Demand Forecasting by probsols

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									     Chapter

Demand Forecasting




                     1
                      Overview

   Introduction
   Qualitative Forecasting Methods
   Quantitative Forecasting Models
   How to Have a Successful Forecasting System
   Computer Software for Forecasting
   Forecasting in Small Businesses and Start-Up
    Ventures
   Wrap-Up: What World-Class Producers Do


                                                   2
               Demand Management

   Independent demand items are the only
    items demand for which needs to be
    forecast
   These items include:
       Finished goods and
       Spare parts



                                            3
              Demand Management


                                              Independent Demand
                                               (finished goods and spare parts)


                     A                            Dependent Demand
                                                            (components)



       B(4)                     C(2)



D(2)          E(1)       D(3)          F(2)




                                                                                  4
       Demand Management

The importance of forecasting in OM




                                      5
                       Introduction

   Demand estimates for products and services are the
    starting point for all the other planning in operations
    management.
   Management teams develop sales forecasts based in
    part on demand estimates.
   The sales forecasts become inputs to both business
    strategy and production resource forecasts.




                                                              6
   Forecasting is an Integral Part
        of Business Planning

 Inputs:       Forecast            Demand
 Market,       Method(s)           Estimates
Economic,
  Other

              Sales             Management
             Forecast             Team



 Business               Production Resource
 Strategy                    Forecasts

                                               7
                Some Reasons Why
           Forecasting is Essential in OM
   New Facility Planning – It can take 5 years to design
    and build a new factory or design and implement a
    new production process.
   Production Planning – Demand for products vary
    from month to month and it can take several months
    to change the capacities of production processes.
   Workforce Scheduling – Demand for services (and
    the necessary staffing) can vary from hour to hour
    and employees weekly work schedules must be
    developed in advance.

                                                        8
 Examples of Production Resource Forecasts
Forecast                                                           Units of
              Time Span       Item Being Forecast
Horizon                                                            Measure
                           Product lines
                           Factory capacities

                           Planning for new products
Long-Range      Years      Capital expenditures
                                                                Dollars, tons, etc.
                           Facility location or expansion

                           R&D


                           Product groups
 Medium-                   Department capacities
                Months     Sales planning
                                                                Dollars, tons, etc.
  Range
                           Production planning and budgeting


                           Specific product quantities
                           Machine capacities

                           Planning

                           Purchasing                          Physical units of
Short-Range     Weeks      Scheduling                             products
                           Workforce levels

                           Production levels

                           Job assignments                                           9
            Forecasting Methods

   Qualitative Approaches
   Quantitative Approaches




                                  10
               Qualitative Approaches

   Usually based on judgments about causal factors that
    underlie the demand of particular products or services
   Do not require a demand history for the product or
    service, therefore are useful for new products/services
   Approaches vary in sophistication from scientifically
    conducted surveys to intuitive hunches about future
    events
   The approach/method that is appropriate depends on a
    product’s life cycle stage


                                                         11
                 Qualitative Methods

   Educated guess                 intuitive hunches
   Executive committee consensus
   Delphi method
   Survey of sales force
   Survey of customers
   Historical analogy
   Market research       scientifically conducted surveys



                                                        12
            Qualitative Forecasting Applications
                                      Small and Large Firms



                   Technique                  Low Sales                 High Sales
                                             (less than $100M)          (more than $500M)

               Manager’s Opinion                  40.7%                      39.6%

                    Executive’s
                                                  40.7%                      41.6%
                     Opinion
                    Sales Force
                                                  29.6%                      35.4%
                    Composite

                Number of Firms                      27                         48


Source: Nada Sanders and Karl Mandrodt (1994) “Practitioners Continue to Rely on Judgmental Forecasting
Methods Instead of Quantitative Methods,” Interfaces, vol. 24, no. 2, pp. 92-100.
Note: More than one response was permitted.

