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).