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ForecastingForecastingBA 339BA 339

Mellie PullmanMellie Pullman

What is a Forecast?What is a Forecast?

• What and why might we wish to What and why might we wish to forecast?forecast?

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ForecastingForecasting• Independent vs. Dependent DemandIndependent vs. Dependent Demand

• Qualitative Forecasting MethodsQualitative Forecasting Methods

• Simple & Weighted Moving Average Simple & Weighted Moving Average ForecastsForecasts

• Exponential Smoothing ForecastExponential Smoothing Forecast

• Causal Forecast (Regression)Causal Forecast (Regression)

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Independent vs. Dependent Independent vs. Dependent DemandDemand

A

Independent Demand:Finished Goods

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand:Raw Materials, Component parts,Sub-assemblies, etc.

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Independent Demand: What a Independent Demand: What a firm can do to manage it.firm can do to manage it.

• Can take an active role to influence Can take an active role to influence demand.demand.

• Can take a passive role and simply Can take a passive role and simply respond to demand. respond to demand.

• Forecasting Independent DemandForecasting Independent Demand

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Types of ForecastsTypes of Forecasts

• Qualitative Qualitative (Judgmental)(Judgmental)

• QuantitativeQuantitative– Time Series Time Series

AnalysisAnalysis

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Qualitative Qualitative MethodsMethods

Grass Roots

Market Research

Panel Consensus

Executive Judgment

Delphi Method

Qualitative

Methods

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Quantitative Method:Quantitative Method:Time Series AnalysisTime Series Analysis

• Uses historical dataUses historical data

• Many types of models Many types of models availableavailable

• Pick a model based on:Pick a model based on:

1. Fits previous data best 1. Fits previous data best

2. Time horizon to 2. Time horizon to forecastforecast

3. Data availability3. Data availability

4. Accuracy required4. Accuracy required

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Patterns of Patterns of DemandDemand

Qu

an

tity

Time(a) Horizontal (Random): Data cluster about a horizontal line.

Qu

an

tity

Time(b) Trend: Data consistently increase or decrease.

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Patterns of Patterns of DemandDemand

Qu

an

tity

| | | | | |1 2 3 4 5 years

(d) Cyclical: Data reveal gradual increases and decreases over extended periods.

Qu

an

tity

| | | | | | | | | | | |J F M A M J J A S O N

D

Year 1

Year 2

(c) Seasonal: Data consistently show peaks and valleys.

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Finding Components of Finding Components of DemandDemand

1 2 3 4

x

x xx

xx

x xx

xx x x x

xxxxxx x x

xx

x x xx

xx

xx

x

xx

xx

xx

xx

xx

xx

x

x

Year

Sal

es

Seasonal variation

Linear

Trend

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Simple Moving AverageSimple Moving Average

n

D+...+D +D +D =F 1n-t2-t1-tt

1t

• DDtt = actual demand from period t = actual demand from period t

• FFt+1t+1 = forecast of demand for period = forecast of demand for period t+1 t+1 (next period that has not (next period that has not occurred yet)occurred yet)

• Forecast for the next period t+1 = Forecast for the next period t+1 = average from the last n periods of average from the last n periods of actual demand.actual demand.

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Simple Moving AverageSimple Moving AverageWeek Demand

1 6502 6783 7204 7855 8596 9207 8508 7589 89210 92011 78912 844

n

D+...+D +D +D =F 1n-t2-t1-tt

1t

• Let’s develop 3-week and Let’s develop 3-week and 6-week moving average 6-week moving average forecasts for demand. forecasts for demand.

• Assume you only have 3 Assume you only have 3 weeks and 6 weeks of weeks and 6 weeks of actual demand data for actual demand data for the respective forecasts the respective forecasts

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Week Demand 3-Week 6-Week1 6502 6783 7204 785 682.675 859 727.676 920 788.007 850 854.67 768.678 758 876.33 802.009 892 842.67 815.33

10 920 833.33 844.0011 789 856.67 866.5012 844 867.00 854.83

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500

550

600

650

700

750

800

850

900

950

1 2 3 4 5 6 7 8 9 10 11 12Week

Dem

and

Demand

3-Week

6-Week

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In-Class ExerciseIn-Class Exercise

Week Demand1 8202 7753 6804 6555 6206 6007 575

• Develop 3-week and 5-Develop 3-week and 5-week moving average week moving average forecasts for demand forecasts for demand for week 8for week 8

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Weighted Moving Weighted Moving AverageAverage

1-n-t1-n-t2-t2-t1-t1-ttt1t Dw+...+Dw+D w+D w=F

w = 1ii=1

n

Determine the 3-period weighted moving average forecast for period 4.

