Reducing Risk

Forecasting

Chapter 3

McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

ForecastForecast – a statement about the future

value of a variable of interestWe make forecasts about such things as

weather, demand, and resource availabilityForecasts are an important element in making

informed decisions

Instructor Slides 3-2

Two Important Aspects of ForecastsExpected level of demand

The level of demand may be a function of some structural variation such as trend or seasonal variation

AccuracyRelated to the potential size of forecast error


Elements of a Good ForecastThe forecast should be timely should be accurate should be reliable should be expressed in meaningful units should be in writing technique should be simple to understand

and use should be cost effective

Steps in the Forecasting Process1. Determine the purpose of the forecast2. Establish a time horizon3. Select a forecasting technique4. Obtain, clean, and analyze appropriate

data5. Make the forecast6. Monitor the forecast

Features Common to All Forecasts1. Techniques assume some underlying causal

system that existed in the past will persist into the future

2. Forecasts are not perfect3. Forecasts for groups of items are more

accurate than those for individual items4. Forecast accuracy decreases as the forecasting

horizon increases


Forecast Accuracy and Control

Forecast errors should be monitored Error = Actual – Forecast If errors fall beyond acceptable bounds,

corrective action may be necessary

Forecast Accuracy Metrics

n

tt ForecastActualMAD

2

tt

1

ForecastActualMSE

n

100Actual

ForecastActualMAPE

t

tt

n

MAD weights all errors evenly

MSE weights errors according to their squared values

MAPE weights errors according to relative error

Forecast Error CalculationPeriod

Actual(A)

Forecast(F)

(A-F) Error |Error| Error2

1 107 110 -3 3 9

2 125 121 4 4 16

3 115 112 3 3 9

4 118 120 -2 2 4

5 108 109 -1 1 1

AVG(A) 114.6 Sum 13 39

n = 5 n-1 = 4

MAD MSE MAPE=MAD / AVG(A)

= 2.6 = 9.75 =2.6/114.6= 2.27%

Forecasting Approaches Qualitative Forecasting

Qualitative techniques permit the inclusion of soft information such as:Human factorsPersonal opinionsHunches

These factors are difficult, or impossible, to quantify Quantitative Forecasting

Quantitative techniques involve either the projection of historical data or the development of associative methods that attempt to use causal variables to make a forecast

These techniques rely on hard data

Judgmental ForecastsForecasts that use subjective inputs such

as opinions from consumer surveys, sales staff, managers, executives, and expertsExecutive opinionsSales force opinionsConsumer surveysDelphi method

Time-Series ForecastsForecasts that project patterns identified

in recent time-series observationsTime-series - a time-ordered sequence of

observations taken at regular time intervalsAssume that future values of the time-

series can be estimated from past values of the time-series

Time-Series BehaviorsTrendSeasonalityCyclesIrregular variationsRandom variation

Historical Monthly Product Demand Consisting of a Growth Trend, Cyclical Factor, and Seasonal Demand

Exhibit 9.4

Common Types of Trends

Exhibit 9.5a

Common Types of Trends (cont’d)

Exhibit 9.5b

Trends and SeasonalityTrend

A long-term upward or downward movement in dataPopulation shiftsChanging income

Seasonality Short-term, fairly regular variations related to the

calendar or time of day Restaurants, service call centers, and theaters all

experience seasonal demand

3-18

Trend, Cyclical, with Variations

Cycles and VariationsCycle

Wavelike variations lasting more than one yearThese are often related to a variety of economic, political,

or even agricultural conditions

Random Variation Residual variation that remains after all other behaviors

have been accounted for

Irregular variation Due to unusual circumstances that do not reflect typical

behaviorLabor strikeWeather event

Time-Series Forecasting - Naïve ForecastNaïve Forecast

Uses a single previous value of a time series as the basis for a forecastThe forecast for a time period is equal to the

previous time period’s valueCan be used when

The time series is stableThere is a trendThere is seasonality

Time-Series Forecasting - AveragingThese Techniques work best when a

series tends to vary about an averageAveraging techniques smooth variations in the

dataThey can handle step changes or gradual

changes in the level of a seriesTechniques

Moving averageWeighted moving averageExponential smoothing

Moving AverageTechnique that averages a number of the

most recent actual values in generating a forecast

average moving in the periods ofNumber

1 periodin valueActual

average moving period MA

period for timeForecast

where

MA

1

1t

n

tA

n

tF

n

AF

t

t

t

n

iit

t

Forecast Demand Based on a Three- andFive-Week Simple Moving Average

Week Demand Forecast Forecast

(3-week) (5-week)

1 800

2 1400

3 1000

4 1500 (1000+1400+800)/3 =1067

5 1500 (1500+1000+1400)/3 = 1300

6 1300 (1500+1500+1000)/3 = 1333 (1500+1500+1000+1400+ 800)/5 =1240

7 1800 (1300+1500+1500)/3 = 1433 (1300+1500+1500+1000+1400)/5 =1340

8 1700 (1800+1300+1500)/3 = 1533 (1800+1300+1500+1500+1000)/5 =1420

9 1300 1600 (1700+1800+1300+1500+1500)/5 =1560

10 1700 1600 (1300+1700+1800+1300+1500)/5 =1520

11 1700 1567 (1700+1300+1700+1800+1300)/5 =1560

Moving AverageAs new data become available, the

forecast is updated by adding the newest value and dropping the oldest and then recomputing the the average

The number of data points included in the average determines the model’s sensitivityFewer data points used-- more responsiveMore data points used-- less responsive

Forecast Demand Based on a Three- andNine-Week Simple Moving Average

Exhibit 9.6

Moving Average Forecast of Three- andNine-Week Periods versus Actual Demand

Exhibit 9.7

Weighted Moving AverageThe most recent values in a time series

are given more weight in computing a forecastThe choice of weights, w, is somewhat

arbitrary and involves some trial and error

Ft wn At n wn 1At (n 1) ... w1At 1

where

wt weight for period t, wt 1 weight for period t 1, etc.

