Forecasting
Chapter 9
Chapter Objectives
Be able to:
Discuss the importance of forecasting and identify the
most appropriate type of forecasting approach, given
different forecasting situations.
Apply a variety of time series forecasting models,
including moving average, exponential smoothing, and
linear regression models.
Develop causal forecasting models using linear
regression and multiple regression.
Calculate measures of forecasting accuracy and
interpret the results.
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Forecasting
 Forecast – An estimate of the future level of
some variable.
 Why Forecast?
 Assess long-term capacity needs
 Develop budgets, hiring plans, etc.
 Plan production or order materials
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Types of Forecasts
 Demand
 Firm-level
 Market-level
 Supply
 Number of current producers and suppliers
 Projected aggregate supply levels
 Technological and political trends
 Price
 Cost of supplies and services
 Market price for firm’s product or service
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Laws of Forecasting
 Forecasts are almost always wrong by some amount
(but they are still useful).
 Forecasts for the near term tend to be more
accurate.
 Forecasts for groups of products or services tend to
be more accurate.
 Forecasts are no substitute for calculated values.
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Forecasting Methods
 Qualitative forecasting techniques – Forecasting
techniques based on intuition or informed opinion.
 Used when data are scarce, not available, or
irrelevant.
 Quantitative forecasting models – Forecasting
models that use measurable, historical data to
generate forecasts.
 Time series and causal models
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Selecting a Forecasting Method
Figure 9.2
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Qualitative Forecasting Methods
 Market surveys
 Build-up forecasts
 Life-cycle analogy method
 Panel consensus forecasting
 Delphi method
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Quantitative Forecasting Methods
 Time series forecasting models – Models that
use a series of observations in chronological
order to develop forecasts.
 Causal forecasting models – Models in which
forecasts are modeled as a function of
something other than time.
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Demand movement
 Randomness – Unpredictable movement from one
time period to the next.
 Trend – Long-term movement up or down in a time
series.
 Seasonality – A repeated pattern of spikes or drops
in a time series associated with certain times of the
year.
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Time series with randomness
Figure 9.3
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Time series with
Trend and Seasonality
Figure 9.4
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Last Period Model
 Last Period Model - The simplest time series
model that uses demand for the current
period as a forecast for the next period.
Ft+1 = Dt
where Ft+1= forecast for the next period, t+1
and Dt = demand for the current period, t
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Last Period Model
Table 9.3
Figure 9.5
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Moving Average Model
 Moving Average Model – A time series
forecasting model that derives a forecast by
taking an average of recent demand value.
n
Ft 1 
D
i 1
t 1i
n
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Moving Average Model
Period
1
2
3
4
5
6
7
8
Demand
12
15
11
9
10
8
14
12
n
Ft 1 
 Dt 1i
i 1
n
3-period moving average
forecast for Period 8:
=
=
(14 + 8 + 10) / 3
10.67
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Weighted Moving Average Model
 Weighted Moving Average Model – A form of
the moving average model that allows the
actual weights applied to past observations
to differ.
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Weighted Moving Average Model
Period
1
2
3
4
5
6
7
8
Demand
12
15
11
9
10
8
14
12
3-period weighted moving
average forecast for Period 8=
[(0.5  14) + (0.3  8) + (0.2  10)] / 1 =
11.4
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Exponential Smoothing Model
 Exponential Smoothing Model – A form of the
moving average model in which the forecast for the
next period is calculated as the weighted average of
the current period’s actual value and forecast.
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Exponential Smoothing Model
a = .3
Period Demand
1
50
Forecast
40
2
46
.3 * 50 + (1-.3) * 40 = 43
3
52
.3 * 46 + (1-.3) * 43 = 43.9
4
48
.3 * 52 + (1-.3) * 43.9 = 46.33
5
47
.3 * 48 + (1-.3) * 46.33 = 46.83
6
.3 * 47 + (1-.3) * 46.83 = 46.88
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Adjusted Exponential Smoothing
 Adjusted Exponential Smoothing Model – An expanded
version of the exponential smoothing model that includes a
trend adjustment factor.
