Planning Forecast Customer Production Process Finished Goods Inputs
Marketin g : forecasts sales for new and
Productio n : uses sales forecasts to plan
production and operations; sometimes
involved in generating sales forecasts.
Characteristics of Forecasts
They are usually wrong
A good forecast is usually more than a single number
Aggregate forecast are more accurate
The longer the forecasting horizon, the less accurate the forecasts will be
Forecasts should not be used to the exclusion of known information
(inventory management, production plans..)
(sales patterns for product families..)
(long term planning of capacity needs)
Forecasting Techniques Judgmental Models Time Series Methods Causal Methods Forecasting Technique Delphi Method Moving Average Exponential Smoothing Regression Analysis Seasonality Models
Types of forecasting Methods
Sales force composites
Jury of executive opinion
The Delphi method
Time series methods
Don’t have data
Don’t have time to develop a forecast
Often used in practice
Depend on expert opinions
More appropriate for long term forecasts
A method to obtain a consensus forecast by using opinions from a group of “experts”
Causal methods use data from sources other than the series being predicted.
If Y is the phenomenon to be forecast and X 1 , X 2 , . .., X n are the n variables we believe to be related to Y, then a causal model is one in which the forecast for Y is some function of these variables:
Y = f (X 1 , X 2 , . .., X n )
Econometric models are causal models in which the relationship between Y and (X 1 , X 2 , . .., X n ) is linear.
Y = a o + a 1 X 1 + a 2 X 2 + … a n X n
for some constants a 1 , a 2 , . . . , a n
Forecasting Steps for Quantitative Methods
Build and evaluate model(s)
Forecast (model extrapolation)
Track the forecast
Identify the correct pattern
Collect data. Look for possible cause/effect relationships
Determine which form can be used to generate the pattern
Determine specific values of the parameters
Plot data over time. (remove outliers & get right scale).
Using part of the data, estimate model parameters.
Forecast the rest of the data with the model.
Evaluate accuracy of the model.
Use judgment to modify.
Keep track of model accuracy over time (redo, if needed).
Forecasting Stationary Series
Time series Analysis
Patterns that arise most often
Time Series Patterns Fig. 2-2
: Observed value of the demand during period t
time series we would like to predict
forecast made for period t in period t-1
forecast made at the end of t-1 after having
observed , , …
Time Series Forecast
For some set of weights
Forecast error in period t
Mean Absolute Deviation
Mean Square Error
Forecast Errors Over Time Fig. 2-3
TIME SERIES METHODS Stationary Series
A stationary time series is represented by a
constant plus a random fluctuation:
D t = µ+ ε t
where µ is an unknown constant corresponding to the mean of the series and ε t is a random error with mean 0 and variance σ 2 .
The methods described for stationary series are:
Methods of Forecasting Stationary Series
90 Oct 110 Sep 130 Aug 75 Jul 50 Jun 110 May 75 Apr 100 Mar 90 Feb 120 Jan Deliveries Month
94 110 92 90 83 91 MA(6) 105 85 78 78 95 88 103 MA(3) 90 Oct 110 Sep 130 Aug 75 Jul 50 Jun 110 May 75 Apr 100 Mar 90 Feb 120 Jan Deliveries Month
Moving-Average Forecasts Lag Behind a Trend Fig. 2-4
Current forecast is a weighted average of the last forecast and the current value of demand
New forecast = α (current observation of demand)
+ (1- α ) (last forecast)
Exponential Smoothing F t = F t-1 – (fraction of the observed forecast error in t-1) If we forecast high in period t-1 error is positive adjustment to decrease current forecast If we forecast low in period t-1 error is negative adjustment to increase current forecast