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Quantitative Forecasting Methods(Non-Naive)

QuantitativeForecasting

MultipleRegression

AssociativeModels

ExponentialSmoothing

MovingAverage

Time SeriesModels

TrendProjection

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Time Series Assume that what has occurred in the past will continue to

occur in the future Relate the forecast to only one factor TIMETIME Include

naive forecast simple average moving average exponential smoothing linear trend analysis

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Moving Averages Naive forecast

Demand of the current period is used as next period’s forecast

Simple moving average stable demand with no pronounced behavioral patterns

Weighted moving average weights are assigned to most recent data

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Naive forecast

JanJan 120120FebFeb 9090MarMar 100100AprApr 7575MayMay 110110JuneJune 5050JulyJuly 7575AugAug 130130SeptSept 110110OctOct 9090

ORDERSORDERSMONTHMONTH PER MONTHPER MONTH

--120120

9090100100

7575110110

50507575

130130110110

9090Nov -Nov -

FORECASTFORECAST

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Simple Moving Average

MAMAnn = =

nn

ii = 1= 1 DDii

nnwherewhere

nn ==number of periods in the number of periods in the moving averagemoving average

DDii ==demand in period demand in period ii

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3-month Simple Moving Average

JanJan 120120

FebFeb 9090

MarMar 100100

AprApr 7575

MayMay 110110

JuneJune 5050

JulyJuly 7575

AugAug 130130

SeptSept 110110

OctOct 9090NovNov --

ORDERSORDERS

MONTHMONTH PER PER MONTHMONTH

MAMA33 = =

33

ii = 1= 1 DDii

33

==90 + 110 + 13090 + 110 + 130

33

= 110 orders= 110 ordersfor Novfor Nov

––––––

103.3103.388.388.395.095.078.378.378.378.385.085.0

105.0105.0110.0110.0

MOVING MOVING AVERAGEAVERAGE

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Weighted Moving Average

WMAWMAnn = = ii = 1 = 1 WWii D Dii

wherewhere

WWii = the weight for period = the weight for period ii, , between 0 and 100 between 0 and 100 percentpercent

WWii = 1.00= 1.00

Adjusts Adjusts moving moving average average method to method to more closely more closely reflect data reflect data fluctuationsfluctuations

Copyright 2006 John Wiley & Sons, Inc.

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Weighted Moving Average Example

MONTH MONTH WEIGHT WEIGHT DATADATAAugustAugust 17%17% 130130SeptemberSeptember 33%33% 110110OctoberOctober 50%50% 9090

WMAWMA33 = = 33

ii = 1 = 1 WWii D Dii

= (0.50)(90) + (0.33)(110) + (0.17)(130)= (0.50)(90) + (0.33)(110) + (0.17)(130)

= 103.4 orders= 103.4 orders

November ForecastNovember Forecast

Copyright 2006 John Wiley & Sons, Inc.

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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

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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

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Exponential SmoothingExponential Smoothing

New forecast =New forecast = last period’s forecastlast period’s forecast+ + (last period’s actual demand (last period’s actual demand

– – last period’s forecast)last period’s forecast)

FFtt = F = Ft – 1t – 1 + + (A(At – 1t – 1 - F - Ft – 1t – 1))

wherewhere FFtt == new forecastnew forecast

FFt – 1t – 1 == previous forecastprevious forecast

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

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Exponential Smoothing ExampleExponential Smoothing Example

Predicted demand = 142 Ford MustangsPredicted demand = 142 Ford MustangsActual demand = 153Actual demand = 153

Smoothing constant Smoothing constant = .20 = .20

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Exponential Smoothing ExampleExponential Smoothing Example

Predicted demand = 142 Ford MustangsPredicted demand = 142 Ford MustangsActual demand = 153Actual demand = 153

Smoothing constant Smoothing constant = .20 = .20

New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)

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Exponential Smoothing ExampleExponential Smoothing Example

Predicted demand = 142 Ford MustangsPredicted demand = 142 Ford MustangsActual demand = 153Actual demand = 153

Smoothing constant Smoothing constant = .20 = .20

New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)= 142 + 2.2= 142 + 2.2

= 144.2 ≈ 144 cars= 144.2 ≈ 144 cars

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Common Measures of ErrorCommon Measures of Error

Mean Absolute Deviation (MAD)Mean Absolute Deviation (MAD)

MAD =MAD =∑∑ |actual - forecast||actual - forecast|

nn

Mean Squared Error (MSE)Mean Squared Error (MSE)

MSE =MSE =∑∑ (forecast errors)(forecast errors)22

nn

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Trend analysis Many trends are possible:

Linear Exponential Logarithmic S-growth curve

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Linear Trend AnalysisDemand

0

1000

2000

3000

4000

5000

6000

0 5 10 15 20 25 30