AFt+1 = Ft+1 +Tt+1
where AFt+1 = adjusted forecast for the next period
Ft+1 = unadjusted forecast for the next period = aDt + (1 – a) Ft
Tt+1 = trend factor for the next period = (Ft+1 – Ft) + (1 – )Tt
Tt = trend factor for the current period
 smoothing constant for the trend adjustment factor
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Linear Regression

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Linear Regression
 How to calculate the a and b
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Linear Regression – Example 9.3
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Linear Regression – Example 9.3
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Linear Regression – Example 9.3
Figure 9.12
The graph shows an upward trend of 7.33 sales per month.
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Seasonal Adjustments
 Seasonality – Repeated patterns or drops in a
time series associated with certain times of
the year.
Table 9.8
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Seasonal Adjustments
 Four-step procedure:
 For each of the demand values in the time series, calculate the
corresponding forecast using the unadjusted forecast model.
 For each demand value, calculate (Demand/Forecast). If the ratio is
less than 1, then the forecast model overforecasted; if it is greater
than 1, then the model underforecasted.
 If the time series covers multiple years, take the average
(Demand/Forecast) for corresponding months or quarters to derive
the seasonal index. Otherwise use (Demand/Forecast) calculated in
Step 2 as the seasonal index.
 Multiply the unadjusted forecast by the seasonal index to get the
seasonally adjusted forecast value.
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Seasonality – Example 9.4
Note that the
regression forecast does
not reflect the
seasonality.
Figure 9.15
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Seasonality – Example 9.4
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Seasonality – Example 9.4
Calculate the (Demand/Forecast) for each of the time periods:
January 2012: (Demand/Forecast) = 51/106.9 = .477
January 2013: (Demand/Forecast) = 112/205.6 = .545
Calculate the monthly seasonal indices:
Monthly seasonal index, January = (.477 + .545)/2 = .511
Calculate the seasonally adjusted forecasts
Seasonally adjusted forecast = unadjusted forecast x seasonal index
January 2012: 106.9 x .511 = 54.63
January 2013: 205.6 x .511 = 105.06
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Seasonality – Example 9.4
Note that the
regression forecast now
does reflect the
seasonality.
Figure 9.16
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Causal Forecasting Models
 Linear Regression
 Multiple Regression
 Examples:
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Multiple Regression
 Multiple Regression – A generalized form of linear regression
that allows for more than one independent variable.
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Forecast Accuracy
How do we know:
 If a forecast model is “best”?
 If a forecast model is still working?
 What types of errors a particular forecasting model
is prone to make?
Need measures of forecast accuracy
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Measures of Forecast Accuracy
 Forecast error for period (i) =
 Mean forecast error (MFE) =
 Mean absolute deviation (MAD) =
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Measures of Forecast Accuracy
 Mean absolute percentage error (MAPE) =
 Tracking Signal =
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Forecast Accuracy – Example 9.7
Table 9.11
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Forecast Accuracy – Example 9.7
 Calculate the forecast error for each week,
the absolute deviation of the forecast error,
and absolute percent errors.
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Forecast Accuracy – Example 9.7
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Forecast Accuracy – Example 9.7
 Model 2 has the lowest MFE so it is the least
biased.
 Model 2 also has the lowest MAD and MAPE
values so it appears to be superior.
 Calculate the tracking signal for the first 10
weeks.
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Forecast Accuracy – Example 9.7
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Forecast Accuracy – Example 9.7
 The tracking signal for Model 2 gets very low
in week 5, however the model recovers.
 You need to continue to update the tracking
signal in the future.
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Collaborative Planning,
Forecasting, and Replenishment (CPFR)
 CPFR – A set of business processes, backed
up by information technology, in which
members agree to mutual business
objectives and measures, develop joint sales
and operational plans, and collaborate
electronically to generate and update sales
forecasts and replenishment plans.
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Forecasting
Case Study
Top-Slice Drivers
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