                                                                                                          13
      Quantitative Forecasting Approaches

   Based on the assumption that the “forces” that
    generated the past demand will generate the future
    demand, i.e., history will tend to repeat itself
   Analysis of the past demand pattern provides a good
    basis for forecasting future demand
   Majority of quantitative approaches fall in the
    category of time series analysis




                                                          14
          Quantitative Forecasting Applications
                                       Small and Large Firms


                   Technique                  Low Sales                 High Sales
                                             (less than $100M)          (more than $500M)
                   Moving Average                  29.6%                       29.2
               Simple Linear Regression            14.8%                       14.6

                        Naive                      18.5%                       14.6
                  Single Exponential
                                                   14.8%                       20.8
                      Smoothing
                 Multiple Regression               22.2%                       27.1
                      Simulation                    3.7%                       10.4
               Classical Decomposition              3.7%                        8.3
                     Box-Jenkins                    3.7%                        6.3
                   Number of Firms                   27                         48


Source: Nada Sanders and Karl Mandrodt (1994) “Practitioners Continue to Rely on Judgmental Forecasting
Methods Instead of Quantitative Methods,” Interfaces, vol. 24, no. 2, pp. 92-100.
Note: More than one response was permitted.
                                                                                                          15
                 Time Series Analysis

   A time series is a set of numbers where the order or
    sequence of the numbers is important, e.g., historical
    demand
   Analysis of the time series identifies patterns
   Once the patterns are identified, they can be used to
    develop a forecast




                                                             16
             Components of Time Series

   Trends are noted by an upward or downward sloping
    line
   Seasonality is a data pattern that repeats itself over
    the period of one year or less
   Cycle is a data pattern that repeats itself... may take
    years
   Irregular variations are jumps in the level of the series
    due to extraordinary events
   Random fluctuation from random variation or
    unexplained causes
                                                           17
            Seasonal Patterns

Length of Time                  Number of
Before Pattern   Length of       Seasons
 Is Repeated      Season        in Pattern
    Year          Quarter           4
    Year          Month            12
    Year           Week            52
    Month          Day            28-31
    Week           Day              7

                                             18
      Quantitative Forecasting Approaches

   Linear Regression
   Simple Moving Average
   Weighted Moving Average
   Exponential Smoothing (exponentially weighted
    moving average)
   Exponential Smoothing with Trend (double
    exponential smoothing)




                                                    19
                Long-Range Forecasts

   Time spans usually greater than one year
   Necessary to support strategic decisions about
    planning products, processes, and facilities




                                                     20
              Simple Linear Regression

   Linear regression analysis establishes a relationship
    between a dependent variable and one or more
    independent variables.
   In simple linear regression analysis there is only one
    independent variable.
   If the data is a time series, the independent variable is
    the time period.
   The dependent variable is whatever we wish to
    forecast.


                                                            21
              Simple Linear Regression

   Regression Equation
    This model is of the form:
                       Y = a + bX
                Y = dependent variable
                X = independent variable
                a = y-axis intercept
                b = slope of regression line


                                               22
             Simple Linear Regression

   Constants a and b
    The constants a and b are computed using the
    following equations:

                 a=
                       x2  y- x xy
                        n  x2 -(  x)2

                        n xy- x y
                   b=
                        n  x2 -(  x)2


                                                   23
              Simple Linear Regression

   Once the a and b values are computed, a future value
    of X can be entered into the regression equation and a
    corresponding value of Y (the forecast) can be
    calculated.




