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Title: Forecasting

Chapter 13
Designing the Forecast System
  • Deciding what to forecast
  • Level of aggregation.
  • Units of measure.
  • Choosing the type of forecasting method
  • Qualitative methods
  • Judgment
  • Quantitative methods
  • Causal
  • Time-series

Deciding What To Forecast
  • Few companies err by more than 5 percent when
    forecasting total demand for all their services
    or products. Errors in forecasts for individual
    items may be much higher.
  • Level of Aggregation The act of clustering
    several similar services or products so that
    companies can obtain more accurate forecasts.
  • Units of measurement Forecasts of sales revenue
    are not helpful because prices fluctuate.
  • Forecast the number of units of demand then
    translate into sales revenue estimates
  • Stock-keeping unit (SKU) An individual item or
    product that has an identifying code and is held
    in inventory somewhere along the value chain.

Choosing the Type ofForecasting Technique
  • Judgment methods A type of qualitative method
    that translates the opinions of managers, expert
    opinions, consumer surveys, and sales force
    estimates into quantitative estimates.
  • Causal methods A type of quantitative method
    that uses historical data on independent
    variables, such as promotional campaigns,
    economic conditions, and competitors actions, to
    predict demand.
  • Time-series analysis A statistical approach that
    relies heavily on historical demand data to
    project the future size of demand and recognizes
    trends and seasonal patterns.

Demand Forecast Applications
Judgment Methods
  • Sales force estimates The forecasts that are
    compiled from estimates of future demands made
    periodically by members of a companys sales
  • Executive opinion A forecasting method in which
    the opinions, experience, and technical knowledge
    of one or more managers are summarized to arrive
    at a single forecast.
  • Executive opinion can also be used for
    technological forecasting to keep abreast of the
    latest advances in technology.
  • Market research A systematic approach to
    determine external consumer interest in a service
    or product by creating and testing hypotheses
    through data-gathering surveys.
  • Delphi method A process of gaining consensus
    from a group of experts while maintaining their

Guidelines for Using Judgment Forecasts
  • Judgment forecasting is clearly needed when no
    quantitative data are available to use
    quantitative forecasting approaches.
  • Guidelines for the use of judgment to adjust
    quantitative forecasts to improve forecast
    quality are as follows
  • Adjust quantitative forecasts when they tend to
    be inaccurate and the decision maker has
    important contextual knowledge.
  • Make adjustments to quantitative forecasts to
    compensate for specific events, such as
    advertising campaigns, the actions of
    competitors, or international developments.

Forecasting Error
  • For any forecasting method, it is important to
    measure the accuracy of its forecasts.
  • Forecast error is the difference found by
    subtracting the forecast from actual demand for a
    given period.
  • Et Dt - Ft where
  • Et forecast error for period t
  • Dt actual demand for period t
  • Ft forecast for period t

Measures of Forecast Error
  • Cumulative sum of forecast errors (CFE) A
    measurement of the total forecast error that
    assesses the bias in a forecast.
  • Mean squared error (MSE) A measurement of the
    dispersion of forecast errors.
  • Mean absolute deviation (MAD) A measurement of
    the dispersion of forecast errors.

Measures of Forecast Error
Mean absolute percent error (MAPE) A measurement
that relates the forecast error to the level of
demand and is useful for putting forecast
performance in the proper perspective.
Calculating Forecast Error Example 13.6
The following table shows the actual sales of
upholstered chairs for a furniture manufacturer
and the forecasts made for each of the last eight
months. Calculate CFE, MSE, MAD, and MAPE for
this product.
Example 13.6 Forecast Error Measures
Causal Methods Linear Regression
  • Causal methods are used when historical data are
    available and the relationship between the factor
    to be forecasted and other external or internal
    factors can be identified.
  • Linear regression A causal method in which one
    variable (the dependent variable) is related to
    one or more independent variables by a linear
  • Dependent variable The variable that one wants
    to forecast.
  • Independent variables Variables that are assumed
    to affect the dependent variable and thereby
    cause the results observed in the past.

