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Lecture3

ForecastingCT – Chapter 3

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A statement about the future value of a variable of interest such as demand.

Forecasts affect decisions and activities throughout an organization Accounting, finance Human resources Marketing Operations Product / service design

ForecastForecast

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Accounting Cost/profit estimates

Finance Cash flow and funding

Human Resources Hiring/recruiting/training

Marketing Pricing, promotion, strategy

Operations Schedules, MRP, workloads

Product/service design New products and services

Uses of ForecastsUses of Forecasts

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Elements of a Good ForecastElements of a Good Forecast

Timely

AccurateReliable

Mea

ningfu

l

Written

Easy

to u

se

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Steps in the Forecasting ProcessSteps in the Forecasting Process

Step 1 Determine purpose of forecast

Step 2 Establish a time horizon

Step 3 Select a forecasting technique

Step 4 Gather and analyze data

Step 5 Prepare the forecast

Step 6 Monitor the forecast

“The forecast”

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Types of ForecastsTypes of Forecasts

Judgmental - uses subjective inputs

Time series - uses historical data assuming the future will be like the past

Associative models - uses explanatory variables to predict the future

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Judgmental ForecastsJudgmental Forecasts

Executive opinions Sales force opinions Consumer surveys Outside opinion Delphi method

Opinions of managers and staff Achieves a consensus forecast

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Time Series ForecastsTime Series Forecasts

Trend - long-term movement in data Seasonality - short-term regular variations in

data Cycle – wavelike variations of more than one

year’s duration Irregular variations - caused by unusual

circumstances

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Forecast VariationsForecast Variations

Trend

Irregularvariation

Seasonal variations

908988

Figure 3.1

Cycles

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Smoothing/Averaging MethodsSmoothing/Averaging Methods

Used in cases in which the time series is fairly stable and has no significant trend, seasonal, or cyclical effects

Purpose of averaging - to smooth out the irregular components of the time series.

Four common smoothing/averaging methods are: Moving averages Weighted moving averages Exponential smoothing

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Sales of gasoline for the past 12 weeks at your Sales of gasoline for the past 12 weeks at your local Chevron (in ‘000 gallons). If the dealer local Chevron (in ‘000 gallons). If the dealer uses a 3-period moving average to forecast uses a 3-period moving average to forecast sales, what is the forecast for Week 13?sales, what is the forecast for Week 13?

Example of Moving Average

Past Sales

WeekWeek SalesSales WeekWeek SalesSales 1 17 7 201 17 7 20 2 21 8 182 21 8 18 3 19 9 223 19 9 22 4 23 10 204 23 10 20 5 18 11 155 18 11 15

6 166 16 12 12 22 22

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Management Scientist SolutionsManagement Scientist Solutions

MA(3) for period 4

= (17+21+19)/3 = 19

Forecast error for period 3 = Actual – Forecast = 23 – 19

= 4

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MA(5) versus MA(3)MA(5) versus MA(3)

Week Actual MA(3) MA(5)1 172 213 194 23 195 18 216 16 20 19.67 20 19 19.48 18 18 19.29 22 18 19

10 20 20 18.811 15 20 19.212 22 19 19

MA Forecast Graph

0

5

10

15

20

25

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

Week

Actu

al/M

A Fo

reca

st s

ale

valu

es

Actual

MA(3)

MA(5)

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Review of last classReview of last class

Forecasting What is a forecast? Organizational functions that use forecasts Desirable characteristics of a forecast Types of forecasts Types of time series

Smoothing/averaging method Moving averages Weighted moving averages

Advantage

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Exponential SmoothingExponential Smoothing

• Premise - The most recent observations might have the highest predictive value. Therefore, we should give more weight to the more recent time periods

when forecasting.

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Exponential SmoothingExponential Smoothing

Weighted averaging method based on previous forecast plus a percentage of the forecast error

A-F is the error term, is the % feedback

Ft+1 = Ft + (At - Ft)

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Picking a Smoothing ConstantPicking a Smoothing Constant

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40

45

50

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

Period

Dem

and .1

.4

Actual

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Linear Trend EquationLinear Trend Equation

Ft = Forecast for period t t = Specified number of time periods a = Value of Ft at t = 0 b = Slope of the line

Ft = a + bt

0 1 2 3 4 5 t

Ft

a

Suitable for time series data that exhibit a long term linear trend

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Linear Trend ExampleLinear Trend Example

F11 = 20.4 + 1.1(11) = 32.5

Linear trend equation

Sale increases every time period @ 1.1

units

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Actual Actual vsvs Forecast Forecast

Linear Trend Example

0

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9 10

Week

Act

ual

/Fo

reca

sted

sal

es

Actual

Forecast

F(t) = 20.4 + 1.1t

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Forecasting with Trends and Seasonal Forecasting with Trends and Seasonal Components – An ExampleComponents – An Example

Business at Terry's Tie Shop can be viewed as falling into three distinct seasons: (1) Christmas (November-December); (2) Father's Day (late May - mid-June); and (3) all other times.

Average weekly sales ($) during each of the three seasonsduring the past four years are known and given below.

Determine a forecast for the average weekly sales in year 5 for each of the three seasons.

Year Season 1 2 3 4 1 1856 1995 2241 2280 2 2012 2168 2306 2408 3 985 1072 1105 1120

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Management Scientist SolutionsManagement Scientist Solutions

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Interpretation of Seasonal IndicesInterpretation of Seasonal Indices Seasonal index for season 2 (Father’s Day) = 1.236

Means that the sale value of ties during season 2 is 23.6% higher than the average sale value over the year

Seasonal index for season 3 (all other times) = 0.586 Means that the sale value of ties during season 3 is 41.4%

lower than the average sale value over the year

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Forecast AccuracyForecast Accuracy

Error - difference between actual value and predicted value

Mean Absolute Deviation (MAD)

Average absolute error

Mean Squared Error (MSE)

Average of squared error

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MAD and MSEMAD and MSE

MAD = Actual forecast

n

MSE = Actual forecast)

2

n

(

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Measure of Forecast AccuracyMeasure of Forecast Accuracy MSE = Mean Squared Error

Week # Actual (A) Forecast(F) Error =E =A-F E(squared)1 21.6 21.5 0.1 0.012 22.9 22.6 0.3 0.093 25.5 23.7 1.8 3.244 21.9 24.8 -2.9 8.415 23.9 25.9 -2 46 27.5 27 0.5 0.257 31.5 28.1 3.4 11.568 29.7 29.2 0.5 0.259 28.6 30.3 -1.7 2.89

10 31.4 31.4 0 0

Sum of E(squared) 30.7

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Forecasting Accuracy Estimates Forecasting Accuracy Estimates Example 10 of textbookExample 10 of textbook

Period Actual Forecast (A-F) |A-F| (A-F)^21 217 215 2 2 42 213 216 -3 3 93 216 215 1 1 14 210 214 -4 4 165 213 211 2 2 46 219 214 5 5 257 216 217 -1 1 18 212 216 -4 4 16

-2 22 76

MAD= 2.75MSE= 9.50

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Sources of Forecast errorsSources of Forecast errors

Model may be inadequate Irregular variations Incorrect use of forecasting technique

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Characteristics of ForecastsCharacteristics of Forecasts

They are usually wrong A good forecast is more than a single number Aggregate forecasts are more accurate The longer the forecast horizon, the less accurate

the forecast will be Forecasts should not be used to the exclusion of

known information

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Choosing a Forecasting TechniqueChoosing a Forecasting Technique

No single technique works in every situation Two most important factors

Cost Accuracy

Other factors include the availability of: Historical data Computers Time needed to gather and analyze the data Forecast horizon