Forecasting

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Chapter 4
Forecasting
The ability to calculate or predict (some future
event or condition) usually as a result of study
and analysis of available pertinent data
especially to predict (weather conditions) on
the basis of correlated meteorological
observations Prop
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Outline of Lecture

• What Is Forecasting?
• Forecasting Time Horizons
• The Influence of Product Life Cycle
• Types Of Forecasts

• The Strategic Importance Of Forecasting
• Human Resources
• Capacity
• Supply-Chain Management
• Seven Steps In The Forecasting System

• Forecasting Approaches
• Overview of Qualitative Methods
• Overview of Quantitative Methods

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Outline of Lecture

• Time-series Forecasting
• Decomposition of a Time Series
• Naïve Approach
• Moving Averages
• Exponential Smoothing
• Exponential Smoothing with Trend Adjustment
• Trend Projections
• Seasonal Variations in Data
• Cyclical Variations in Data

• Associative Forecasting Methods Regression And
  Correlation Analysis
• Using Regression Analysis to Forecast
• Standard Error of the Estimate
• Correlation Coefficients for Regression Lines
• Multiple-Regression Analysis

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Outline of Lecture

• Monitoring and Controlling Forecasts
• Adaptive Smoothing
• Focus Forecasting
• Forecasting In The Service Sector

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What is Forecasting?

• Process of predicting a future event
• Underlying basis of all business decisions
• Production
• Inventory
• Personnel
• Facilities

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Forecasting Time Horizons

• Short-range forecast
• Up to 1 year, generally less than 3 months
• Purchasing, job scheduling, workforce levels, job
  assignments, production levels
• Medium-range forecast
• 3 months to 3 years
• Sales and production planning, budgeting
• Long-range forecast
• 3 years
• New product planning, facility location, research
  and development

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Influence of Product Life Cycle
Introduction Growth Maturity Decline

• Introduction and growth require longer forecasts
  than maturity and decline
• As product passes through life cycle, forecasts
  are useful in projecting
• Staffing levels
• Inventory levels
• Factory capacity

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Product Life Cycle
Qualitative Quantitative Quantitative
Quantitative
Product design and development critical Frequent
product and process design changes Short
production runs High production costs Limited
models Attention to quality
Forecasting critical Product and process
reliability Competitive product improvements and
options Increase capacity Shift toward product
focus Enhance distribution
Standardization Less rapid product changes more
minor changes Optimum capacity Increasing
stability of process Long production runs Product
improvement and cost cutting
Little product differentiation Cost
minimization Overcapacity in the industry Prune
line to eliminate items not returning good
margin Reduce capacity
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Types of Forecasts

• Economic forecasts
• Address business cycle inflation rate, money
  supply, housing starts, etc.
• Technological forecasts
• Predict rate of technological progress
• Impacts development of new products
• Demand forecasts
• Predict sales of existing product

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Seven Steps in Forecasting

• Determine the use of the forecast
• Select the items to be forecasted
• Determine the time horizon of the forecast
• Select the forecasting model(s)
• Gather the data
• Make the forecast
• Validate and implement results

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The Realities!

• Forecasts are seldom perfect
• Most techniques assume an underlying stability in
  the system
• Product family and aggregated forecasts are more
  accurate than individual product forecasts

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Forecasting Approaches
Qualitative Methods

• Used when situation is vague and little data
  exist
• New products
• New technology
• Involves intuition, experience
• e.g., forecasting sales on Internet

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Forecasting Approaches
Quantitative Methods

• Used when situation is stable and historical
  data exist
• Existing products
• Current technology
• Involves mathematical techniques
• e.g., forecasting sales of color televisions

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Overview of Qualitative Methods

• Sales force composite
• Estimates from individual salespersons are
  reviewed for reasonableness, then aggregated
• Consumer Market Survey
• Ask the customer

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Jury of Executive Opinion

• Involves small group of high-level managers
• Group estimates the demand by working together
• Combines managerial experience with statistical
  models
• Relatively quick
• Group-thinkdisadvantage

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Sales Force Composite

• Each salesperson projects his or her sales
• Combined at district and national levels
• Sales reps know customers wants
• Tends to be overly optimistic

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Delphi Method

• Iterative group process, continues until
  consensus is reached
• 3 types of participants
• Decision makers
• Staff
• Respondents

Experts
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Consumer Market Survey

