1 Lecture 3 Forecasting CT – Chapter 3. 2 A statement about the future value of a variable of...
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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
35
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