Weights: t .5t-1 .3t-2 .2

Week Demand1 6502 6783 7204

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SolutionSolution

Week Demand Forecast1 6502 6783 7204 693.4

F= .5(720)+.3(678)+.2(650)4

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In-Class ExerciseIn-Class Exercise

Determine the 3-period weighted moving average forecast for period 5.

Weights: t .7t-1 .2t-2 .1

Week Demand1 8202 7753 6804 655

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Exponential SmoothingExponential Smoothing(( is the smoothing is the smoothing

parameter)parameter)

PremisePremise —— we should determine how much we should determine how much weight to put on recent information versus older weight to put on recent information versus older information. information.

0 0 << << 1 1

High High such as .7 puts weight on recent demand such as .7 puts weight on recent demand

Low Low such as .2 puts weight on many previous such as .2 puts weight on many previous periodsperiods

Ft+1 = Dt + (1-)Ft

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Exponential Smoothing Exponential Smoothing ExampleExample

Week Demand1 8202 7753 6804 6555 7506 8027 7988 6899 775

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Determine Determine exponential exponential smoothing forecasts smoothing forecasts for periods 2-10 for periods 2-10 using using =.10 and =.10 and =.60.=.60.

Let FLet F11=D=D1 1

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Week Demand 0.1 0.61 8202 775 820.00 820.003 680 815.50 793.004 655 801.95 725.205 750 787.26 683.086 802 783.53 723.237 798 785.38 770.498 689 786.64 787.009 775 776.88 728.20

10 776.69 756.28

Forecast

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Effect of Effect of on Forecast on Forecast

500

600

700

800

900

1 2 3 4 5 6 7 8 9 10

Week

Dem

and Demand

0.1

0.6

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In-Class ExerciseIn-Class Exercise

Determine exponential smoothing forecasts for periods 2-3 using =.50

Let F1=D1

Week Demand1 8202 7753 6804 6555

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Forecasting with Forecasting with Causal RelationshipsCausal Relationships

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Potential RelationshipsPotential Relationships

• Temperature and SalesTemperature and Sales• Interest rate and number of loansInterest rate and number of loans• Average daily temperature or Average daily temperature or

rainfall with acre-feet of water usedrainfall with acre-feet of water used• Others?Others?

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What do you notice?What do you notice?

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25

30

35

40

0 1 2 3 4 5 6 7 8 9 10 11

Period

Sal

es

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Simple Linear Simple Linear Regression ModelRegression Model

b represents?b represents?

a represents?a represents?

Yt = a + bx

0 1 2 3 4 5 x (weeks)

Y

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Regression Equation Regression Equation ExampleExample

Week Sales1 1502 1573 1624 1665 177

Develop a regression equation to predict sales

based on these five points.

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y = 143.5 + 6.3t

135140145150155

160165170175180

1 2 3 4 5

Period

Sal

es

Sales

Forecast

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Choosing a Method: Choosing a Method: Depends on Forecast Depends on Forecast

ErrorError

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Forecast Accuracy

Forecasts Consist of 2 Numbers

1. The projection of actual demand (D), called the forecast (F) which projects historical patterns or relationships

2. The error (E) which defines deviation between the forecast and the actual demand

Measures of Forecast Error

Et = Dt - Ft

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Example- Error Example- Error CalculationCalculation

Month Sales Forecast

1 220 n/a

2 250 255

3 210 205

4 300 320

5 325 315

Determine the Error for the four forecast periodsDetermine the Error for the four forecast periods

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Forecast ErrorsForecast Errors

• Study the formula for a Study the formula for a moment. Now, moment. Now, what does what does each calculation tell each calculation tell you?you?

– MFA: mean forecast MFA: mean forecast errorerror

– MAD: mean absolute MAD: mean absolute deviationdeviation

n

FD =MFE

n

1=ttt

n

F-D =MAD

n

1=ttt

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Example--MADExample--MAD

Month Sales Forecast

1 220 n/a

2 250 255

3 210 205

4 300 320

5 325 315

Determine the MAD for the four forecast periodsDetermine the MAD for the four forecast periods

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SolutionSolution

10=4

40=

n

F-D =MAD

n

1=ttt

Month Sales Forecast Abs Error1 220 n/a2 250 255 53 210 205 54 300 320 205 325 315 10

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