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Forecasting

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					Forecasting




              August 29, Wednesday
Course
Structure                       Introduction

               Operations Strategy & Competitiveness


                            Quality Management
                         Strategic Decisions (some)
    Design of Products       Process Selection         Capacity and
      and Services              and Design            Facility Decisions



                  Forecasting




                   Tactical & Operational Decisions
Forecasting


   Predict the next number in the pattern:

  a) 3.7,   3.7,   3.7,   3.7,   3.7,    ?

  b) 2.5,   4.5,   6.5,   8.5,   10.5,   ?

  c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, ?
Forecasting


   Predict the next number in the pattern:

  a) 3.7,   3.7,   3.7,   3.7,   3.7, 3.7

  b) 2.5,   4.5,   6.5,   8.5,   10.5, 12.5

  c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, 9.0
Outline

   What is forecasting?
   Types of forecasts
   Time-Series forecasting
     Naïve
     Moving Average
     Exponential Smoothing
     Regression
   Good forecasts
What is Forecasting?

 Process of predicting a future
  event based on historical data
 Educated Guessing
 Underlying basis of
  all business decisions
     Production
     Inventory
     Personnel
     Facilities
  Why do we need to forecast?

In general, forecasts are almost always wrong. So,
Throughout the day we forecast very different
things such as weather, traffic, stock market, state
of our company from different perspectives.

Virtually every business attempt is based on
forecasting. Not all of them are derived from
sophisticated methods. However, “Best" educated
guesses about future are more valuable for
purpose of Planning than no forecasts and hence
no planning.
Importance of Forecasting in OM
Departments throughout the organization depend on
forecasts to formulate and execute their plans.

Finance needs forecasts to project cash flows and
capital requirements.

Human resources need forecasts to anticipate hiring
needs.

Production needs forecasts to plan production
levels, workforce, material requirements,
inventories, etc.
Importance of Forecasting in OM

Demand is not the only variable of interest to
forecasters.

Manufacturers also forecast worker
absenteeism, machine availability, material
costs, transportation and production lead
times, etc.

Besides demand, service providers are also
interested in forecasts of population, of other
demographic variables, of weather, etc.
Types of Forecasts by Time Horizon
                                                       Quantitative
 Short-range forecast                                  methods

    Usually < 3 months
      Job scheduling, worker assignments   Detailed
                                            use of
 Medium-range forecast                     system

    3 months to 2 years
      Sales/production planning

 Long-range forecast
    > 2 years                              Design
                                            of system
      New product planning                             Qualitative
                                                         Methods
Forecasting During the Life Cycle

     Introduction             Growth            Maturity        Decline




         Qualitative models             Quantitative models
     - Executive judgment
                                       - Time series analysis
     - Market research
                                       - Regression analysis
     -Survey of sales force
     -Delphi method
        Sales




                                                     Time
Qualitative Forecasting Methods

                    Qualitative
                    Forecasting



                                        Models
            Sales                      Delphi
Executive                Market
            Force                      Method
Judgement                Research/
            Composite
                         Survey

                           Smoothing
               Qualitative Methods
Briefly, the qualitative methods are:

Executive Judgment: Opinion of a group of high level
experts or managers is pooled

Sales Force Composite: Each regional salesperson
provides his/her sales estimates. Those forecasts are then
reviewed to make sure they are realistic. All regional
forecasts are then pooled at the district and national levels
to obtain an overall forecast.

Market Research/Survey: Solicits input from customers
pertaining to their future purchasing plans. It involves the
use of questionnaires, consumer panels and tests of new
products and services.
                 Qualitative Methods
Delphi Method: As opposed to regular panels where the individuals
involved are in direct communication, this method eliminates the
effects of group potential dominance of the most vocal members. The
group involves individuals from inside as well as outside the
organization.