                                                         24
           Example: College Enrollment

   Simple Linear Regression
    At a small regional college enrollments have grown
    steadily over the past six years, as evidenced below.
    Use time series regression to forecast the student
    enrollments for the next three years.
               Students                     Students
    Year    Enrolled (1000s)    Year    Enrolled (1000s)
     1             2.5           4             3.2
     2             2.8           5             3.3
     3             2.9           6             3.4
                                                            25
          Example: College Enrollment

   Simple Linear Regression
              x     y      x2      xy
              1    2.5     1      2.5
              2    2.8     4      5.6
              3    2.9     9      8.7
              4    3.2     16     12.8
              5    3.3     25     16.5
              6    3.4     36     20.4
          Sx=21 Sy=18.1 Sx2=91   Sxy=66.5


                                            26
          Example: College Enrollment

   Simple Linear Regression

                91(18.1)  21(66.5)
             a                      2.387
                   6(91)  (21)2



                 6(66.5)  21(18.1)
              b                     0.180
                        105

                 Y = 2.387 + 0.180X



                                              27
          Example: College Enrollment

   Simple Linear Regression
      Y7 = 2.387 + 0.180(7) = 3.65 or 3,650 students
      Y8 = 2.387 + 0.180(8) = 3.83 or 3,830 students
      Y9 = 2.387 + 0.180(9) = 4.01 or 4,010 students

    Note: Enrollment is expected to increase by 180
          students per year.



                                                       28
              Simple Linear Regression

   Simple linear regression can also be used when the
    independent variable X represents a variable other
    than time.
   In this case, linear regression is representative of a
    class of forecasting models called causal forecasting
    models.




                                                             29
         Example: Railroad Products Co.

   Simple Linear Regression – Causal Model
         The manager of RPC wants to project the firm’s
    sales for the next 3 years. He knows that RPC’s long-
    range sales are tied very closely to national freight car
    loadings. On the next slide are 7 years of relevant
    historical data.
         Develop a simple linear regression model
    between RPC sales and national freight car loadings.
    Forecast RPC sales for the next 3 years, given that the
    rail industry estimates car loadings of 250, 270, and
    300 million.
                                                           30
         Example: Railroad Products Co.

   Simple Linear Regression – Causal Model
                   RPC Sales     Car Loadings
         Year      ($millions)    (millions)
          1           9.5            120
          2           11.0           135
          3           12.0           130
          4           12.5           150
          5           14.0           170
          6           16.0           190
          7           18.0           220

                                                31
         Example: Railroad Products Co.

   Simple Linear Regression – Causal Model
             x      y       x2        xy
            120    9.5    14,400    1,140
            135    11.0   18,225    1,485
            130    12.0   16,900    1,560
            150    12.5   22,500    1,875
            170    14.0   28,900    2,380
            190    16.0   36,100    3,040
            220    18.0   48,400    3,960
           1,115   93.0   185,425   15,440
                                              32
         Example: Railroad Products Co.

   Simple Linear Regression – Causal Model

            185, 425(93)  1,115(15, 440)
         a                                0.528
               7(185, 425)  (1,115) 2


              7(15, 440)  1,115(93)
           b                          0.0801
              7(185, 425)  (1,115) 2



                  Y = 0.528 + 0.0801X



                                                    33
         Example: Railroad Products Co.

   Simple Linear Regression – Causal Model
       Y8 = 0.528 + 0.0801(250) = $20.55 million
       Y9 = 0.528 + 0.0801(270) = $22.16 million
       Y10 = 0.528 + 0.0801(300) = $24.56 million

    Note: RPC sales are expected to increase by
    $80,100 for each additional million national freight
    car loadings.



                                                           34
            Multiple Regression Analysis

   Multiple regression analysis is used when there are
    two or more independent variables.
   An example of a multiple regression equation is:
          Y = 50.0 + 0.05X1 + 0.10X2 – 0.03X3
    where: Y = firm’s annual sales ($millions)
           X1 = industry sales ($millions)
           X2 = regional per capita income ($thousands)
           X3 = regional per capita debt ($thousands)

                                                          35
            Coefficient of Correlation (r)

   The coefficient of correlation, r, explains the relative
    importance of the relationship between x and y.
   The sign of r shows the direction of the relationship.
   The absolute value of r shows the strength of the
    relationship.
   The sign of r is always the same as the sign of b.
   r can take on any value between –1 and +1.




