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Ram C. PoudelPulchowk CampusNovember 1, 2009
Project Planning and Management (EG853ME)
Forecasting HorizonsLong Term
5+ years into the futureR&D, plant location, product planningPrincipally judgement-based
Medium Term1 season to 2 yearsAggregate planning, capacity planning, sales forecastsMixture of quantitative methods and judgement
Short Term1 day to 1 year, less than 1 seasonDemand forecasting, staffing levels, purchasing,
inventory levelsQuantitative methods
Short Term Forecasting:Needs and UsesScheduling existing resources
NEA for Load Dispatch CenterAcquiring additional resources
How much power stations needs to be added?
Determining what resources are neededRenewable EnergyNuclear Energy
Types of Forecasting ModelsTypes of Forecasts
Qualitative --- based on experience, judgement, knowledge;Quantitative --- based on data, statistics;
Methods of ForecastingNaive Methods --- eye-balling the numbers;Formal Methods --- systematically reduce forecasting errors;
time series models (e.g. exponential smoothing);causal models (e.g. regression).
Focus here on Time Series ModelsAssumptions of Time Series Models
There is information about the past;This information can be quantified in the form of
data;The pattern of the past will continue into the
future.
Methods of demand forecasting1. Jury of expert’s opinion
2. Delphi method: Individual experts act separately
3. Consumer’s Survey
4. Sales forecast composite
5. Naïve models
6. Smoothing techniquesa. Moving average
b. Exponential smoothing
7. Analysis of time series and trend projections
8. Use of economic indicators
9. Controlled experiments
10. Judgemental approach
Approach to forecasting1. Identify and clearly state the objectives of forecasting.2. Select appropriate method of forecasting.3. Identify the variables.4. Gather relevant data.5. Determine the most probable relationship.6. For forecasting the company’s share in the demand, two different
assumptions may be made:(a) Ratio of company sales to the total industry sales will continue as in
the past.(b) On the basis of an analysis of likely competition and industry
trends, the company may assume a market share different from that of the past. (alternative / rolling forecasts)
7. Forecasts may be made either in terms of units or sales in rupees.8. May be made in terms of product groups and then broken for
individual products.9. May be made on annual basis and then divided month-wise, etc.
Statistical MethodsTrend Analysis
Curve fittingMoving Average methodWeighted moving average methodExponential smoothing method (w/ Trend and
Seasonality)Time Series decomposition method
Curve Fitting
Method of Least Squares:
Principle of maxima and minima
Find the value of m and b that minimize the sum of square of residuals.
How do we know how good the fit is?Correlation Coefficient, R2
y = 9x - 17.333R2 = 0.9743
0
10
20
30
40
50
60
0 2 4 6 8
Simple Moving AverageForecast Ft is average of n previous observations or
actuals Dt :Note that the n past observations are equally
weighted.Issues with moving average forecasts:
All n past observations treated equally;Observations older than n are not included at all;Requires that n past observations be retained;Problem when 1000's of items are being forecast.
t
ntiit
ntttt
Dn
F
DDDn
F
11
111
1
)(1
Simple Moving AverageInclude n most recent observationsWeight equallyIgnore older observations
weight
today123...n
1/n
Moving Average
n = 3
Exponential Smoothing IInclude all past observationsWeight recent observations much more
heavily than very old observations:
weight
today
Decreasing weight given to older observations
Exponential Smoothing: ConceptInclude all past observationsWeight recent observations much more
heavily than very old observations:
weight
today
Decreasing weight given to older observations
0 1
( )
( )
( )
1
1
1
2
3
Exponential Smoothing: Math
1)1( ttt FaaDF
21
22
1
)1()1(
)1()1(
tttt
tttt
DaDDF
DDDF
Exponential Smoothing: Math
Thus, new forecast is weighted sum of old forecast and actual demand
Notes:Only 2 values (Dt and Ft-1 ) are required, compared with n
for moving averageParameter a determined empirically (whatever works best)Rule of thumb: < 0.5Typically, = 0.2 or = 0.3 work well
Forecast for k periods into future is:
1
22
1
)1(
)1()1(
ttt
tttt
FaaDF
DaaDaaaDF
tkt FF
Exponential Smoothing
= 0.2
Complicating Factors
Simple Exponential Smoothing works well with data that is “moving sideways” (stationary)
Must be adapted for data series which exhibit a definite trend
Must be further adapted for data series which exhibit seasonal and cyclic patterns
Time Series Decomposition Approach Y = f(Xt) where Xt = f(Tt, St, Ct, Rt).
The trend component (Tt) and Cyclic component (Ct) Seasonal Componet (St) Random component (Rt) of the series.
Attached Lecture Video from IIT,Delhi: Prof Arun Kunda
De-seasonalizing Time SeriesIf the time series represents a seasonal
pattern of L period, then by taking moving average Mt of L periods, we could get mean value for the year
Thus Mt = Tt ×Ct, Tt by regression or inspection, linear, quadratic, exponential or other function
Seasonality = Xt/Mt = St × RtAveraging over same month removes Rt.Put them together and get the forecast.
there is a way out...
Forecasting Performance
Mean Forecast Error (MFE or Bias): Measures average deviation of forecast from actuals.
Mean Absolute Deviation (MAD): Measures average absolute deviation of forecast from actuals.
Mean Absolute Percentage Error (MAPE): Measures absolute error as a percentage of the forecast.
Standard Squared Error (MSE): Measures variance of forecast error
How good is the forecast?
Forecasting Performance Measures
)(1
1t
n
tt FD
nMFE
n
ttt FD
nMAD
1
1
n
t t
tt
D
FD
nMAPE
1
100
2
1
)(1
t
n
tt FD
nMSE
Want MFE to be as close to zero as possible -- minimum bias
A large positive (negative) MFE means that the forecast is undershooting (overshooting) the actual observations
Note that zero MFE does not imply that forecasts are perfect (no error) -- only that mean is “on target”
Also called forecast BIAS
Mean Forecast Error (MFE or Bias)
)(1
1t
n
tt FD
nMFE
Mean Absolute Deviation (MAD)
Measures absolute errorPositive and negative errors thus do not cancel out
(as with MFE)Want MAD to be as small as possibleNo way to know if MAD error is large or small in
relation to the actual data
n
ttt FD
nMAD
1
1
Mean Absolute Percentage Error (MAPE)
Same as MAD, except ...Measures deviation as a percentage of
actual data
n
t t
tt
D
FD
nMAPE
1
100
Mean Squared Error (MSE)
Measures squared forecast error -- error varianceRecognizes that large errors are disproportionately
more “expensive” than small errorsBut is not as easily interpreted as MAD, MAPE --
not as intuitive
2
1
)(1
t
n
tt FD
nMSE
Suggested ReadingsLecture - 35 The Analysis of Time
Series Prof. Arun Kanda ITT/Delhi Available at:
Youtube.com
Chapter 3 : Textbook (Page 60 ~ 76).