    Typically, the procedure consists of the following steps:
    Each expert in the group makes his/her own forecasts in form of
    statements
        The coordinator collects all group statements and
        summarizes them
        The coordinator provides this summary and gives another set
        of questions to each
          group member including feedback as to the input of other
        experts.
        The above steps are repeated until a consensus is reached.

.
Quantitative Forecasting Methods

                     Quantitative
                     Forecasting


            Time Series                     Regression
              Models                          Models




              2. Moving   3. Exponential
 1. Naive
                Average     Smoothing
            a) simple      a) level
            b) weighted    b) trend
                           c) seasonality
Quantitative Forecasting Methods

                     Quantitative
                     Forecasting


            Time Series                     Regression
              Models                          Models




              2. Moving   3. Exponential
 1. Naive
                Average     Smoothing
            a) simple      a) level
            b) weighted    b) trend
                           c) seasonality
Time Series Models


  Try to predict the future based on past
   data

    Assume that factors influencing the past will
     continue to influence the future
Time Series Models: Components


      Random                Trend




    Seasonal              Composite
Product Demand over Time
Demand for product or service




                                Year   Year   Year   Year
                                 1      2      3      4
         Product Demand over Time
                                                                                                          Trend component
                                             Seasonal peaks
             Demand for product or service




                                                                                                          Actual
                                                                          Random                          demand line
                                                                          variation
                                                  Year                            Year                 Year       Year
                                                   1                               2                    3          4
            Now let’s look at some time series approaches to forecasting…
Borrowed from Heizer/Render - Principles of Operations Management, 5e, and Operations Management, 7e
Quantitative Forecasting Methods

                  Quantitative
                  Time Series
                    Models

                                          Models

                    2. Moving    3. Exponential
       1. Naive
                      Average      Smoothing
                  a) simple       a) level
                  b) weighted     b) trend
                                  c) seasonality
1. Naive Approach

  Demand in next period is the same as
   demand in most recent period
    May sales = 48 → June forecast = 48


  Usually not good
2a. Simple Moving Average

 Assumes an average is a good estimator of
  future behavior
   Used if little or no trend
   Used for smoothing

                      A t + A t -1 + A t -2 + ... + A t -n 1
              Ft 1 =
                                      n
               Ft+1      = Forecast for the upcoming period, t+1
               n         = Number of periods to be averaged
               At        = Actual occurrence in period t
                                           A t + A t -1 + A t -2 + ... + A t -n 1
                                 Ft 1 =
                                                           n
2a. Simple Moving Average
   You’re manager in Amazon’s electronics
   department. You want to forecast ipod sales for
   months 4-6 using a 3-period moving average.
               Sales
    Month      (000)
     1          4
     2          6
     3          5
     4          ?
     5          ?
     6          ?
                                           A t + A t -1 + A t -2 + ... + A t -n 1
                                 Ft 1 =
                                                           n
2a. Simple Moving Average
   You’re manager in Amazon’s electronics
   department. You want to forecast ipod sales for
   months 4-6 using a 3-period moving average.
               Sales          Moving Average
    Month      (000)               (n=3)
     1          4                   NA
     2          6                   NA
     3          5                   NA
     4          ?               (4+6+5)/3=5
     5          ?
     6          ?
2a. Simple Moving Average

What if ipod sales were actually 3 in month 4

             Sales       Moving Average
    Month    (000)            (n=3)
     1        4                NA
     2        6                NA
     3        5                NA
     4        ?
              3                 5
     5        ?
     6        ?
2a. Simple Moving Average

Forecast for Month 5?

            Sales       Moving Average
    Month   (000)            (n=3)
     1       4                NA
     2       6                NA
     3       5                NA
     4       3                 5
     5       ?            (6+5+3)/3=4.667
     6       ?
2a. Simple Moving Average

Actual Demand for Month 5 = 7

            Sales       Moving Average
    Month   (000)            (n=3)
     1       4                NA
     2       6                NA
     3       5                NA
     4       3                 5
     5       ?
             7                 4.667
     6       ?
2a. Simple Moving Average

Forecast for Month 6?