                                                           36
            Coefficient of Correlation (r)

   Meanings of several values of r:
      -1 a perfect negative relationship (as x goes up, y
         goes down by one unit, and vice versa)
     +1 a perfect positive relationship (as x goes up, y
         goes up by one unit, and vice versa)
       0 no relationship exists between x and y
    +0.3 a weak positive relationship
    -0.8 a strong negative relationship


                                                            37
           Coefficient of Correlation (r)

   r is computed by:

                        n xy   x  y
          r
               n x 2  ( x )2  n y 2  ( y )2 
                                                  




                                                         38
          Coefficient of Determination (r2)

   The coefficient of determination, r2, is the square of
    the coefficient of correlation.
   The modification of r to r2 allows us to shift from
    subjective measures of relationship to a more specific
    measure.
   r2 is determined by the ratio of explained variation to
    total variation:

                       r2 
                               (Y  y )2
                               ( y  y )2


                                                          39
         Example: Railroad Products Co.

   Coefficient of Correlation
          x      y       x2       xy       y2
         120   9.5     14,400    1,140   90.25
         135   11.0    18,225    1,485   121.00
         130   12.0    16,900    1,560   144.00
         150   12.5    22,500    1,875   156.25
         170   14.0    28,900    2,380   196.00
         190   16.0    36,100    3,040   256.00
         220   18.0    48,400    3,960   324.00
        1,115 93.0 185,425 15,440 1,287.50
                                                  40
         Example: Railroad Products Co.

   Coefficient of Correlation
                    7(15, 440)  1,115(93)
    r
         7(185, 425)  (1,115)2  7(1,287.5)  (93)2 
                                                    
                        r = .9829




                                                           41
         Example: Railroad Products Co.

   Coefficient of Determination
                   r2 = (.9829)2 = .966
    96.6% of the variation in RPC sales is explained by
    national freight car loadings.




                                                          42
                  Ranging Forecasts

   Forecasts for future periods are only estimates and are
    subject to error.
   One way to deal with uncertainty is to develop best-
    estimate forecasts and the ranges within which the
    actual data are likely to fall.
   The ranges of a forecast are defined by the upper and
    lower limits of a confidence interval.




                                                         43
                  Ranging Forecasts

   The ranges or limits of a forecast are estimated by:
                 Upper limit = Y + t(syx)
                 Lower limit = Y - t(syx)
    where:
      Y = best-estimate forecast
      t = number of standard deviations from the mean
           of the distribution to provide a given
           probability of exceeding the limits through
           chance
     syx = standard error of the forecast
                                                           44
                   Ranging Forecasts

   The standard error (deviation) of the forecast is
    computed as:


              s yx =
                        y 2 - a y - b xy
                                n-2




                                                        45
         Example: Railroad Products Co.

   Ranging Forecasts
        Recall that linear regression analysis provided a
    forecast of annual sales for RPC in year 8 equal to
    $20.55 million.
        Set the limits (ranges) of the forecast so that there
    is only a 5 percent probability of exceeding the limits
    by chance.




                                                            46
          Example: Railroad Products Co.

   Ranging Forecasts
     Step 1: Compute the standard error of the
              forecasts, syx.
                1287.5  .528(93)  .0801(15, 440)
         syx                                       .5748
                              72
       Step 2: Determine the appropriate value for t.
               n = 7, so degrees of freedom = n – 2 = 5.
               Area in upper tail = .05/2 = .025
               Appendix B, Table 2 shows t = 2.571.
                                                           47
          Example: Railroad Products Co.

   Ranging Forecasts
     Step 3: Compute upper and lower limits.
                 Upper limit = 20.55 + 2.571(.5748)
                             = 20.55 + 1.478
                             = 22.028
                Lower limit = 20.55 - 2.571(.5748)
                             = 20.55 - 1.478
                             = 19.072
        We are 95% confident the actual sales for year 8
        will be between $19.072 and $22.028 million.
                                                           48
Seasonalized Time Series Regression Analysis

   Select a representative historical data set.
   Develop a seasonal index for each season.
   Use the seasonal indexes to deseasonalize the data.
   Perform linear regression analysis on the
    deseasonalized data.
   Use the regression equation to compute the forecasts.
   Use the seasonal indexes to reapply the seasonal
    patterns to the forecasts.


