forecasting mba

4 - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall

What is Forecasting?What is Forecasting?

Process of predicting a future event

Underlying basis of all business decisions Production

Inventory

Personnel

Facilities

??


The Realities!The Realities!

Forecasts are seldom perfect

Most techniques assume an underlying stability in the system

Product family and aggregated forecasts are more accurate than individual product forecasts


Short-range forecast Up to 1 year, generally less than 3 months

Purchasing, job scheduling, workforce levels, job assignments, production levels

Medium-range forecast 3 months to 3 years

Sales and production planning, budgeting

Long-range forecast 3+ years

New product planning, facility location, research and development

Forecasting Time HorizonsForecasting Time Horizons


Forecasting ApproachesForecasting Approaches

Used when little data exist New products

New technology

Involves intuition, experience e.g., forecasting sales on

Internet

Qualitative MethodsQualitative Methods


Qualitative MethodsQualitative Methods

1. Jury of executive opinion (Pool opinions of high-level experts, sometimes augment by statistical models)

2. Delphi method (Panel of experts, queried iteratively until consensus is reached)

3. Sales force composite (Estimates from individual salespersons are reviewed for reasonableness, then aggregated)

4. Consumer Market Survey (Ask the customer)


Quantitative ApproachesQuantitative Approaches

Used when situation is ‘stable’ and historical data exist Existing products

Current technology

Involves mathematical techniques e.g., forecasting sales of LCD

televisions


Quantitative ApproachesQuantitative Approaches

1. Naive approach

2. Moving averages

3. Exponential smoothing

4. Trend projection

5. Linear regression

time-series models

associative model


Set of evenly spaced numerical data Obtained by observing response

variable at regular time periods

Forecast based only on past values, no other variables important Assumes that factors influencing

past and present will continue influence in future

Time Series ForecastingTime Series Forecasting


Trend

Seasonal

Cyclical

Random

Time Series ComponentsTime Series Components


Components of DemandComponents of DemandD

eman

d f

or

pro

du

ct o

r se

rvic

e

| | | |1 2 3 4

Time (years)

Average demand over 4 years

Trend component

Actual demand line

Random variation

Figure 4.1

Seasonal peaks


Persistent, overall upward or downward pattern

Changes due to population, technology, age, culture, etc.

Typically several years duration

Trend ComponentTrend Component


Regular pattern of up and down fluctuations

Due to weather, customs, etc.

Occurs within a single year

Seasonal ComponentSeasonal Component

Number ofPeriod Length Seasons

Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52


Repeating up and down movements

Affected by business cycle, political, and economic factors

Multiple years duration

Cyclical ComponentCyclical Component

0 5 10 15 20


Erratic, unsystematic, ‘residual’ fluctuations

Due to random variation or unforeseen events

Short duration and nonrepeating

Random ComponentRandom Component

M T W T F


Naive ApproachNaive Approach

Assumes demand in next period is the same as demand in most recent period e.g., If January sales were 68, then

February sales will be 68

Sometimes cost effective and efficient

Can be good starting point


MA is a series of arithmetic means

Used if little or no trend

Used often for smoothing Provides overall impression of data

over time

Moving Average MethodMoving Average Method

Moving average =∑ demand in previous n periods

n


Used when some trend might be present Older data usually less important

Weights based on experience and intuition

Weighted Moving AverageWeighted Moving Average

Weightedmoving average =

∑ (weight for period n) x (demand in period n)

∑ weights


Increasing n smooths the forecast but makes it less sensitive to changes

Do not forecast trends well

Require extensive historical data

Potential Problems WithPotential Problems With Moving Average Moving Average


Form of weighted moving average Weights decline exponentially

Most recent data weighted most

Requires smoothing constant () Ranges from 0 to 1

Subjectively chosen

Involves little record keeping of past data

Exponential SmoothingExponential Smoothing


Exponential SmoothingExponential Smoothing

New forecast = Last period’s forecast+ (Last period’s actual demand

– Last period’s forecast)

Ft = Ft – 1 + (At – 1 - Ft – 1)

where Ft = new forecast

Ft – 1 = previous forecast

= smoothing (or weighting) constant (0 ≤ ≤ 1)


Common Measures of ErrorCommon Measures of Error

Mean Absolute Deviation (MAD)

MAD =∑ |Actual - Forecast|

n

Mean Squared Error (MSE)

MSE =∑ (Forecast Errors)2

n


Common Measures of ErrorCommon Measures of Error

Mean Absolute Percent Error (MAPE)

MAPE =∑100|Actuali - Forecasti|/Actuali

n

n

i = 1


Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment

When a trend is present, exponential smoothing must be modified to respond to trend