            Sales       Moving Average
    Month   (000)            (n=3)
     1       4                NA
     2       6                NA
     3       5                NA
     4       3                 5
     5       7                 4.667
     6       ?            (5+3+7)/3=5
2b. Weighted Moving Average
  Gives more emphasis to recent data
   Ft 1 = w1A t + w 2 A t -1 + w 3A t -2 + ... + w n A t -n 1

  Weights
    decrease for older data
    sum to 1.0                    Simple moving
                                   average models
                                  weight all previous
                                   periods equally
                Ft 1 = w1A t + w 2 A t -1 + w 3A t -2 + ... + w n A t -n 1
2b. Weighted Moving Average: 3/6, 2/6, 1/6

       Month    Sales               Weighted
                (000)                Moving
                                     Average
         1      4                      NA
         2      6                      NA
         3      5                      NA
         4      ?                 31/6 = 5.167
         5      ?
         6      ?
                Ft 1 = w1A t + w 2 A t -1 + w 3A t -2 + ... + w n A t -n 1
2b. Weighted Moving Average: 3/6, 2/6, 1/6

       Month    Sales               Weighted
                (000)                Moving
                                     Average
         1      4                      NA
         2      6                      NA
         3      5                      NA
         4      3                 31/6 = 5.167
         5      7                 25/6 = 4.167
         6                        32/6 = 5.333
3a. Exponential Smoothing

 Assumes the most recent observations
  have the highest predictive value
   gives more weight to recent time periods

     Ft+1 = Ft + a(At - Ft)
                                et

       Ft+1 = Forecast value for time t+1      Need initial
       At   = Actual value at time t           forecast Ft
       a    = Smoothing constant                 to start.
3a. Exponential Smoothing – Example 1
    Ft+1 = Ft + a(At - Ft)
     i      Ai

    Week   Demand
       1      820   Given the weekly demand
       2      775   data what are the exponential
       3      680   smoothing forecasts for
       4      655   periods 2-10 using a=0.10?
       5      750
       6      802   Assume F1=D1
       7      798
       8      689
       9      775
      10
3a. Exponential Smoothing – Example 1
    Ft+1 = Ft + a(At - Ft)
     i      Ai        Fi

    Week   Demand   a = 0.1      0.6
       1      820   820.00    820.00
       2      775   820.00    820.00
       3      680 F2815.50 a(A1–F1) =820+.1(820–820)
                     = F1+    793.00
       4      655   801.95    725.20=820
       5      750   787.26    683.08
       6      802   783.53    723.23
       7      798   785.38    770.49
       8      689   786.64    787.00
       9      775   776.88    728.20
      10            776.69    756.28
3a. Exponential Smoothing – Example 1
    Ft+1 = Ft + a(At - Ft)
     i      Ai        Fi

    Week   Demand   a = 0.1      0.6
       1      820   820.00    820.00
       2      775   820.00    820.00
       3      680   815.50    793.00
                  F3 = F2+ a(A2–F2) =820+.1(775–820)
       4      655   801.95    725.20
       5      750   787.26    683.08=815.5
       6      802   783.53    723.23
       7      798   785.38    770.49
       8      689   786.64    787.00
       9      775   776.88    728.20
      10            776.69    756.28
3a. Exponential Smoothing – Example 1
    Ft+1 = Ft + a(At - Ft)
     i      Ai       Fi

    Week   Demand   a = 0.1      0.6
       1      820   820.00    820.00
       2      775   820.00    820.00
       3      680   815.50    793.00
       4      655   801.95    725.20
       5      750   787.26    683.08
                                     This process
       6      802   783.53    723.23
                                      continues
       7      798   785.38    770.49
                                    through week
       8      689   786.64    787.00
                                          10
       9      775   776.88    728.20
      10            776.69    756.28
3a. Exponential Smoothing – Example 1
    Ft+1 = Ft + a(At - Ft)
     i      Ai       Fi

