3-1 forecasting i see that you will get an a this semester. 10 th ed
TRANSCRIPT
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Forecasting
I see that you willget an A this semester.
10th ed.
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FORECAST: A statement about the future value of a
variable of interest such as demand. Forecasting is used to make informed
decisions. Long-range Short-range
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Assumes causal systempast ==> future
Forecasts rarely perfect because of randomness
Forecasts more accurate forgroups vs. individuals
Forecast accuracy decreases as time horizon increases
Features of ForecastsFeatures of Forecasts
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Uses of ForecastsUses of Forecasts
Forecasts affect decisions and activities throughout an organization Accounting, finance Human resources Marketing MIS Operations Product / service design
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Examples of Forecasting UsesExamples of Forecasting Uses
Accounting Cost/profit estimates
Finance Cash flow and funding
Human Resources Hiring/recruiting/training
Marketing Pricing, promotion, strategy
MIS IT/IS systems, services
Operations Schedules, MRP, workloads
Product/service design Timing of new products and services
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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 Obtain, clean and analyze data
Step 5 Make the forecast
Step 6 Monitor the forecast
“The forecast”
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Types of ForecastsTypes of Forecasts Judgmental - uses subjective inputs (e.g., sales force
estimates).
Time series - uses historical data assuming the future will be like the past. Time could be in weeks, months, years, etc., and is based on t=1,2,3,…
Associative models - uses explanatory variables to predict the future. It suggests a causal relationship, such as personal consumption being based on per capita income of households.
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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 that are not random Random variations - caused by chance
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Forecast VariationsForecast Variations
Trend
Irregularvariation
Seasonal variations
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Cycles
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Some Common Time Series Techniques Some Common Time Series Techniques or Time Series Forecasting Modelsor Time Series Forecasting Models
Naïve forecasts
Moving average
Weighted moving average
Exponential smoothing
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Naive ForecastsNaive Forecasts
The forecast for any period equals the previous period’s actual value.
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Simple to use Virtually no cost Quick and easy to prepare Data analysis is nonexistent Easily understandable Cannot provide high accuracy Can be a standard for accuracy
Naïve ForecastsNaïve Forecasts
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Ft = At-1
Formula for Naïve ForecastsFormula for Naïve Forecasts
This is the forecasting that is the most responsive to changes in the past actual demand.
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Moving Average FormulaMoving Average Formula
Moving average – A technique that averages a number of recent actual values, updated as new values become available.
Weighted moving average – More recent values in a series are given more weight in computing the forecast.
Ft = MAn= n
At-n + … At-2 + At-1
Ft = WMAn= wnAt-n + … wn-1At-2 + w1At-1
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Simple Moving AverageSimple Moving Average
35
37
39
41
43
45
47
1 2 3 4 5 6 7 8 9 10 11 12
Actual Demand
MA3
MA5
Ft = MAn= n
At-1 + At-2 + … At-n
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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 = Ft-1 + (At-1 - Ft-1)
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Exponential Smoothing FormulaExponential Smoothing Formula
• 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.
The symbol “α” is the Greek letter “alpha.” Alpha is called the smoothing constant. Note that alpha varies from zero to one.
Ft = Ft-1 + (At-1 - Ft-1)
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Exponential SmoothingExponential Smoothing
iti
ttt
ttt
AAAA
FAF
111
1
22
1
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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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900
950
1000
1050
1100
1150
1200
1250
1300
1350
1400
April July October January
Demand
F (.05)
F(.2)
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Homework Problem
Referring to page 118 in the text, do problems 2a and 2b, but skip problem 2b(1) which asks for a linear trend equation.
Complete and partial solutions of homework problems are found on the slides at the end of this session.
For this problem and for all homework problems, do not go to the solutions until you have made a strong effort tosolve the problems.
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Linear Trend EquationLinear Trend Equation
Ft = Forecast for period t t = The time period being forecasted a = Value of Ft at t = 0 b = Slope of the line
Ft = Yt = a + bt
0 1 2 3 4 5 t
Ft
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Calculating a and bCalculating a and b
b = n (ty) - t y
n t2 - ( t)2
a = y - b t
n
Yt = a + bt
where b and a follow from the following formulae:
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79.55538510
996555958102
22
ttn
YttYnb
78.67
10
5579.5996
n
tbYa
Linear Trend Equation Linear Trend Equation ExampleExample
Calculations of b and a are from the sums given in the table on the left.
Period (t) Sales (Yt) t*Y t squared
1 67 67 12 74 148 43 102 305 94 87 346 165 106 530 256 86 516 367 117 817 498 113 904 649 130 1168 81
10 116 1156 10055 996 5958 385
n = 10 Ft = Yt = a + bt
Ft = Yt = a + bt = 67.78 + 5.79t
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0
20
40
60
80
100
120
140
160
180
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Actual
Trend
Plot of Previous SlidePlot of Previous Slide
Y
t
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Homework Problem
Referring to page 118 in the text, do 2b(1), which asks for a linear trend equation. Also,do problem 2c. However, change problem 2c to read as follows:
“Which method seems MOST appropriate?Why?”
