Notes on Forecasting

Please see the notes below

Forecasting

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Goals
By the end of this chapter, you should know:
Importance of Forecasting
Various Forecasting Techniques
Choosing a Forecasting Method

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Forecasting
Forecasts are done to predict future events for planning
Finance, human resources, marketing, operations, and supply chain managers need forecasts to plan
Forecasts are made on many different variables
Forecasts are important to managing both processes and managing supply chains

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Key Decisions in Forecasting
Deciding what to forecast
Level of aggregation
Units of measurement
Choosing a forecasting system
Choosing a forecasting technique

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Forecasting Techniques

Qualitative (Judgment) Methods

Sales force Estimates

Time-series Methods

Naïve Method

Causal Methods

Executive Opinion

Market Research

Delphi Method

Moving Averages

Exponential Smoothing

Regression Analysis

Qualitative (Judgment) methods
Salesforce estimates
Executive opinion
Market Research
The Delphi Method

Salesforce estimates: Forecasts derived from estimates provided by salesforce.
Executive opinion: Method in which opinions, experience, and technical knowledge of one or more managers are summarized to arrive at a single forecast.
Market research: A scientific study and analysis of data gathered from consumer surveys intended to learn consumer interest in a product or service.
Delphi method: A process of gaining consensus from a group of experts while maintaining their anonymity.

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Case Study

Reference: Krajewski, Ritzman, Malhotra. (2010). Operations Management: Processes and Supply Chains, Ninth Edition. Pearson Prentice Hall. P. 42-43.
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Case study questions
What information system is used by UNILEVER to manage forecasts?
What does UNILEVER do when statistical information is not useful for forecasting?
What types of qualitative methods are used by UNILEVER?
What were some suggestions provided to improve forecasting?

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Causal methods – Linear Regression
A dependent variable is related to one or more independent variables by a linear equation
The independent variables are assumed to “cause” the results observed in the past
Simple linear regression model assumes a straight line relationship

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Causal methods – Linear Regression
Y = a + bX
where
Y = dependent variable
X = independent variable
a = Y-intercept of the line
b = slope of the line

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Causal methods – Linear Regression
Fit of the regression model
Coefficient of determination
Standard error of the estimate
Please go to in-class exercise sheet

Coefficient of determination: Also called r-squared. Measures the amount of variation in the dependent variable about its mean that is explained by the regression line. Range between 0 and 1. In general, larger values are better.
Standard error of the estimate: Measures how closely the data on the dependent variable cluster around the regression line. Smaller values are better.
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Time Series
A time series is the repeated observations of demand for a service or product in their order of occurrence
There are five basic time series patterns
Horizontal
Trend
Seasonal
Cyclical
Random

Time series methods use historical information regarding only the dependent variable.
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Demand Patterns

Quantity
Time
(a) Horizontal: Data cluster about a horizontal line

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Demand Patterns

Quantity
Time
(b) Trend: Data consistently increase or decrease

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Demand Patterns
Quantity
| | | | | | | | | | | |
J F M A M J J A S O N D
Months
(c) Seasonal: Data consistently show peaks and valleys
Year 1
Year 2

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Demand Patterns
Quantity
| | | | | |
1 2 3 4 5 6
Years
(d) Cyclical: Data reveal gradual increases and decreases over extended periods

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The extended periods of time could be years or even decades. Cyclical patterns could arise from product life cycle and business cycle.

Demand Patterns
Four of the patterns – horizontal, trend, seasonal, and cyclical – combine in varying degrees to define the underlying time pattern
Fifth pattern
Random variation: Results from chance causes and cannot be predicted
Random variation is what makes every forecast ultimately wrong

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Time-Series methods
Use only historical information rather than independent variables (as used by Regression)
Assumption is that past pattern continues in future
In a naive forecast the forecast for the next period equals the demand for the current period (Forecast = Dt)

Naïve forecast works well when horizontal, trend, or seasonal patterns are stable and random variation is small.
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Time-Series methods
This section considers time-series methods with demand that has no trend, seasonal, or cyclical patterns
All variation in time series is due to random variation, so the following techniques are appropriate:
Simple moving average
Weighted moving average
Exponential smoothing

Simple Moving Average
The forecast for period t + 1 can be calculated at the end of period t (after the actual demand for period t is known) as
Ft+1 = =
Sum of last n demands
n
Dt + Dt-1 + Dt-2 + … + Dt-n+1
n
where
Dt = actual demand in period t
n = total number of periods in the average
Ft+1 = forecast for period t + 1

Forecast error
For any forecasting method, it is important to measure the accuracy of its forecasts. Forecast error is simply the difference found by subtracting the forecast from actual demand for a given period, or
where
Et = forecast error for period t
Dt = actual demand in period t
Ft = forecast for period t
Et = Dt – Ft

Simple Moving Average
Please refer to problem in the in-class exercise

Using this method, each historical demand in the average can have its own weight, provided that the sum of the weights equals 1.0.
Weighted Moving Average
Ft+1 = W1D1 + W2D2 + … + WnDt-n+1
A three-period weighted moving average model with the most recent period weight of 0.50, the second most recent weight of 0.30, and the third most recent might be weight of 0.20
Ft+1 = 0.50Dt + 0.30Dt–1 + 0.20Dt–2