                                                        49
       Example: Computer Products Corp.

   Seasonalized Times Series Regression Analysis
        An analyst at CPC wants to develop next year’s
    quarterly forecasts of sales revenue for CPC’s line of
    Epsilon Computers. She believes that the most recent
    8 quarters of sales (shown on the next slide) are
    representative of next year’s sales.




                                                        50
        Example: Computer Products Corp.

   Seasonalized Times Series Regression Analysis
     Representative Historical Data Set
        Year Qtr. ($mil.)    Year Qtr. ($mil.)
         1     1    7.4       2     1    8.3
         1     2    6.5       2     2    7.4
         1     3    4.9       2     3    5.4
         1     4    16.1      2     4    18.0



                                                    51
        Example: Computer Products Corp.

   Seasonalized Times Series Regression Analysis
     Compute the Seasonal Indexes
                      Quarterly Sales
         Year     Q1    Q2 Q3         Q4 Total
           1      7.4   6.5 4.9 16.1 34.9
           2      8.3   7.4 5.4 18.0 39.1
        Totals   15.7 13.9 10.3 34.1 74.0
     Qtr. Avg.   7.85 6.95 5.15 17.05 9.25
     Seas.Ind.   .849 .751 .557 1.843 4.000
                                                    52
        Example: Computer Products Corp.

   Seasonalized Times Series Regression Analysis
     Deseasonalize the Data
                          Quarterly Sales
          Year      Q1      Q2       Q3      Q4
           1       8.72    8.66     8.80    8.74
           2       9.78    9.85     9.69    9.77




                                                    53
        Example: Computer Products Corp.

   Seasonalized Times Series Regression Analysis
     Perform Regression on Deseasonalized Data
          Yr.    Qtr.     x      y     x2      xy
           1      1       1    8.72     1     8.72
           1      2       2    8.66     4    17.32
           1      3       3    8.80     9    26.40
           1      4       4    8.74    16    34.96
           2      1       5    9.78    25    48.90
           2      2       6    9.85    36    59.10
           2      3       7    9.69    49    67.83
           2      4       8    9.77    64    78.16
                Totals   36   74.01   204   341.39
                                                     54
        Example: Computer Products Corp.

   Seasonalized Times Series Regression Analysis
     Perform Regression on Deseasonalized Data
              204(74.01)  36(341.39)
           a                          8.357
                  8(204)  (36) 2


               8(341.39)  36(74.01)
            b                        0.199
                  8(204)  (36)2



                 Y = 8.357 + 0.199X


                                                    55
        Example: Computer Products Corp.

   Seasonalized Times Series Regression Analysis
     Compute the Deseasonalized Forecasts

             Y9    = 8.357 + 0.199(9) = 10.148
             Y10   = 8.357 + 0.199(10) = 10.347
             Y11   = 8.357 + 0.199(11) = 10.546
             Y12   = 8.357 + 0.199(12) = 10.745
    Note: Average sales are expected to increase by
          .199 million (about $200,000) per quarter.