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Associative ForecastingAssociative Forecasting
Associative models - uses explanatory variables to predict the future. It suggests a causal relationship, such as personal consumption being based on per capita income of households
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Example of an Associative Example of an Associative Forecast: Using x to Predict yForecast: Using x to Predict y
A straight line is fitted to a set of sample points.
0
10
20
30
40
50
0 5 10 15 20 25
X Y7 152 106 134 15
14 2515 2716 2412 2014 2720 4415 347 17
Computedrelationship
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Example of an Associative Forecast Equation for Automobiles(with several variables, and nonlinear)
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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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Some Measures of Some Measures of Forecasting AccuracyForecasting Accuracy
MAD = Actual forecast
n
MSE = Actual forecast)
-1
2
n
(
Note that the errors are taken for each of the past n periods where the actual demand is known.
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Some Characteristics Some Characteristics of MAD and MSEof MAD and MSE
MAD Easy to compute Weights errors linearly
MSE Squares error More weight to large errors
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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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The next two slides ask some basic questions about forecasting, and give some examples of measuring forecasting error. These slides make up an in-class assignment. You can try to answer thequestions on the slides. However, if you have difficulty with allor some of the questions, we will do them in class. At least become familiar with the questions before the next class.
If you find the next two slides difficult to read, simply magnify the size of the slides. If you can, please try to print a hardcopy of the nexttwo slides and bring them to class. If you can set the resolution of your printer, it is suggested that you set it to a high resolution for the bestprinted copy.
In-class assignment
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Choosing a Forecasting Choosing a Forecasting TechniqueTechnique
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
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Good Operations StrategyGood Operations Strategy
Understand that forecasts are the basis for many decisions
Work to improve short-term forecasts Understand that accurate short-term
forecasts have benefits for the following: Profits Lower inventory levels Reduce inventory shortages Improve customer service levels Enhance forecasting credibility
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Supply Chain ForecastsSupply Chain Forecasts
Sharing forecasts with suppliers can Improve forecast quality in the supply chain Lower costs Lead to shorter lead times
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Common Nonlinear TrendsCommon Nonlinear Trends
Parabolic
Exponential
Growth
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Exponential SmoothingExponential Smoothing
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Linear Trend EquationLinear Trend Equation
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Simple Linear RegressionSimple Linear Regression
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Homework Problem Solutions
Month
Sales
F M A M J J A S
20
0
2a
3-50
50.)28(28)140(7
)132(28)542(7
)t(tn
YttYnb
22
86.167
)28(50.132
n
tbYa
2b(1)
Hence, n = 7, t = 28, t2 = 140
t Y tY t2
1 19
19
1
2 18
36
4
3 15
45
9
4 20
80
16
5 18
90
25
6 22
132
36
7 20
140
49
28 132
542
140
For the September forecast, t = 8, and Yt = 16.86 + .50(8) = 20.86
Therefore, Yt = 16.86 + .50t
To solve this problem, we need to plugthe appropriate values into the equation Ft = Yt = a + bt
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195
2022182015MA5
2b(2)
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Ft = Ft-1 + (At-1 - Ft-1)2b(3)
Month Forecast = F(old) + .20[Actual – F(old)]
April 18.8 = 19 + .20[ 18 – 19 ]
May 18.04 = 18.8 + .20[ 15 – 18.8 ]
June 18.43 = 18.04 + .20[ 20 – 18.04 ]
July 18.34 = 18.43 + .20[ 18 – 18.43 ]
August 19.07 = 18.34 + .20[ 22 – 18.34 ]
September 19.26 = 19.07 + .20[ 20 – 19.07 ]
Answer is 19.26 (or actually, 19,260 units).
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Ft = At-1
This formula is telling us that the forecast in period t is simply the actual demand for period t-1, or simply, the actual demand of the previous period. For the September forecast, the answer would be the actual demand in August.
Hence, the answer is 20 (or 20,000 units)
2b(4)
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2b(5)2b(5)
Ft = WMAn= wnAt-n + … wn-1At-2 + w1At-1
= .6 (20) + .3(22) + .1(18) = 20.4, (or 20,400 units)
Note that the more recent actual demand values are usually given more weight in computing the forecast.
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2c
Change this problem to read “which method seems the most appropriate?”
To logically find the answer, go back to the plot in 2a, and make your best guess as to where the Septemberactual demand might be on the plot or graph. Hence, you need to see a pattern on the plot.
Once you have September on the plot, find the method from part b of the problem which comesthe closest to your guess on the plot.
The answer should be the linear trend equation.
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See you next class