• Ask customers about purchasing plans
• What consumers say, and what they actually do are
  often different
• Sometimes difficult to answer

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Overview of Quantitative Approaches

• Naive approach
• Moving averages
• Exponential smoothing
• Trend projection
• Linear regression

Meat of lecture
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Time Series Forecasting

• Set of evenly spaced numerical data
• Obtained by observing response variable at
  regular time periods
• Forecast based only on past values
• Assumes that factors influencing past and present
  will continue influence in future

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Time Series Components
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Components of Demand
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Trend Component

• Persistent, overall upward or downward pattern
• Changes due to population, technology, age,
  culture, etc.
• Typically several years duration

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Seasonal Component

• Regular pattern of up and down fluctuations
• Due to weather, customs, etc.
• Occurs within a single year

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Cyclical Component

• Repeating up and down movements
• Affected by business cycle, political, and
  economic factors
• Multiple years duration

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Random Component

• Erratic, unsystematic, residual fluctuations
• Due to random variation or unforeseen events
• Short duration and nonrepeating

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Naive or Seat of the Pants
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Naive Approach

• Assumes demand in next period is the same as
  demand in most recent period
• e.g., If May sales were 48, then June sales will
  be 48
• Sometimes cost effective and efficient
• Based upon experience

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Moving Average Method

• MA is a series of arithmetic means
• Used if little or no trend
• Used often for smoothing
• Provides overall impression of data over time
• Historical Basis

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Moving Average Example
(12 13 16)/3 13 2/3 (13
16 19)/3 16 (16 19 23)/3 19 1/3
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Graph of Moving Average
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Weighted Moving Average

• Used when trend is present
• Older data usually less important
• Weights based on experience and intuition

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(3 x 16) (2 x 13) (12)/6
141/3 (3 x 19) (2 x 16) (13)/6 17 (3
x 23) (2 x 19) (16)/6 201/2
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Potential Problems With Moving Average

• Increasing n smooths the forecast but makes it
  less sensitive to changes
• Do not forecast trends well
• Require extensive historical data

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Moving Average And Weighted Moving Average
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Exponential Smoothing

• Form of weighted moving average
• Weights decline exponentially
• Most recent data weighted most
• Requires smoothing constant (?)
• Ranges from 0 to 1
• Subjectively chosen
• Involves little record keeping of past data

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Exponential Smoothing
New forecast last periods forecast a (last
periods actual demand last periods
forecast)

Ft Ft 1 a(At 1 - Ft 1)
Error
where Ft new forecast Ft 1 previous
forecast a smoothing (or weighting)
constant (0 ? a ? 1) At - 1
Actual value previously
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Exponential Smoothing Example
Example
For this period
Predicted demand 142 Ford Mustangs Actual
demand 153 Smoothing constant a .20 What is
prediction for next period ?
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Exponential Smoothing Example
Predicted demand 142 Ford Mustangs Actual
demand 153 Smoothing constant a .20
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Exponential Smoothing Example
Predicted demand 142 Ford Mustangs Actual
demand 153 Smoothing constant a .20
New forecast 142 .2(153 142) 142
2.2 144.2 144 cars
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Effect of Smoothing Constants
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Impact of Different ?
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Choosing ?
The objective is to obtain the most accurate
forecast no matter the technique
We generally do this by selecting the model that
gives us the lowest forecast error
Forecast error Actual demand - Forecast
value At - Ft
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Error
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Common Measures of Error
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Common Measures of Error
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Comparison of Forecast Error
Given this data let us find the be alpha
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Comparison of Forecast Error
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Comparison of Forecast Error
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Comparison of Forecast Error
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Comparison of Forecast Error
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Trends
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Exponential Smoothing with Trend Adjustment
When a trend is present, exponential smoothing
must be modified
FITt Ft Tt
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Exponential Smoothing with Trend Adjustment
Ft a(At - 1) (1 - a)(Ft - 1 Tt - 1)
Tt b(Ft - Ft - 1) (1 - b)Tt - 1
Step 1 Compute Ft Step 2 Compute Tt Step 3
Calculate the forecast FITt Ft Tt
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Exponential Smoothing with Trend Adjustment
Example
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Exponential Smoothing with Trend Adjustment
Example
Step 1 Forecast for Month 2
F2 aA1 (1 - a)(F1 T1) F2 (.2)(12) (1
- .2)(11 2) 2.4 10.4 12.8 units
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Exponential Smoothing with Trend Adjustment
Example
Step 2 Trend for Month 2
T2 b(F2 - F1) (1 - b)T1 T2 (.4)(12.8 -
11) (1 - .4)(2) .72 1.2 1.92 units
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Exponential Smoothing with Trend Adjustment
Example
Step 3 Calculate FIT for Month 2
FIT2 F2 T1 FIT2 12.8 1.92 14.72 units
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Exponential Smoothing with Trend Adjustment
Example
15.18 2.10 17.28 17.82 2.32 20.14 19.91
2.23 22.14 22.51 2.38 24.89 24.11 2.07 26.18
27.14 2.45 29.59 29.28 2.32 31.60 32.48
2.68 35.16
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Exponential Smoothing with Trend Adjustment
Example
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Linear Analysis
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Linear Projections
aka Linear Regression
Fitting a trend line to historical data points to
project into the medium-to-long-range
Linear trends can be found using the least
squares technique
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Least Squares Method
Y intercept a
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Least Squares Method
Least squares method minimizes the sum of the
squared errors (deviations)
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Least Squares Method
Equations to calculate the regression variables
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Least Squares Example
Y 56.7 10.54X
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Least Squares Example
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Least Squares Example
80.54
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80.54 70 10.54
Know as Slope of the line
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Seasonality
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Seasonal Variations In Data
The multiplicative seasonal model can modify
trend data to accommodate seasonal variations in
demand
Rules