                                                       56
        Example: Computer Products Corp.

   Seasonalized Times Series Regression Analysis
     Seasonalize the Forecasts
                  Seas.     Deseas.     Seas.
         Yr. Qtr. Index     Forecast   Forecast
          3    1    .849    10.148       8.62
          3    2    .751    10.347       7.77
          3    3    .557    10.546       5.87
          3    4    1.843   10.745      19.80


                                                    57
                Short-Range Forecasts

   Time spans ranging from a few days to a few weeks
   Cycles, seasonality, and trend may have little effect
   Random fluctuation is main data component




                                                            58
   Evaluating Forecast-Model Performance

   Short-range forecasting models are evaluated on the
basis of three characteristics:
    Impulse response
    Noise-dampening ability
    Accuracy




                                                     59
    Evaluating Forecast-Model Performance

   Impulse Response and Noise-Dampening Ability
     If forecasts have little period-to-period fluctuation,
      they are said to be noise dampening.
     Forecasts that respond quickly to changes in data
      are said to have a high impulse response.
     A forecast system that responds quickly to data
      changes necessarily picks up a great deal of
      random fluctuation (noise).
     Hence, there is a trade-off between high impulse
      response and high noise dampening.
                                                           60
    Evaluating Forecast-Model Performance

   Accuracy
     Accuracy is the typical criterion for judging the
      performance of a forecasting approach
     Accuracy is how well the forecasted values match
      the actual values




                                                          61
                Monitoring Accuracy

   Accuracy of a forecasting approach needs to be
    monitored to assess the confidence you can have in its
    forecasts and changes in the market may require
    reevaluation of the approach
   Accuracy can be measured in several ways
      Standard error of the forecast (covered earlier)
      Mean absolute deviation (MAD)
      Mean squared error (MSE)



                                                        62
                  Monitoring Accuracy

   Mean Absolute Deviation (MAD)
           Sum of absolute deviation for n periods
     MAD =
                             n
             n

             Actual demand -Forecast demand
                               i                     i
    MAD =   i=1

                               n




                                                         63
               Monitoring Accuracy

   Mean Squared Error (MSE)

                     MSE = (Syx)2
        A small value for Syx means data points are
    tightly grouped around the line and error range is
    small.
        When the forecast errors are normally
    distributed, the values of MAD and syx are related:

                 MSE = 1.25(MAD)

                                                          64
        Short-Range Forecasting Methods

   (Simple) Moving Average
   Weighted Moving Average
   Exponential Smoothing
   Exponential Smoothing with Trend




                                          65
              Simple Moving Average

   An averaging period (AP) is given or selected
   The forecast for the next period is the arithmetic
    average of the AP most recent actual demands
   It is called a “simple” average because each period
    used to compute the average is equally weighted
   . . . more




                                                          66
               Simple Moving Average

   It is called “moving” because as new demand data
    becomes available, the oldest data is not used
   By increasing the AP, the forecast is less responsive
    to fluctuations in demand (low impulse response and
    high noise dampening)
   By decreasing the AP, the forecast is more responsive
    to fluctuations in demand (high impulse response and
    low noise dampening)



                                                       67
             Weighted Moving Average

   This is a variation on the simple moving average
    where the weights used to compute the average are
    not equal.
   This allows more recent demand data to have a
    greater effect on the moving average, therefore the
    forecast.
   . . . more




                                                          68
             Weighted Moving Average

   The weights must add to 1.0 and generally decrease
    in value with the age of the data.
   The distribution of the weights determine the impulse
    response of the forecast.




                                                        69
                 Exponential Smoothing

   The weights used to compute the forecast (moving
    average) are exponentially distributed.
   The forecast is the sum of the old forecast and a
    portion (a) of the forecast error (A t-1 - Ft-1).
                  Ft = Ft-1 + a(A t-1 - Ft-1)
   . . . more




                                                        70
               Exponential Smoothing

   The smoothing constant, a, must be between 0.0 and
    1.0.
   A large a provides a high impulse response forecast.
   A small a provides a low impulse response forecast.




                                                       71
           Example: Central Call Center

   Moving Average
         CCC wishes to forecast the number of incoming
    calls it receives in a day from the customers of one of
    its clients, BMI. CCC schedules the appropriate
    number of telephone operators based on projected call
    volumes.
         CCC believes that the most recent 12 days of call
    volumes (shown on the next slide) are representative
    of the near future call volumes.