At the actual value for period t, At 1 the actual value for period t 1, etc.

Exponential SmoothingA weighted averaging method that is

based on the previous forecast plus a percentage of the forecast error

1 1 1

1

1

( )

where

Forecast for period

Forecast for the previous period

=Smoothing constant

Actual demand or sales from the previous period

t t t t

t

t

t

F F A F

F t

F

A

Exponential Smoothing

Saturday Hotel Occupancy ( =0.5) Forecast Period Occupancy Forecast Error t At Ft |At - Ft| 1 79 --- 2 84 79.00 5 3 83 79+.5(84-79)=81.50 or 82 1 4 81 81.5+.5(83-81.5)=82.25 or 82 1 5 98 82.25+.5(81-82.25)=81.63 or 82 16 6 100 81.63+.5(98-81.63)= 89.81 or 90 10 MAD =33/5= 6.6 Forecast Error (Mean Absolute Deviation) = ΣlAt – Ftl / n

The first actual value as the forecast for period 2

17-29

Linear TrendA simple data plot can reveal the

existence and nature of a trendLinear trend equation

Ft a bt

where

Ft Forecast for period t

a Value of Ft at t 0

b Slope of the line

t Specified number of time periods from t 0

Estimating slope and interceptSlope and intercept can be estimated

from historical data

22

or

where

Number of periods

Value of the time series

n ty t yb

n t t

y b ta y bt

n

n

y

Figure 3-9

3-32

Linear Trend Example

Week (t) Sales (y) t2 ty

1 150 1 150

2 157 4 314

3 162 9 486

4 166 16 664

5 177 25 885

t= 15 y= 812 t2=55 (ty)=2499


22

5(2499) 15(812)

5(55) 225

12495 121806.3

275 225

812-6.3(15) = 143.5

5143.5 6.3

n ty t yb

n t t

y b ta

ny t


Substituting values of t into this equation, the forecast for next 2 periods are:

F6= 143.5+6.3 (6) = 181.3

F7= 143.5+6.3 (7) = 187.6

Techniques for SeasonalitySeasonality – regularly repeating movements in

series values that can be tied to recurring eventsExpressed in terms of the amount that actual

values deviate from the average value of a seriesModels of seasonality

AdditiveSeasonality is expressed as a quantity that gets added to

or subtracted from the time-series average in order to incorporate seasonality

MultiplicativeSeasonality is expressed as a percentage of the average

(or trend) amount which is then used to multiply the value of a series in order to incorporate seasonality


Models of Seasonality


Computing Seasonal Relatives Using Simple Average (SA) MethodExample 8A, page 150

Manager of a Call center recorded the volume of calls received between 9 and 10 a.m. for 21 days and wants to obtain a seasonal index for each day for that hour.

Volume Season Overall

Day Week 1 Week 2 Week 3 Average ÷ Average = SA Index

Tues 67 60 64 63.667 ÷ 71.571 = 0.8896

Wed 75 73 76 74.667 ÷ 71.571 = 1.0432

Thurs 82 85 87 84.667 ÷ 71.571 = 1.1830

Fri 98 99 96 97.667 ÷ 71.571 = 1.3646

Sat 90 86 88 88.000 ÷ 71.571 = 1.2295

Sun 36 40 44 40.000 ÷ 71.571 = 0.5589

Mon 55 52 50 52.333 ÷ 71.571 = 0.7312

Overall Avg 71.571 7.0000

Seasonal RelativesSeasonal relatives

The seasonal percentage used in the multiplicative seasonally adjusted forecasting model

Using seasonal relatives To deseasonalize data

Done in order to get a clearer picture of the nonseasonal components of the data series

Divide each data point by its seasonal relative To incorporate seasonality in a forecast

Obtain trend estimates for desired periods using a trend equation

Add seasonality by multiplying these trend estimates by the corresponding seasonal relative

Seasonal Relatives ExampleExample 7, page 149

A coffee shop owner wants to predict quarterly

demand for hot chocolate for periods 9 and 10, which

happen to be the 1st and 2nd quarters of a particular

year. The sales data consist of both trend and

seasonality. The trend portion of demand is projected

using the equation Ft = 124 + 7.5 t. Quarter relatives

are

Q1 = 1.20, Q2 = 1.10, Q3 = 0.75, Q4 = 0.95,

Seasonal Relatives Example (Con’d)Example 7, page 149

Use this information to deseasonalize sales for Q1 through Q8.

Period Quarter Sales ÷ Quarter Relative

= Deseasonalized sales

1 1 158.4 ÷ 1.20 = 132.0

2 2 153.0 ÷ 1.10 = 139.1

3 3 110.0 ÷ 0.75 = 146.7

4 4 146.3 ÷ 0.95 = 154.0

5 1 192.0 ÷ 1.20 = 160.0

6 2 187.0 ÷ 1.10 = 170.0

7 3 132.0 ÷ 0.75 = 176.0

8 4 173.8 ÷ 0.95 = 182.9

Seasonal Relatives Example (Con’d)Example 7, page 149

Use this information to predict for periods 9 and 10.

F9 = 124 +7.5( 9) = 191.5 F10= 124 +7.5(10) = 199.0

Multiplying the trend value by the appropriate quarter relative yields a forecast that includes both trend and seasonality.

Given that t =9 is a 1st quarter and t = 10 is a 2nd quarter.

The forecast demand for period 9 = 191.5(1.20) = 229.8 The forecast demand for period 10 = 199.0(1.10) = 218.9

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