Post on 12-Jan-2016
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Forecasting
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Learning Objectives
• List the elements of a good forecast.
• Outline the steps in the forecasting process.
• Describe at least three qualitative forecasting techniques and the advantages and disadvantages of each.
• Compare and contrast qualitative and quantitative approaches to forecasting.
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Learning Objectives
• Briefly describe averaging techniques, trend and seasonal techniques, and regression analysis, and solve typical problems.
• Describe two measures of forecast accuracy.
• Describe two ways of evaluating and controlling forecasts.
• Identify the major factors to consider when choosing a forecasting technique.
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FORECAST:• The art and science of predicting future (It may
involve using statistics and mathematical model, or may be a subjective prediction).
• Forecasting is used to make informed decisions.
• Short-range (up to 1 Yr): planning purchasing, job scheduling, workforce levels, job assignment.
• Medium-rang (3 Mth – 3 Yr): sales planning, production planning and budgeting.
• Long-range (more than 3 Yr): planning for new products, facility location or expansion, and R&D.
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Forecasts• Forecasts affect decisions and activities
throughout an organization– Accounting, finance
– Human resources
– Marketing
– MIS
– Operations
– Product / service design
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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 Forecasts
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• Assumes causal systempast ==> future
• Forecasts rarely perfect because of randomness
• Forecasts more accurate forgroups cf. (compared to) individuals
• Forecast accuracy decreases as time horizon increases
I see that you willget an A this semester.
Features of Forecasts
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Elements of a Good Forecast
Timely
AccurateReliable
Be Writ
ten
Easy
to u
se
Mea
ningfu
l Units
Cost-e
ffect
ive
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6 Steps in the Forecasting Process
Step 1 Determine purpose of forecast (How/when it will be used?, Resources)
Step 2 Establish a time horizon (How long?)
Step 3 Select a forecasting technique (Moving AVG, Weighted AVG, etc)
Step 4 Obtain, clean and analyze data (eliminate outliers, incorrect data)
Step 5 Make the forecast
Step 6 Monitor the forecast (modify, revise)
“The forecast”
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Forecast 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
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MAD, MSE, and MAPE
MAD = Actual forecast
n
MSE = Actual forecast)
-1
2
n
(
MAPE = Actual forecas
t
n
/ Actual*100)
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MAD, MSE and MAPE
• MAD– Easy to compute– Weights errors linearly
• MSE– Squares error– More weight to large errors
• MAPE– Puts errors in perspective (the errors are
presented as percentage)
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Example 1
Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*1001 217 2152 213 2163 216 2154 210 2145 213 2116 219 2147 216 2178 212 216
MAD=MSE=
MAPE=
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Ans: Example 1
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
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Types 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
Qualitative method
Quantitative method
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Qualitative method (Judgmental forecast)
• Executive opinions (long-range planning, new product development)
• Sales force opinions (direct contact with customers; however, sales staff are overly influenced by recent experience)
• Consumer surveys (specific information; but money and time-consuming)
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Quantitative method
• Naïve approach
• Moving average
• Exponential smoothing
• Trend projection
• Linear regression
Time series models
Associative model
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Time 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
• Random variations - caused by chance and unusual circumstances
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Forecast Variations
Seasonal variations
Year 1Year 2Year 3
Trend
Randomvariation
Time
Cycles
Time
Month
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Naive ForecastsUh, 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.
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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 Forecasts
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• Stable time series data– F(t) = A(t-1)
• Seasonal variations– F(t) = A(t-n)
• Data with trends– F(t) = A(t-1) + (A(t-1) – A(t-2))
Uses for Naïve Forecasts
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Techniques for Averaging
• Moving average
• Weighted moving average
• Exponential smoothing
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Moving 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.
Ft = MAn= n
At-n + … At-2 + At-1
Ft = WMAn= n
wnAt-n + … wn-1At-2 + w1At-1
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Simple Moving Average
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1 2 3 4 5 6 7 8 9 10 11 12
Actual
MA3
MA5
Ft = MAn= n
At-n + … At-2 + At-1
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Exponential 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)
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Exponential 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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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
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Picking a Smoothing Constant
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40
45
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1 2 3 4 5 6 7 8 9 10 11 12
Period
Dem
and .1
.4
Actual
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Period Actual 0.05 Error 0.7 Error1 422 40 42 -2.00 42 -23 43 41.90 1.10 40.60 2.44 40 41.96 -1.96 42.28 -2.285 41 41.86 -0.86 40.68 0.326 39 41.81 -2.81 40.91 -1.917 46 41.67 4.33 39.57 6.438 44 41.89 2.11 44.07 -0.079 45 42.00 3.00 44.02 0.98
10 38 42.15 -4.15 44.71 -6.7111 40 41.94 -1.94 40.01 -0.0112 41.84 40.00
Alpha = Alpha =
Example 3 - Exponential SmoothingExample 3 - Exponential Smoothing
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Common Nonlinear Trends
Parabolic
Exponential
Growth
Figure 3.5
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Linear 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
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Calculating a and b
b = n (ty) - t y
n t2 - ( t)2
a = y - b t
n
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Linear Trend Equation Examplet y
W e e k t 2 S a l e s t y1 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
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Linear 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
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Techniques for Seasonality
• Seasonal variations– Regularly repeating movements in series
values that can be tied to recurring events.
• Seasonal relative– Percentage of average or trend
• Centered moving average– A moving average positioned at the center of
the data that were used to compute it.
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Associative 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
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Linear 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
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Linear Regression Assumptions• Variations around the line are random• Deviations around the line normally distributed• Predictions are being made only within the
range of observed values• For best results:
– Always plot the data to verify linearity– Check for data being time-dependent– Small correlation may imply that other variables
are important
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Controlling 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
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Sources of Forecast errors• Model may be inadequate
• Irregular variations
• Incorrect use of forecasting technique
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Tracking Signal
Tracking signal = (Actual-forecast)
MAD
•Tracking signal
–Ratio of cumulative error to MAD
Bias – Persistent tendency for forecasts to beGreater or less than actual values.
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Choosing 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
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Operations Strategy
• Forecasts are the basis for many decisions• Work to improve short-term forecasts• Accurate short-term forecasts improve
– Profits– Lower inventory levels– Reduce inventory shortages– Improve customer service levels– Enhance forecasting credibility
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Supply Chain Forecasts
• Sharing forecasts with supply can– Improve forecast quality in the supply chain– Lower costs– Shorter lead times
• Gazing at the Crystal Ball (reading in text)
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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