                                                         72
          Example: Central Call Center

   Moving Average
    Representative Historical Data

           Day     Calls        Day   Calls
            1      159           7    203
            2      217           8    195
            3      186           9    188
            4      161          10    168
            5      173          11    198
            6      157          12    159

                                              73
           Example: Central Call Center

   Moving Average
        Use the moving average method with an AP = 3
    days to develop a forecast of the call volume in Day
    13.

          F13 = (168 + 198 + 159)/3 = 175.0 calls




                                                           74
           Example: Central Call Center

   Weighted Moving Average
        Use the weighted moving average method with an
    AP = 3 days and weights of .1 (for oldest datum), .3,
    and .6 to develop a forecast of the call volume in Day
    13.
      F13 = .1(168) + .3(198) + .6(159) = 171.6 calls
    Note: The WMA forecast is lower than the MA
    forecast because Day 13’s relatively low call volume
    carries almost twice as much weight in the WMA
    (.60) as it does in the MA (.33).
                                                        75
          Example: Central Call Center

   Exponential Smoothing
        If a smoothing constant value of .25 is used and
    the exponential smoothing forecast for Day 11 was
    180.76 calls, what is the exponential smoothing
    forecast for Day 13?
        F12 = 180.76 + .25(198 – 180.76) = 185.07
        F13 = 185.07 + .25(159 – 185.07) = 178.55




                                                           76
          Example: Central Call Center

   Forecast Accuracy - MAD
        Which forecasting method (the AP = 3 moving
    average or the a = .25 exponential smoothing) is
    preferred, based on the MAD over the most recent 9
    days? (Assume that the exponential smoothing
    forecast for Day 3 is the same as the actual call
    volume.)




                                                         77
   Example: Central Call Center

              AP = 3            a = .25
Day Calls   Forec. |Error|   Forec.   |Error|
 4  161     187.3 26.3       186.0     25.0
 5  173     188.0 15.0       179.8      6.8
 6  157     173.3 16.3       178.1     21.1
 7  203     163.7 39.3       172.8     30.2
 8  195     177.7 17.3       180.4     14.6
 9  188     185.0    3.0     184.0      4.0
10  168     195.3 27.3       185.0     17.0
11  198     183.7 14.3       180.8     17.2
12  159     184.7 25.7       185.1     26.1
    MAD             20.5               18.0
                                                78
        Exponential Smoothing with Trend

   As we move toward medium-range forecasts, trend
    becomes more important.
   Incorporating a trend component into exponentially
    smoothed forecasts is called double exponential
    smoothing.
   The estimate for the average and the estimate for the
    trend are both smoothed.




                                                            79
        Exponential Smoothing with Trend

   Model Form
                     FTt = St-1 + Tt-1
    where:
       FTt = forecast with trend in period t
       St-1 = smoothed forecast (average) in period t-1
       Tt-1 = smoothed trend estimate in period t-1




                                                          80
       Exponential Smoothing with Trend

   Smoothing the Average
                 St = FTt + a (At – FTt)

   Smoothing the Trend
             Tt = Tt-1 + b (FTt – FTt-1 - Tt-1)

    where:   a = smoothing constant for the average
             b = smoothing constant for the trend


                                                      81
               Criteria for Selecting
               a Forecasting Method
   Cost
   Accuracy
   Data available
   Time span
   Nature of products and services
   Impulse response and noise dampening




                                           82
                Criteria for Selecting
                a Forecasting Method
   Cost and Accuracy
     There is a trade-off between cost and accuracy;
      generally, more forecast accuracy can be obtained
      at a cost.
     High-accuracy approaches have disadvantages:
        Use more data
        Data are ordinarily more difficult to obtain
        The models are more costly to design,
         implement, and operate
        Take longer to use
                                                          83
                Criteria for Selecting
                a Forecasting Method
   Cost and Accuracy
     Low/Moderate-Cost Approaches – statistical
      models, historical analogies, executive-committee
      consensus
     High-Cost Approaches – complex econometric
      models, Delphi, and market research




                                                          84
                Criteria for Selecting
                a Forecasting Method
   Data Available
     Is the necessary data available or can it be
      economically obtained?
     If the need is to forecast sales of a new product,
      then a customer survey may not be practical;
      instead, historical analogy or market research may
      have to be used.