Causal Methods Linear Regression
Linear Regression Example 13.1
The following are sales and advertising data for
the past 5 months for brass door hinges. The
marketing manager says that next month the
company will spend 1,750 on advertising for the
product. Use linear regression to develop an
equation and a forecast for this product.
Example 13.1Causal Methods Linear Regression
Sales Advertising Month (000 units) (000
) 1 264 2.5 2 116 1.3 3 165 1.4 4 101 1.
0 5 209 2.0
Regression equation for forecast Y a bx,
Example 13.1
Example 13.1Causal Methods Linear Regression
Sales, Y Advertising, X Month (000 units) (000
) XY X 2 Y 2 1 264 2.5 660.0 6.25 69,696 2 116
1.3 150.8 1.69 13,456 3 165 1.4 231.0 1.96 27,22
5 4 101 1.0 101.0 1.00 10,201 5 209 2.0 418.0 4.
00 43,681
Example 13.1
Example 13.1Causal Methods Linear Regression
Sales, Y Advertising, X Month (000 units) (000
) XY X 2 Y 2 1 264 2.5 660.0 6.25 69,696 2 116
1.3 150.8 1.69 13,456 3 165 1.4 231.0 1.96 27,22
5 4 101 1.0 101.0 1.00 10,201 5 209 2.0 418.0 4.
00 43,681 Total 855 8.2 1560.8 14.90 164,259 n
5 Y 171 X 1.64
Example 13.1
Example 13.1Causal Methods Linear Regression
Example 13.1
Example 13.1Causal Methods Linear Regression
Example 13.1
Example 13.1Causal Methods Linear Regression
Example 13.1
Example 13.1Causal Methods Linear Regression
Example 13.1
Example 13.1Causal Methods Linear Regression
Example 13.1
Example 13.1Causal Methods Linear Regression
Example 13.1
Example 13.1Causal Methods Linear Regression
Figure 13.3
Example 13.1Causal Methods Linear Regression
Figure 13.3
Example 13.1Causal Methods Linear Regression
Figure 13.3
Example 13.1Causal Methods Linear Regression
Example 13.1
Example 13.1Causal Methods Linear Regression
Example 13.1
Example 13.1Causal Methods Linear Regression
Example 13.1
Example 13.1Causal Methods Linear Regression
Example 13.1
Example 13.1Causal Methods Linear Regression
Example 13.1
Example 13.1Causal Methods Linear Regression
Example 13.1
Components of a Time Series
  • Time Series The repeated observations of demand
    for a service or product in their order of
  • There are four basic patterns of most time
  • Trend. The systematic increase or decrease in the
    mean of the series over time.
  • Seasonal. A repeatable pattern of increases or
    decreases in demand, depending on the time of
    day, week, month, or season.
  • Cyclical. The less predictable gradual increases
    or decreases over longer periods of time (years
    or decades).
  • Random. The unforecastable variation in demand.

Demand Patterns
Time Series Methods
  • Naive forecast A time-series method whereby the
    forecast for the next period equals the demand
    for the current period, or Forecast Dt
  • Simple moving average method A time-series
    method used to estimate the average of a demand
    time series by averaging the demand for the n
    most recent time periods.
  • It removes the effects of random fluctuation and
    is most useful when demand has no pronounced
    trend or seasonal influences.

Moving Average Method Example 13.2
  • a. Compute a three-week moving average forecast
  • the arrival of medical clinic patients in
    week 4.
  • The numbers of arrivals for the past 3 weeks

Patient Week Arrivals 1 400 2 380 3 411
b. If the actual number of patient arrivals in
week 4 is 415, what is the forecast error
for week 4? c. What is the forecast for week 5?
Example 13.2Solution
The moving average method may involve the use of
as many periods of past demand as desired. The
stability of the demand series generally
determines how many periods to include.
Example 13.2 Solution continued
Forecast error for week 4 is 18. It is the
difference between the actual arrivals (415) for
week 4 and the average of 397 that was used as a
forecast for week 4. (415 397 18)
Comparison of 3- and 6-Week MA Forecasts
Application 13.1
  • We will use the following customer-arrival data
    in this moving average application

Application 13.1a Moving Average Method
780 customer arrivals
802 customer arrivals
Weighted Moving Averages
  • Weighted moving average method A time-series
    method in which each historical demand in the
    average can have its own weight the sum of the
    weights equals 1.0.