    Week   Demand   a = 0.1   a = 0.6
       1      820   820.00    820.00
       2      775   820.00    820.00
       3      680   815.50    793.00
       4      655   801.95    725.20
       5      750   787.26    683.08    What if the
       6      802   783.53    723.23    a constant
       7      798   785.38    770.49    equals 0.6
       8      689   786.64    787.00
       9      775   776.88    728.20
      10            776.69    756.28
3a. Exponential Smoothing – Example 2
     Ft+1 = Ft + a(At - Ft)
     i      Ai        Fi

      Month Demand   a = 0.3   a = 0.6
 January       120   100.00    100.00
 February       90   106.00    112.00
 March         101   101.20     98.80
 April          91   101.14    100.12
 May           115    98.10     94.65    What if the
 June           83   103.17    106.86    a constant
 July                 97.12     92.54    equals 0.6
 August
 September
 3a. Exponential Smoothing – Example 3

Company A, a personal computer producer
purchases generic parts and assembles them to
final product. Even though most of the orders
require customization, they have many common
components. Thus, managers of Company A need
a good forecast of demand so that they can
purchase computer parts accordingly to minimize
inventory cost while meeting acceptable service
level. Demand data for its computers for the past 5
months is given in the following table.
3a. Exponential Smoothing – Example 3
      Ft+1 = Ft + a(At - Ft)
      i        Ai            Fi

      Month   Demand        a = 0.3        a = 0.5
 January          80         84.00           84.00
 February         84         82.80           82.00
 March            82         83.16           83.00
 April            85         82.81           82.50
 May              89         83.47           83.75   What if the
 June                        85.13           86.38   a constant
 July                  ??             ??             equals 0.5
3a. Exponential Smoothing

 How to choose α
   depends on the emphasis you want to place
    on the most recent data

 Increasing α makes forecast more
  sensitive to recent data
Forecast Effects of
Smoothing Constant a
      Ft+1 = Ft + a (At - Ft)
 or   Ft+1 = a At + a(1- a) At - 1 + a(1- a)2At - 2 + ...
                 w1            w2                 w3

                                     Weights
        a=            Prior Period   2 periods ago 3 periods ago
                           a           a(1 - a)        a(1 - a)2

       a= 0.10
                          10%            9%             8.1%
       a= 0.90            90%            9%             0.9%
To Use a Forecasting Method

   Collect historical data
   Select a model
     Moving average methods
        Select n (number of periods)
        For weighted moving average: select weights
     Exponential smoothing
        Select a

   Selections should produce a good forecast
         …but what is a good forecast?
A Good Forecast

 Has a small error
    Error = Demand - Forecast
Measures of Forecast Error
                                                                 et
                                                         n

a. MAD = Mean Absolute Deviation                       A
                                                       t=1
                                                                 t   - Ft
                                         MAD =
                                                             n

                                                   n

b. MSE = Mean Squared Error                        A t - Ft 2
                                                  t =1
                                         MSE =
                                                             n

c. RMSE = Root Mean Squared Error RMSE = MSE


  Ideal values =0 (i.e., no forecasting error)
                                    n


MAD Example                        A
                                    t=1
                                           t   - Ft   = 40 =10
                           MAD =                        4
                                          n

 What is the MAD value given the
 forecast values in the table below?
               At         Ft
  Month       Sales Forecast       |At – Ft|
          1       220     n/a
          2       250    255              5
          3       210    205              5
          4       300    320              20
          5       325    315              10
                                        = 40
                                n

                                A t - Ft 2
                               t =1             = 550 =137.5
MSE/RMSE Example      MSE =
                                       n          4

