3-1forecasting. 3-2forecasting forecast: a statement about the future value of a variable of...
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3-1 Forecasting
Forecasting
3-2 Forecasting
FORECAST: 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 MIS Operations Product / service design
3-3 Forecasting
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 New products and services
Uses of ForecastsUses of Forecasts
3-4 Forecasting
Assumes causal systempast ==> future
Forecasts rarely perfect because of randomness
Forecasts more accurate forgroups vs. individuals
Forecast accuracy decreases as time horizon increases I see that you will
get an A this semester.
3-5 Forecasting
Elements of a Good ForecastElements of a Good Forecast
Timely
AccurateReliable
Mea
ningfu
l
Written
Easy
to u
se
3-6 Forecasting
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”
3-7 Forecasting
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
3-8 Forecasting
Judgmental ForecastsJudgmental Forecasts
Executive opinions Sales force opinions Consumer surveys Outside opinion Delphi method
Opinions of managers and staff Achieves a consensus forecast
3-9 Forecasting
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 Random variations - caused by chance
3-10 Forecasting
Forecast VariationsForecast Variations
Trend
Irregularvariation
Seasonal variations
908988
Figure 3.1
Cycles
3-11 Forecasting
Naive ForecastsNaive Forecasts
Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....
The forecast for any period equals the previous period’s actual value.
3-12 Forecasting
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
3-13 Forecasting
Techniques for AveragingTechniques for Averaging
Moving average
Weighted moving average
Exponential smoothing
3-14 Forecasting
Moving AveragesMoving Averages
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.
MAn = n
Aii = 1n
3-15 Forecasting
Moving AveragesMoving Averages
Moving average –
MAn = n
Aii = 1n
Period Sales Average Forecast for next period1 402 413 42 123/3 414 ?5 ?6 ?
3-16 Forecasting
Moving AveragesMoving Averages
Moving average –
MAn = n
Aii = 1n
Period Sales Average Forecast for next period Actual1 40 412 41 423 42 123/3 41 424 425 ?6 ?
3-17 Forecasting
Moving AveragesMoving Averages
Moving average –
MAn = n
Aii = 1n
Period Sales Average Forecast for next period Actual1 40 412 41 423 42 123/3 41 424 42 125/3 41.67 445 446 ?
3-18 Forecasting
Moving AveragesMoving Averages
Moving average –
MAn = n
Aii = 1n
Period Sales Average Forecast for next period Actual1 40 412 41 423 42 123/3 41 424 42 125/3 41.67 445 44 128/3 42.67 436 ?
3-19 Forecasting
Moving AveragesMoving Averages
Moving average –
MAn = n
Aii = 1n
Period Sales Average Forecast for next period Actual1 40 412 41 423 42 123/3 41 424 42 125/3 41.67 445 44 128/3 42.67 436 43 129/3 43 43
3-20 Forecasting
Simple Moving AverageSimple Moving Average
MAn = n
Aii = 1n
35
37
39
41
43
45
47
1 2 3 4 5 6 7 8 9 10 11 12
Actual
MA3
MA5
3-21 Forecasting
Weighted Moving AveragesWeighted Moving Averages
Weighted Moving average –
WMAn = A*wi
i = 1n
Period Sales Weight Result Forecast Actual1 40 20%2 41 30%3 42 50%4 ?5 ?6 ?
3-22 Forecasting
Weighted Moving AveragesWeighted Moving Averages
Weighted Moving average –
WMAn = A*wi
i = 1n
Period Sales Weight Result Forecast Actual1 40 20% 82 41 30% 12.33 42 50% 21 41.3 424 ?5 ?6 ?
3-23 Forecasting
Weighted Moving AveragesWeighted Moving Averages
Weighted Moving average –
WMAn = A*wi
i = 1n
Period Sales Weight Result Forecast Actual1 402 41 20% 8.23 42 30% 12.64 42 50% 21 41.8 445 ?6 ?
3-24 Forecasting
Weighted Moving AveragesWeighted Moving Averages
Weighted Moving average –
WMAn = A*wi
i = 1n
Period Sales Weight Result Forecast Actual1 402 413 42 20% 8.44 42 30% 12.65 44 50% 22 43 436 ?