Ft1 W1Dt W2Dt-1 WnDt-n1
Application 13.1b Weighted Moving Average
786 customer arrivals
802 customer arrivals
Exponential Smoothing
  • Exponential smoothing method A sophisticated
    weighted moving average method that calculates
    the average of a time series by giving recent
    demands more weight than earlier demands.
  • Ft1 ?(Demand this period) (1 ?)(Forecast
    calculated last period)
  • ? Dt (1?)Ft
  • Or an equivalent equation Ft1 Ft ??(Dt
    Ft )
  • Where alpha (???is a smoothing parameter with a
    value between 0 and 1.0

Exponential smoothing is the most frequently used
formal forecasting method because of its
simplicity and the small amount of data needed to
support it.
Exponential SmoothingExample 13.3
  • Reconsider the medical clinic patient
    arrival data. It is now the end of week 3.
    a. Using ? 0.10, calculate the
    exponential smoothing forecast for
    week 4. Ft1 ? Dt (1-?)Ft
  • F4 0.10(411) 0.90(390) 392.1
  • b. What is the forecast error for week 4 if the
    actual demand turned out to be 415?
  • E4 415 - 392 23
  • c. What is the forecast for week 5?
  • F5 0.10(415) 0.90(392.1) 394.4

Application 13.1c Exponential Smoothing
784 customer arrivals
789 customer arrivals
Trend-Adjusted Exponential Smoothing
  • A trend in a time series is a systematic increase
    or decrease in the average of the series over
  • Where a significant trend is present, exponential
    smoothing approaches must be modified otherwise,
    the forecasts tend to be below or above the
    actual demand.
  • Trend-adjusted exponential smoothing method The
    method for incorporating a trend in an
    exponentially smoothed forecast.
  • With this approach, the estimates for both the
    average and the trend are smoothed, requiring two
    smoothing constants. For each period, we
    calculate the average and the trend.

Trend-Adjusted Exponential Smoothing Formula
  • Ft1 At Tt
  • where At ??Dt (1 ?)(At-1 Tt-1)
  • Tt ??(At At-1) (1 ?)Tt-1
  • At exponentially smoothed average of the series
    in period t
  • Tt exponentially smoothed average of the trend
    in period t
  • ? smoothing parameter for the average
  • ? smoothing parameter for the trend
  • Dt demand for period t
  • Ft1 forecast for period t 1

Trend-Adjusted Exponential Smoothing
Example 13.4 Medanalysis ran an average of 28
blood tests per week during the past four weeks.
The trend over that period was 3 additional
patients per week. This weeks demand was for 27
blood tests. We use ? 0.20 and ? 0.20 to
calculate the forecast for next week.
  • A0 28 patients and Tt 3 patients
  • At ??Dt (1 ?)(At-1 Tt-1)
  • A1 0.20(27) 0.80(28 3) 30.2
  • Tt ??(At At-1) (1 ?)Tt-1
  • T1 0.20(30.2 2.8) 0.80(3) 2.8
  • Ft1 At Tt
  • F2 30.2 2.8 33 blood tests

Example 13.4 Medanalysis Trend-Adjusted
Exponential Smoothing
Forecast for Medanalysis Using the
Trend-Adjusted Exponential Smoothing Model
Application 13.2
  • The forecaster for Canine Gourmet dog breath
    fresheners estimated (in March) the sales average
    to be 300,000 cases sold per month and the trend
    to be 8,000 per month.
  • The actual sales for April were 330,000 cases.
  • What is the forecast for May,
  • assuming ? 0.20 and ? 0.10?

