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McGraw-Hill/Irwin Copyright 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 3
Forecasting
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Chapter 3: Learning Objectives
You should be able to:
List the elements of a good forecast
Outline the steps in the forecasting process
Describe qualitative forecasting techniques and their
advantages and disadvantages Compare and contrast qualitative and quantitative
approaches to forecasting
Briefly describe averaging techniques, trend and seasonaltechniques, and regression analysis, and solve typical
problems Describe three measures of forecast accuracy
Describe two ways of evaluating and controlling forecasts
Identify the major factors to consider when choosing aforecasting technique
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Forecast
Forecast a statement about the future valueof a variable of interest
We make forecasts about such things as weather,
demand, and resource availability Forecasts are an important element in making
informed decisions
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An Important Input to Decision Making
The primary goal operations and supply chainmanagement is to match supply to demand
A demand forecast is essential for determining how
much supply will be needed to match demand: Budget preparation
Capacity decisions (e.g., staff and equipment)
Purchasing decisions
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Forecast Uses
Plan the system Generally involves long-range plans related to:
Types of products and services to offer
Facility and equipment levels
Facility location
Plan the use of the system Generally involves short- and medium-range plans related to:
Inventory management
Workforce levels
Purchasing
Budgeting
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Elements of a Good Forecast
The 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
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Steps in the Forecasting Process
1. Determine the purpose of the forecast
2. Establish a time horizon
3. Select a forecasting technique
4. Obtain, clean, and analyze appropriate data
5. Make the forecast
6. Monitor the forecast
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Forecasting Approaches
Qualitative Forecasting
Qualitative techniques permit the inclusion of softinformationsuch as:
Human factors
Personal opinions Hunches
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 touse causal variablesto make a forecast
These techniques rely on harddata
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Judgemental Forecasting
Executive opinions
Sales force opinion
Consumer surveys
Other approaches
Delphi method
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Time-Series Behaviors
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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 Forecasts
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Assumes causal systempast ==> future
Forecasts rarely perfect because ofrandomness
Forecasts more accurate forgroups vs. individuals
Forecast accuracy decreases
as time horizon increases
I see that you will
get an A this semester.
Features of Forecasts
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Naive Forecasts
Uh, give me a minute....We sold 250 wheels last
week.... Now, next week
we should sell....
The forecast for any period equalsthe previous periods actual value.
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Simple to use Quick and easy to prepare
Easily understandable
Cannot provide high accuracy
Nave 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 Nave Forecasts
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Techniques for Averaging
Moving average
Weighted moving average
Exponential smoothing
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Muffins Cinemon buns Cupcakes
30 18 45
34 17 26
32 19 27
34 19 23
35 22 22
30 23 48
34 23 29
36 25 20
29 24 14
31 26 18
35 27 4731 28 26
37 29 27
34 31 24
33 33 22
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Moving Averages
Moving average
A technique that averages anumber of recent actual values, updated asnew values become available.
Weighted moving average More recent valuesin 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
35
37
39
41
43
45
47
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 mighthave the highest predictive value.
Therefore, we should give more weight to the morerecent time periods when forecasting.
Ft = Ft-1 + (At-1 - Ft-1)month Sales (000)
Feb 19
Mar 18
Apr 15
May 20
June 18
Jul 22
aug 20
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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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Picking a Smoothing Constant
35
40
45
50
1 2 3 4 5 6 7 8 9 10 11 12
Period
Dem
and .1
.4
Actu
al
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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 Example
t yWeek t
2Sales ty
1 1 150 150
2 4 157 314
3 9 162 4864 16 166 664
5 25 177 885
t = 15 t2 = 55 y = 812 ty = 2499( t)
2= 225
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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 -12180275 - 225
= 6.3
143.5
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Techniques for Seasonality
Seasonal variations
Regularly repeating movements in series values thatcan 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 ofvariable 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 15
2 10
6 13
4 15
14 2515 27
16 24
12 20
14 27
20 4415 34
7 17
Computedrelationship
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Forecast Accuracy
Error - difference between actual value andpredicted 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 forecast
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
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Example 10
Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*100
1 217 215 2 2 4 0.92
2 213 216 -3 3 9 1.41
3 216 215 1 1 1 0.46
4 210 214 -4 4 16 1.90
5 213 211 2 2 4 0.94
6 219 214 5 5 25 2.28
7 216 217 -1 1 1 0.46
8 212 216 -4 4 16 1.89
-2 22 76 10.26
MAD= 2.75
MSE= 10.86
MAPE= 1.28
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Controlling the Forecast
Control chart A visual tool for monitoring forecast 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.
Choosing a Forecasting
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Choosing a ForecastingTechnique
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 Smoothing
i i
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Linear Trend Equation
Si l i i
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Simple Linear Regression
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Time-Series Forecasting - Averaging
These Techniques work best when a seriestends to vary about an average Averaging techniques smooth variations in the data
They can handle step changes or gradual changes in
the level of a series Techniques
Moving average
Weighted moving average
Exponential smoothing
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Simple Linear Regression
Regression - a technique for fitting a line to aset of data points
Simple linear regression - the simplest form ofregression that involves a linear relationship betweentwo variables
The object of simple linear regression is to obtain anequation of a straight line that minimizes the sum ofsquared vertical deviations from the line (i.e., the least
squares criterion)
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Monitoring the Forecast
Tracking forecast errors and analyzing them can provide usefulinsight into whether forecasts are performing satisfactorily
Sources of forecast errors
The model may be inadequate
Irregular variations may have occurred
The forecasting technique has been incorrectly applied
Random error
Control charts are useful for identifying the presence of non-random error in forecasts
Tracking signals can be used to detect forecast bias
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Choosing a Forecasting Technique
Factors to consider Cost
Accuracy
Availability of historical data Availability of forecasting software
Time needed to gather and analyze data and preparea forecast
Forecast horizon
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Using Forecast Information
Reactive approach View forecasts as probable future demand
React to meet that demand
Proactive approach
Seeks to actively influence demand Advertising
Pricing
Product/service modifications
Generally requires either and explanatory model or a subjective
assessment of the influence on demand
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Operations Strategy
The better forecasts are, the more able organizationswill be to take advantage of future opportunities andreduce potential risks
A worthwhile strategy is to work to improve short-term forecasts
Accurate up-to-date information can have a significant effecton forecast accuracy:
Prices
Demand
Other important variables
Reduce the time horizon forecasts have to cover Sharing forecasts or demand data through the
supply chain can improve forecast quality