FORECASTING

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FORECASTING

• A Forecast is a PREDICTION of the future. It
  often examines historical data to determine
  relationships between key variables in a problem
  and uses those relationships to make statements
  about the future.
• Forecasts are usually the result of examining
  past experiences to gain insights into the
  future. These insights often take the form of
  mathematical models that are used to predict the
  future.
• For any organization, forecasts are essential
  part of planning. It would be illogical to PLAN
  for tomorrow without some vision of what MIGHT
  happen. The critical word is MIGHT

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STEPS IN FORECASTING
Determine ObjectivesWhat is The purpose?, what
variables, Who will use the forecast?
Develop and Test Model Moving Average,
weighted Moving average, Time series Analysis,
regression analysis etc.
Consider constraints Real world constraints
Apply the Model
Revise and Evaluate the Forecast. Human judgment
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FORECASTING METHODS

• TIME-SERIES ANALYSIS
• Simple Moving Average
• Weighted Moving Average
• Exponential Smoothing
• Regression and Correlation analysis

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Example

• We are given the following data of a
  manufacturing company
• YearQuarter Exports (Rs000)
• 20031 4.100
• 20032 2,000
• 20033 5,700
• 20034 2,500
• 20041 7,300
• 20042 9,200
• 20043 6,300
• 20044 ?

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FORECASTING TIME LINE
Present
Past
Future
x (t-3)
x (t-2)
f(t1)
f (t2)
x (t-1)
x(t)
F (t3)
x(t) The actual value of the item to be
forecast for the most recent time period ( t).
Prior observations are noted by subtracting 1
from the time period (t). f (t1) The
forecasted value for the next period. Following
periods are designated by adding 1 to the time
period (t1) F (t1)
Where f (t1) the forecast for time period
t1 That is, the next time period. X (t-i) the
observed value for period t-i, Where t is the
last period for which data are available and i
0,., n-1
n-1
(x (t-i)
i0
n
n the number of time periods in the average
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COMPONENTS OF DEMAND

• Mainly we deal with Five components of Demand in
  a forecasting system
• Average
• Trend
• Seasonal Influence
• Cyclical Movement
• Random Error (Which makes every forecast wrong)
• Every forecasting system is designed to forecast
  at
• least one of these components, and some systems
  are
• designed to forecast more than one.

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TIME SERIES METHODS

• Assumptions
• what has happened in the past will continue in
  the future.
• No changes occur in the internal or external
  factors that determine the underlying demand
  pattern.
• Not suitable for forecasting medium or long
  term demand. Generally used for short-term
  forecasting.

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Exponential Smoothing

• Exponential Smoothing is really another form of a
  weighted moving average. It is a procedure for
  continually revising an estimate in light of more
  recent data. The method is based on averaging
  (smoothing) past values. This method is
  distinguishable by the special way it weighs each
  past demand. The pattern of weights is
  EXPONENTIAL in form. Demand for the most recent
  period is weighted more heavily the weights
  placed on successively older periods decrease
  exponentially. In other words, the weights
  decrease in magnitude the further back in time
  the data are weighted the decrease is nonlinear
  (exponential).
• Forecast of next
• periods demand (alpha) (actual demand for
  the most recent period) (1-alpha) (demand
  forecast for most recent period)

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Example

• Q.1 In a Company A, the demand for a product for
  September was 300 units and for October, 350
  units. The old forecast procedure was to use last
  years average monthly demand as the forecast for
  each month this year. Last years average monthly
  demand was 200units. Using 200 units as the
  September forecast and a smoothing coefficient of
  .7 to weight recent demand most heavily,
  calculate the forecast for the month of October
  and November.
• Solution
• F (October) .7 (Demand for September i.e 300)
  (1-.7) (Forecast for September, i.e 200) 210
  60 270
• F (November) .7 ( Demand for October, 350)
  (1-.7) (Forecast for October, 270) 245 81
  326.
• Instead of last years monthly demand for 200
  units, Novembers forecast is 326 units. The old
  forecasting method, based on simple average,
  provided a considerably different forecast from
  the exponential smoothing model.

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How do you select the Smoothing Coefficient?

• A high (Alpha) places heavy weight on the most
  recent demand.
• A high smoothing coefficient (.7,.8,.9) could be
  more appropriate for new products or item for
  which the demand is shifting (dynamic or
  unstable)
• If the demand is very stable, select a low alpha
  value (.1,.2 or.3).
• For slightly stable demand, smoothing coefficient
  of .4, .5 or .6 may provide the most accurate
  forecasts.

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Forecast Error

• Forecast Error is the numeric difference of
  forecasted demand and actual demand. A forecast
  method yielding large errors is less desirable
  than one yielding smaller errors.
• MEAN ABSOLUTE DEVIATION (MAD) sum of the
  absolute value of forecast error for all
  period/number of periods (Actual demand
  Forecasted demand)/n
• For each forecast period (i), we will find the
  difference between the forecasted demand and the
  actual demand. Notice that MAD is an average of
  the absolute value of forecast errors errors are
  measured without regard to sign. MAD expresses
  the magnitude but not the direction of the error.
• MEAN SQUARED ERROR (MSE)
• Bias Sum of forecast error for all
  period/Number of periods

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Solved Example

• An Manufacturer forecasted the demand for product
  XYZ to be 500 per month for each of three months.
  The actual demands turned out to be 400, 560 and
  700. Calculate MAD, Bias and Mean Squared Error
• Solution
• MAD (500-400) (500-560) (500-700)/3 360/3
  120
• Bias (500-400) (500-560) (500-700)/3
• 100 60 200/3 -53 Units
• Interpretation Since MAD is 120 units (which is
  high) and it measures the overall accuracy of the
  forecasting method, we can say that the
  Manufacturer does not have a very accurate
  forecasting model. He has a high average absolute
  error of 24 percent of the forecasted number.
• Bias measures the tendency related to over or
  underforecast. In this example, the manufacturer
  has a tendency to underestimate by 53 units,
  since actual demand averages 553 units, Bias is,
  on the average, a 9.6 percent underforecast.

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Solved Example

• Company ABC has experienced the following demand
  for refrigerators during the past 6 months.
• January 200 units
• February 300
• March 200
• April 400
• May 500
• June 600
• Calculate
• (a) July sales forecast using a six-period moving
  average.
• (b) A July forecast using a three-month moving
  average.
• (c) Forecast of demand for July using a
  three-period model with the most recent periods
  demand weighted twice as heavily as each of the
  previous two periods demand.

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• Solution
• Moving Average (MA) 6-month average
  200300200400500600/6 367
• MA using 3-month average
• 400500600/3 500
• c.
• WMA .25 (400) .25 (500) .5 (600) 525

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Problem

• Q. 1 A motorcycle producer has experienced the
  following actual and forecasted demand of
  motorcycles
• Month Forecasted Demand Actual
• Jan 200 210
• Feb 202 192
• March 200 220
• April 204 204
• May 204 209
• Calculate
• (a) Calculate Mean Squared Error (MSR), MAD and
  BIAS

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• (b) Using a simple exponential smoothing model
  with alpha .2, what is the forecasted demand
  for June and July?
• C Using a 3-month moving average, what is the
  forecasted demand for the month of June and July?
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