                                                       85
                Criteria for Selecting
                a Forecasting Method
   Time Span
     What operations resource is being forecast and for
      what purpose?
     Short-term staffing needs might best be forecast
      with moving average or exponential smoothing
      models.
     Long-term factory capacity needs might best be
      predicted with regression or executive-committee
      consensus methods.


                                                       86
                Criteria for Selecting
                a Forecasting Method
   Nature of Products and Services
     Is the product/service high cost or high volume?
     Where is the product/service in its life cycle?
     Does the product/service have seasonal demand
      fluctuations?




                                                         87
               Criteria for Selecting
               a Forecasting Method
   Impulse Response and Noise Dampening
     An appropriate balance must be achieved between:
        How responsive we want the forecasting model
         to be to changes in the actual demand data
        Our desire to suppress undesirable chance
         variation or noise in the demand data




                                                     88
        Reasons for Ineffective Forecasting

   Not involving a broad cross section of people
   Not recognizing that forecasting is integral to
    business planning
   Not recognizing that forecasts will always be wrong
   Not forecasting the right things
   Not selecting an appropriate forecasting method
   Not tracking the accuracy of the forecasting models




                                                          89
               Monitoring and Controlling
                 a Forecasting Model
   Tracking Signal (TS)
     The TS measures the cumulative forecast error
      over n periods in terms of MAD
                n

               (Actual demand
               i 1
                                   i   - Forecast demandi )
        TS =
                                  MAD
       If the forecasting model is performing well, the TS
        should be around zero
       The TS indicates the direction of the forecasting
        error; if the TS is positive -- increase the forecasts,
        if the TS is negative -- decrease the forecasts.
                                                              90
             Monitoring and Controlling
               a Forecasting Model
   Tracking Signal
     The value of the TS can be used to automatically
      trigger new parameter values of a model, thereby
      correcting model performance.
     If the limits are set too narrow, the parameter
      values will be changed too often.
     If the limits are set too wide, the parameter values
      will not be changed often enough and accuracy
      will suffer.


                                                             91
Tracking Signal: What do you notice?




                                       92
        Computer Software for Forecasting

   Examples of computer software with forecasting
    capabilities
     Forecast Pro
                                      Primarily for
     Autobox
                                       forecasting
     SmartForecasts for Windows
     SAS
     SPSS                                Have
                                       Forecasting
     SAP
                                         modules
     POM Software Library

                                                      93
          Forecasting in Small Businesses
              and Start-Up Ventures
   Forecasting for these businesses can be difficult for
    the following reasons:
      Not enough personnel with the time to forecast
      Personnel lack the necessary skills to develop good
       forecasts
      Such businesses are not data-rich environments
      Forecasting for new products/services is always
       difficult, even for the experienced forecaster



                                                        94
      Sources of Forecasting Data and Help

   Government agencies at the local, regional, state, and
    federal levels
   Industry associations
   Consulting companies




                                                         95
          Some Specific Forecasting Data

   Consumer Confidence Index
   Consumer Price Index (CPI)
   Gross Domestic Product (GDP)
   Housing Starts
   Index of Leading Economic Indicators
   Personal Income and Consumption
   Producer Price Index (PPI)
   Purchasing Manager’s Index
   Retail Sales
                                           96
          Wrap-Up: World-Class Practice

   Predisposed to have effective methods of forecasting
    because they have exceptional long-range business
    planning
   Formal forecasting effort
   Develop methods to monitor the performance of their
    forecasting models
   Do not overlook the short run.... excellent short range
    forecasts as well



                                                          97
End of Chapter 3




                   98

								
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