• Find average historical demand for each season
• Compute the average demand over all seasons
• Compute a seasonal index for each season
• Estimate next years total demand
• Divide this estimate of total demand by the
  number of seasons, then multiply it by the
  seasonal index for that season

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Seasonal Index Example
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Seasonal Index Example
0.957
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Seasonal Index Example
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Seasonal Index Example
Expected annual demand 1,200
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Seasonal Index Example
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Associative Forecasting
Used when changes in one or more independent
variables can be used to predict the changes in
the dependent variable
Most common technique is linear regression
analysis
We apply this technique just as we did in the
time series example
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Associative Forecasting
Forecasting an outcome based on predictor
variables using the least squares technique
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Associative Forecasting Example
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Associative Forecasting Example
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Associative Forecasting Example
Sales 1.75 .25(payroll)
If payroll next year is estimated to be 600
million, then
Sales 1.75 .25(6) Sales 325,000
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Standard Error of the Estimate

• A forecast is just a point estimate of a future
  value
• This point is actually the mean of a
  probability distribution

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Standard Error of the Estimate
where y y-value of each data point yc compute
d value of the dependent variable, from the
regression equation n number of data points
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Standard Error of the Estimate
Computationally, this equation is considerably
easier to use
We use the standard error to set up prediction
intervals around the point estimate
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Standard Error of the Estimate
Sy,x .306
The standard error of the estimate is 30,600 in
sales
So the sales for 2006 is 325,000 30,600
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Correlation
How good a fit is there between the predicted
value and the data used to predict that value
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Correlation Coefficient
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(No Transcript)
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Correlation

• Coefficient of Determination, r2, measures the
  percent of change in y predicted by the change in
  x
• Values range from 0 to 1
• Easy to interpret

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Correlation

• How strong is the linear relationship between the
  variables?
• Correlation does not necessarily imply causality!
• Coefficient of correlation, r, measures degree of
  association
• Values range from -1 to 1

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Multiple Regression
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Multiple Regression Analysis
If more than one independent variable is to be
used in the model, linear regression can be
extended to multiple regression to accommodate
several independent variables
Computationally, this is quite complex and
generally done on the computer
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Monitoring and Controlling
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Monitoring and Controlling Forecasts
Tracking Signal

• Measures how well the forecast is predicting
  actual values
• Ratio of running sum of forecast errors (RSFE) to
  mean absolute deviation (MAD)
• Good tracking signal has low values
• If forecasts are continually high or low, the
  forecast has a bias error

RSFE Running Sum of Forecasted Errors MAD
Mean Absolute Deviation
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Monitoring and Controlling Forecasts
The idea is to set a range of values within
which the Tracking Signal must remain (i.e., 3
and -3.5)
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Tracking Signal
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Tracking Signal Example
Tracking Limits 2.7 to -3
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Tracking Signal Example
The variation of the tracking signal between -2.0
and 2.5 is within acceptable limits of 2.7 and -3
Tracking Signal 35/14.2 2.46