3-25 Forecasting
Weighted Moving AveragesWeighted Moving Averages
Weighted Moving average –
WMAn = A*wi
i = 1n
Period Sales Weight Result Forecast Actual1 402 413 424 42 20% 8.45 44 30% 13.26 43 50% 21.5 43.1 43
3-26 Forecasting
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.
Ft = Ft-1 + (At-1 - Ft-1)
3-27 Forecasting
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)
3-28 Forecasting
Exponential SmoothingExponential Smoothing
Ft = Next PeriodFt-1= Previous PeriodSmoothing ConstantAt-1 = Actual Result Previous Period
Ft = Ft-1 + (At-1 - Ft-1)
3-29 Forecasting
Exponential Smoothing - ProblemExponential Smoothing - Problem
Ft = Result of formulaFt-1= 42Smoothing = .10At-1 = 44
Ft = Ft-1 + (At-1 - Ft-1)
3-30 Forecasting
Exponential Smoothing - ProblemExponential Smoothing - Problem
Ft = 42 + .10(44-42)Ft = 42 + .10(2)Ft = 42 + .20Ft = 42.20
Ft = Ft-1 + (At-1 - Ft-1)
3-31 Forecasting
Exponential Smoothing - ProblemExponential Smoothing - Problem
Ft = 43 + .10(42.20-43)Ft = 43 + .10(-.80)Ft = 43 + -.080Ft = 42.92
Ft = Ft-1 + (At-1 - Ft-1)
3-32 Forecasting
Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87
10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92
Example 3 - Exponential SmoothingExample 3 - Exponential Smoothing
3-33 Forecasting
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
3-34 Forecasting
Common Nonlinear TrendsCommon Nonlinear Trends
Parabolic
Exponential
Growth
Figure 3.5
3-35 Forecasting
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
3-36 Forecasting
Calculating a and bCalculating a and b
b = n (ty) - t y
n t2 - ( t)2
a = y - b t
n
3-37 Forecasting
Linear Trend Equation ExampleLinear Trend Equation Example
t yW e e k t 2 S a l e s t y
1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5
t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5
3-38 Forecasting
Linear Trend CalculationLinear Trend Calculation
y = 143.5 + 6.3t
a = 812 - 6.3(15)
5 =
b = 5 (2499) - 15(812)
5(55) - 225 =
12495-12180
275 -225 = 6.3
143.5
3-39 Forecasting
Associative ForecastingAssociative Forecasting
Predictor variables - used to predict values of variable interest
Regression - technique for fitting a line to a set of points
Least squares line - minimizes sum of squared deviations around the line
3-40 Forecasting
Linear Model Seems ReasonableLinear Model Seems Reasonable
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
3-41 Forecasting
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
Mean Absolute Percent Error (MAPE)
Average absolute percent error
3-42 Forecasting
MAD, MSE, and MAPEMAD, MSE, and MAPE
MAD = Actual forecast
n
MSE = Actual forecast)
-1
2
n
(
MAPE = Actual forecas
tn
/ Actual*100)
3-43 Forecasting
Example 10Example 10
Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*1001 217 215 2 2 4 0.922 213 216 -3 3 9 1.413 216 215 1 1 1 0.464 210 214 -4 4 16 1.905 213 211 2 2 4 0.946 219 214 5 5 25 2.287 216 217 -1 1 1 0.468 212 216 -4 4 16 1.89
-2 22 76 10.26
MAD= 2.75MSE= 10.86
MAPE= 1.28
3-44 Forecasting
Controlling the ForecastControlling the Forecast
Control chart A visual tool for monitoring forecast errors Used to detect non-randomness in errors
Forecasting errors are in control if All errors are within the control limits No patterns, such as trends or cycles, are
present
3-45 Forecasting
Sources of Forecast errorsSources of Forecast errors
Model may be inadequate Irregular variations Incorrect use of forecasting technique
3-46 Forecasting
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
3-47 Forecasting
Exponential SmoothingExponential Smoothing
3-48 Forecasting
Linear Trend EquationLinear Trend Equation
3-49 Forecasting
Simple Linear RegressionSimple Linear Regression