand is determined, it can be used as a forecasting tool.
Y = Phenomenon to be forecasted
X1 , X2 ,…, Xn = Variables affecting the phenomenon, then
Y = f(X1 , X2 ,…, X n)
23. Forecast Accuracy
At = observed demand during periods t, assume {At , t ≥ 1}
Ft = forecast made for period t during period t-1, one step ahead forecast
et = forecast error, then
et = Ft − At
If e1 , e2 ,..., en = forecast errors observed over n periods
n
MAD = mean absolute deviation = (1 / n)∑ ei
i =1
n
MSE = mean squared error = (1 / n)∑ ei2
i =1
n
MAPE = mean absolute percentage error = (1 / n)∑ ei / Di
i =1
24. Forecast Accuracy
n
Running sum of forecast errors (RSFE) = ∑e
t =1
t
RSFE
TrackingSignal =
MAD
A number of parameters have been defined. Each
one of which provide some sort of advantage over the
other.
Many organizations set targets for Tracking Signal as
a means to improve their forecasts.
25. Collaborative Planning, Forecasting, and
Replenishment (CPFR)
The objective of CPFR is to optimize the supply chain
by improving demand forecasting, delivering the
right product at the right time to the right location,
reducing inventories across the supply chains,
avoiding stock-outs, and improving customer
service.
The real value of CPFR comes from an exchange of
forecasting information rather than from more
sophisticated forecasting algorithms to improve
forecasting accuracy.