Application 13.2 Solution
To make forecasts for periods beyond the next
period, multiply the trend estimate by the number
of additional periods, and add the result to the
current average
Seasonal Patterns
  • Seasonal patterns are regularly repeated upward
    or downward movements in demand measured in
    periods of less than one year.
  • An easy way to account for seasonal effects is to
    use one of the techniques already described but
    to limit the data in the time series to those
    time periods in the same season.
  • If the weighted moving average method is used,
    high weights are placed on prior periods
    belonging to the same season.
  • Multiplicative seasonal method is a method
    whereby seasonal factors are multiplied by an
    estimate of average demand to arrive at a
    seasonal forecast.
  • Additive seasonal method is a method whereby
    seasonal forecasts are generated by adding a
    constant to the estimate of the average demand
    per season.

Multiplicative Seasonal Method
  • Step 1 For each year, calculate the average
    demand for each season by dividing annual demand
    by the number of seasons per year.
  • Step 2 For each year, divide the actual demand
    for each season by the average demand per season,
    resulting in a seasonal index for each season of
    the year, indicating the level of demand relative
    to the average demand.
  • Step 3 Calculate the average seasonal index for
    each season using the results from Step 2. Add
    the seasonal indices for each season and divide
    by the number of years of data.
  • Step 4 Calculate each seasons forecast for next

Using the Multiplicative Seasonal Method
Example 13.5 Stanley Steemer, a carpet cleaning
company needs a quarterly forecast of the number
of customers expected next year. The business is
seasonal, with a peak in the third quarter and a
trough in the first quarter. Forecast customer
demand for each quarter of year 5, based on an
estimate of total year 5 demand of 2,600
Demand has been increasing by an average of 400
customers each year. The forecast demand is found
by extending that trend, and projecting an annual
demand in year 5 of 2,200 400 2,600 customers.
Example 13.5 OM Explorer Solution
Application 13.3 Multiplicative Seasonal Method
1320/4 quarters 330
Comparison of Seasonal Patterns
Tracking Signal
Tracking signal A measure that indicates whether
a method of forecasting is accurately predicting
actual changes in demand.
Forecast Error Ranges
Forecasts stated as a single value can be less
useful because they do not indicate the range of
likely errors. A better approach can be to
provide the manager with a forecasted value and
an error range.
Computer Support
Computer support, such as OM Explorer, makes
error calculations easy when evaluating how well
forecasting models fit with past data.
Results SheetMoving Average
Forecast for 7/17/06
Results SheetWeighted Moving Average
Forecast for 7/17/06
Results SheetExponential Smoothing
Forecast for 7/17/06
Results SheetTrend-Adjusted Exponential
Forecast for 7/17/06 Forecast for
7/24/06 Forecast for 7/31/06 Forecast for
8/7/06 Forecast for 8/14/06 Forecast for 8/21/06

Criteria for Selecting Time-Series Methods
  • Forecast error measures provide important
    information for choosing the best forecasting
    method for a service or product.
  • They also guide managers in selecting the best
    values for the parameters needed for the method
  • n for the moving average method, the weights for
    the weighted moving average method, and ? for
    exponential smoothing.
  • The 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

Using Multiple Techniques
  • Research during the last two decades suggests
    that combining forecasts from multiple sources
    often produces more accurate forecasts.
  • Combination forecasts Forecasts that are
    produced by averaging independent forecasts based
    on different methods or different data or both.
  • Focus forecasting A method of forecasting that
    selects the best forecast from a group of
    forecasts generated by individual techniques.
  • The forecasts are compared to actual demand, and
    the method that produces the forecast with the
    least error is used to make the forecast for the
    next period. The method used for each item may
    change from period to period.

Forecasting as a Process
The forecast process itself, typically done on a
monthly basis, consists of structured steps. They
often are facilitated by someone who might be
called a demand manager, forecast analyst, or
demand/supply planner.
Denver Air-Quality Discussion Question 1