Forecast including (FITt) = trend

Exponentially Exponentiallysmoothed (Ft) + smoothed (Tt)forecast trend


Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment

Ft = (At - 1) + (1 - )(Ft - 1 + Tt - 1)

Tt = (Ft - Ft - 1) + (1 - )Tt - 1

Step 1: Compute Ft

Step 2: Compute Tt

Step 3: Calculate the forecast FITt = Ft + Tt


Trend ProjectionsTrend Projections

Fitting a trend line to historical data points to project into the medium to long-range

Linear trends can be found using the least squares technique

y = a + bx^

where y= computed value of the variable to be predicted (dependent variable)a= y-axis interceptb= slope of the regression linex= the independent variable

^


Least Squares MethodLeast Squares Method

Equations to calculate the regression variables

b =xy - nxy

x2 - nx2

y = a + bx^

a = y - bx


Seasonal Variations In DataSeasonal Variations In Data

The multiplicative seasonal model can adjust trend data for seasonal variations in demand (jet skis, snow mobiles)


Seasonal Variations In DataSeasonal Variations In Data

1. Find average historical demand for each season

2. Compute the average demand over all seasons

3. Compute a seasonal index for each season

4. Estimate next year’s total demand

5. Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season

Steps in the process:Steps in the process:


Associative ForecastingAssociative Forecasting

Used when changes in one or more independent variables can be used to predict

the changes in the dependent variable

Most common technique is linear regression analysis

We apply this technique just as we did We apply this technique just as we did in the time series examplein the time series example


Associative ForecastingAssociative ForecastingForecasting an outcome based on predictor variables using the least squares technique

y = a + bx^

where y= computed value of the variable to be predicted (dependent variable)a= y-axis interceptb= slope of the regression linex= the independent variable though to predict the value of the dependent variable

^


Standard Error of the Standard Error of the EstimateEstimate

A forecast is just a point estimate of a future value

This point is actually the mean of a probability distribution

Figure 4.9

4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

No

del

’s s

ales

Area payroll

3.25



We use the standard error to set up prediction intervals around the

point estimate

Sy,x =∑y2 - a∑y - b∑xy

n - 2



4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

No

del

’s s

ales

Area payroll

3.25

Sy,x = =∑y2 - a∑y - b∑xyn - 2

39.5 - 1.75(15) - .25(51.5)6 - 2

Sy,x = .306

The standard error of the estimate is $306,000 in sales

4 - 35

Prediction Intervals Prediction Intervals

The ranges or limits of a forecast are estimated by:

Upper limit = Y + t*Sy,x

Lower limit = Y - t*Sy,x

where:

Y = forecasted value (point estimate)

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

© 2011 Pearson Education, Inc. publishing as Prentice Hall


How strong is the linear relationship between the variables?

Correlation does not necessarily imply causality!

Coefficient of correlation, r, measures degree of association Values range from -1 to +1

CorrelationCorrelation


Correlation CoefficientCorrelation Coefficient

r = nxy - xy

[nx2 - (x)2][ny2 - (y)2]


Multiple Regression Multiple Regression AnalysisAnalysis

If more than one independent variable is to be used in the model, linear regression can be

extended to multiple regression to accommodate several independent variables

y = a + b1x1 + b2x2 …^

Computationally, this is quite Computationally, this is quite complex and generally done on the complex and generally done on the

computercomputer


Multiple Regression Multiple Regression AnalysisAnalysis

y = 1.80 + .30x1 - 5.0x2^

In the Nodel example, including interest rates in the model gives the new equation:

An improved correlation coefficient of r = .96 means this model does a better job of predicting the change in construction sales

Sales = 1.80 + .30(6) - 5.0(.12) = 3.00Sales = $3,000,000


Measures how well the forecast is predicting actual values

Ratio of cumulative forecast errors to mean absolute deviation (MAD) Good tracking signal has low values

If forecasts are continually high or low, the forecast has a bias error

Monitoring and Controlling Monitoring and Controlling ForecastsForecasts

Tracking SignalTracking Signal


Monitoring and Controlling Monitoring and Controlling ForecastsForecasts

Tracking signal

Cumulative errorMAD

=

Tracking signal =

∑(Actual demand in period i -

Forecast demand in period i)

∑|Actual - Forecast|/n)


Tracking SignalTracking Signal

Tracking signal

+

0 MADs

–

Upper control limit

Lower control limit

Time

Signal exceeding limit

Acceptable range


Forecasting in the Service Forecasting in the Service SectorSector

Presents unusual challenges Special need for short term records

Needs differ greatly as function of industry and product

Holidays and other calendar events

Unusual events

forecasting mba

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