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Weighted Moving Average
Please refer to problem in the in-class exercise

Exponential Smoothing
A sophisticated weighted moving average that calculates the average of a time series by giving recent demands more weight than earlier demands
Requires only three items of data
The last period’s forecast
The demand for this period
A smoothing parameter, alpha (α), where 0 ≤ α ≤ 1.0
The equation for the forecast is
Ft+1 = α(Demand this period) + (1 – α)(Forecast calculated last period)
= αDt + (1 – α)Ft
Ft+1 = Ft + α(Dt – Ft)
or the equivalent

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Exponential Smoothing
Please refer to problem in the in-class exercise

Exponential Smoothing
The emphasis given to the most recent demand levels can be adjusted by changing the smoothing parameter
Larger α values emphasize recent levels of demand and result in forecasts more responsive to changes in the underlying average
Smaller α values treat past demand more uniformly and result in more stable forecasts
Exponential smoothing is simple and requires minimal data
When the underlying average is showing some trend, different model is needed

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Choosing a Time-Series Method
Forecast performance is determined by forecast errors
Forecast errors detect when something is going wrong with the forecasting system
Forecast errors can be classified as either bias errors or random errors
Bias errors (or systematic errors) are the result of consistent mistakes
Random error results from unpredictable factors that cause the forecast to deviate from the actual demand

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So, what do we mean by systematic error?

Operations Management
Introduction to Forecasting
Copyright 2007 by Gary Mitchell. All Rights Reserved.
29
Note that for almost all of the periods, the forecasted value is below the actual data value. This is a systematic error.

Measures of Forecast Error
Forecast Error = Demand value – Forecast Value
Mean absolute deviation (MAD)
Mean signed deviation (MSD)
Tracking signal (TS)
Mean squared error (MSE)
Mean absolute percentage error (MAPE)
Et = Dt – Ft

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Mean Absolute Deviation (MAD)
MAD is the average of the absolute values of the errors.

Stated in the same units as the forecast
Captures the magnitude of the forecasting error
Compute MAD for the example problem in Excel sheet (tab 2) and interpret the results
|Et |
n
MAD =

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Mean Sign Deviation (MSD)
MSD is the average of the errors

Stated in the same units as the forecast
Signs (+/-) of the error terms tend to cancel each other out
A large value (+/-) indicates systematic forecast error
Compute MSD for the example problem in Excel sheet (tab 2) and interpret the results
 Et
n
MSD =

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Tracking Signal (TS)
Tracking Signal (TS) measures systematic error

TS is unitless and is between -1 and 1
Think of it as percentage of forecast error that is systematic
MSD
MAD
TS =

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Tracking Signal (TS)

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Interpreting Tracking Signal (TS)
Absolute Magnitude
Sign Low
(0.0 – 0.2) Medium
(0.2 – 0.5) High
(0.5 and above)
+ Forecast OK Forecast lag below actual Serious lag below actual
– Forecast OK Forecast lag above actual Serious lag above actual

Interpreting Tracking Signal (TS)
Calculate TS for the example problem and interpret it

Mean Squared Error(MSE)
MSE is the average of the square errors

It is a measure of dispersion of forecast error
Smaller values indicate that forecast is typically close to actual demand
Compute MSE for the example problem in Excel sheet (tab 2) and interpret the results
 Et2
n
MSE =

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Mean Absolute Percentage Error(MAPE)
MAPE takes the absolute error of each forecast, and divides it by the value of the demand, multiply that quantity with 100 to get the error as a percentage of the demand, and then averages these percentage errors.

Very useful for comparisons between time series for different SKUs
Compute MAPE for the example problem in Excel sheet (tab 2) and interpret the results
 (|Et |/ Dt)(100)
n
MAPE =

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Criteria for Selecting Methods
Criteria to use in making forecast method and parameter choices include
Minimizing bias
Minimizing MAPE, MAD, or MSE
Meeting managerial expectations of changes in the components of demand
Minimizing the forecast error last period
Statistical performance measures can be used
For projections of more stable demand patterns, use lower α values or larger n values
For projections of more dynamic demand patterns try higher α or smaller n values

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Forecasting as a Process
Forecasting is not a stand-alone activity, but part of a larger process

Finalize
and communicate
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Review by Operating Committee
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Revise forecasts
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Consensus meetings and collaboration
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Prepare initial forecasts
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Adjust history file
1

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Remember, forecasting is like fortune telling…
You’re right only by accident!

Operations Management
Introduction to Forecasting
Copyright 2007 by Gary Mitchell. All Rights Reserved.
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References
Krajewski, Ritzman, Malhotra. (2010). Operations Management: Processes and Supply Chains, Ninth Edition. Pearson Prentice Hall.
Dr. Gary Mitchell, Class Notes
Dr. Min Yu, Class Notes

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