 What is the MSE value?               RMSE = √137.5
                                                =11.73
               At         Ft
  Month       Sales Forecast           |At – Ft| (At – Ft)2
          1       220     n/a
          2       250    255                5             25
          3       210    205                5             25
          4       300    320                20           400
          5       325    315                10           100
                                                      = 550
                     Measures of Error
                                                             1. Mean Absolute Deviation
                                                             (MAD)
                                                                           n
 t      At      Ft        et        |et|          et2                      e
                                                                   MAD    1
                                                                                   t
                                                                                        84   = 14
Jan     120    100        20         20           400                          n
                                                                                         6
                          -16        16
Feb     90     106                                256        2a. Mean Squared Error
                          -1         1            1          (MSE)
Mar     101    102                                                     n

                         -10         10           100                   et  2
April   91     101                                            MSE     1               1,446
                         17          17           289                      n                 = 241
May     115     98                                                                       6
                         -20         20           400
                                                             2b. Root Mean Squared Error
June    83     103                                           (RMSE)
                       -10          84        1,446
        An accurate forecasting system will have small MAD,        RMSE  MSE
        MSE and RMSE; ideally equal to zero. A large error may
        indicate that either the forecasting method used or the      = SQRT(241)
        parameters such as α used in the method are wrong.
        Note: In the above, n is the number of periods, which is
                                                                     =15.52
Forecast Bias


    How can we tell if a forecast has a positive or
     negative bias?

    TS = Tracking Signal
      Good tracking signal has low values


             RSFE       (actual   t    forecastt )
        TS =      = t
             MAD Mean absolute deviation
                           MAD
                                                       30
Quantitative Forecasting Methods

                     Quantitative
                     Forecasting


            Time Series                     Regression
              Models                          Models




              2. Moving   3. Exponential
 1. Naive
                Average     Smoothing
            a) simple      a) level
            b) weighted    b) trend
                           c) seasonality
Exponential Smoothing (continued)

 We looked at using exponential
  smoothing to forecast demand with
  only random variations
          Ft+1 = Ft + a (At - Ft)
          Ft+1 = Ft + a At – a Ft
          Ft+1 = a At + (1-a) Ft
Exponential Smoothing (continued)

 We looked at using exponential
  smoothing to forecast demand with
  only random variations
 What if demand varies due to
  randomness and trend?

 What if we have trend and seasonality
  in the data?
 Regression Analysis as a Method for
            Forecasting
Regression analysis takes advantage
  of the relationship between two
  variables. Demand is then
  forecasted based on the
  knowledge of this relationship and
  for the given value of the related
  variable.

Ex: Sale of Tires (Y), Sale of Autos (X)
   are obviously related

If we analyze the past data of these
    two variables and establish a
    relationship between them, we may
    use that relationship to forecast the
    sales of tires given the sales of
    automobiles.

The simplest form of the relationship
   is, of course, linear, hence it is       Sales of Autos (100,000)
   referred to as a regression line.
     Formulas

      y=a+bx

      where,

          xy  n x y
x


y
      b
          x  nx
                2   2




x
y
       a  y  bx
Regression – Example
      y = a+ b X          b
                              xy  n x y    a  y  bx
                              x  nx
                                  2      2




      MonthAdvertising   Sales          X 2 XY
 January             3       1         9.00     3.00
 February            4       2        16.00     8.00
 March               2       1         4.00     2.00
 April               5       3        25.00    15.00
 May                 4       2        16.00     8.00
 June                2       1         4.00     2.00
 July

 TOTAL             20      10           74        38
      General Guiding Principles for
               Forecasting

1. Forecasts are more accurate for larger groups of items.
2. Forecasts are more accurate for shorter periods of time.
3. Every forecast should include an estimate of error.
4. Before applying any forecasting method, the total system
   should be understood.
5. Before applying any forecasting method, the method
   should be tested and evaluated.
6. Be aware of people; they can prove you wrong very easily
   in forecasting
FOR JULY 2nd MONDAY


    READ THE CHAPTERS ON
      Forecasting
      Product and service design

				
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