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Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
ChapChapterter
Demand Forecasting
33
Slides prepared byLaurel DonaldsonDouglas College
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Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Objectives
2
LO 1
LO 3
LO 2
LO 4
LO 5
LO 6
LO 7
LO 8
Identify uses of demand forecasts, distinguish between forecasting time frames, describe common features of forecasts, list the elements of a good forecast and steps of forecasting process, and contrast different forecasting approaches.
Describe at least three judgmental forecasting methods.
Describe the components of a time series model, and explain averaging techniques and solve typical problems.
Describe trend forecasting and solve typical problems.
Describe seasonality forecasting and solve typical problems.
Describe associative models and solve typical problems.
Describe three measures of forecast accuracy, and two ways of controlling forecasts, and solve typical problems.
Identify the major factors to consider when choosing a forecasting technique.
Identify uses of demand forecasts, distinguish between forecasting time frames, describe common features of forecasts, list the elements of a good forecast and steps of forecasting process, and contrast different forecasting approaches.
Describe at least three judgmental forecasting methods.
Describe the components of a time series model, and explain averaging techniques and solve typical problems.
Describe trend forecasting and solve typical problems.
Describe seasonality forecasting and solve typical problems.
Describe associative models and solve typical problems.
Describe three measures of forecast accuracy, and two ways of controlling forecasts, and solve typical problems.
Identify the major factors to consider when choosing a forecasting technique.
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Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
What is forecasting? Features common to all forecasts Elements of a good forecast Steps in the forecasting process Approaches to forecasting Judgmental methods Time series models Associative models Accuracy and control of forecasts Choosing a forecasting technique Excel Templates
3
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LO 1
What is Forecasting?
4
I see that you willget a 100 in OM this semester.
A demand forecast is an estimate of demand expected over a future
time period
A demand forecast is an estimate of demand expected over a future
time period
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LO 1
How big a facility do I need to manufacture a new videophone?
How much money do I need to run operations of my accounting office?
How many pairs of white shoes should I order for the summer season in my store?
How many operators should I schedule next month for my call centre?
How much lettuce should I buy for next week in my restaurant?
5
Need to FORECAST demand!Need to FORECAST demand!
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LO 1
3 Uses for Forecasts:
6
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LO 1
Features of ForecastsAssumes causal system
past ==> future
Forecasts rarely perfect because of randomness
Forecasts more accurate forgroups vs. individuals
Forecast accuracy decreases as time horizon increases
7
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LO 1
Elements of a Good Forecast
8
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LO 1
Steps in the Forecasting Process
9
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LO 1
Approaches to ForecastingJudgmental
non-quantitative analysis of subjective inputsconsiders “soft” information such as
human factors, experience, gut instinct
Judgmental non-quantitative analysis of subjective inputsconsiders “soft” information such as
human factors, experience, gut instinct
10
QuantitativeTime series models
extends historical patterns of numerical data
Associative models create equations with explanatory variables
to predict the future
QuantitativeTime series models
extends historical patterns of numerical data
Associative models create equations with explanatory variables
to predict the future
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LO 2
Judgmental Methods
Executive opinionspool opinions of high-level executiveslong term strategic or new product
development
11
Expert opinions Delphi method: iterative questionnaires
circulated until consensus is reached. technological forecasting
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LO 2
Judgmental Methods
Sales force opinionsbased on direct customer contact
12
Consumer surveysquestionnaires or focus groups
Historical analogiesuse demand for a similar product
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LO 3
What is a Time Series?Time series:
a time ordered sequence of observations
taken at regular intervals of time
Time series: a time ordered sequence of
observations taken at regular intervals of time
13
Level: (average) horizontal pattern Trend: steady upward or downward movement Seasonality: regular variations related to time of year or
day Cycles: wavelike variations lasting more than one year Irregular variations: caused by unusual circumstances,
not reflective of typical behaviour Random variations: residual variations after all other
behaviours are accounted for (called noise)
The following 6 patterns could be identified in a time series:The following 6 patterns could be identified in a time series:
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LO 3
Patterns of a Time Series
14
Year1
Year2
Year3
Year4
Seasonal peaks (winters) Trend component
Actual demand line
Dem
and
for s
now
boar
ds
Random variation
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LO 3
Time series modelsNaive methodsAveraging methods
Moving averageWeighted moving averageExponential smoothing
Trend modelsLinear and non-linear trendTrend adjusted exponential
smoothingTechniques for seasonality
Techniques for cycles
Naive methodsAveraging methods
Moving averageWeighted moving averageExponential smoothing
Trend modelsLinear and non-linear trendTrend adjusted exponential
smoothingTechniques for seasonality
Techniques for cycles
15
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LO 3
Naive Methods
Next period = last period Simple to use and understand Very low cost Low accuracy
16
211
1
:d with trenData
:s variationSeasonal
:data series timeStable
tttt
ntt
tt
AAAF
AF
AF
F = forecast A = actual
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LO 3
Naive Method - Example
17
Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....
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LO 3
Naive Method with Trend: Example
18
2 years ago we sold 50 memberships. Last year we sold 75 memberships. This year we expect to sell …
100100
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LO 3
Averaging Methods
19
111 :Smoothing
lExponentia tttt FAFF
n
nFt
periods previousin Demand
: Average
Moving
Weights
Demand Weight :
Average Moving
Weighted period period nntF
F = forecast A = actual = smoothing constant
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LO 3
Moving Average
average of last few actual data values, updated each period easy to calculate and understandsmoothes bumps, lags behind changes
choose number of periods to includefewer data points = more sensitive to
changesmore data points = smoother, less
responsive
20
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LO 3
Moving Average - ExampleCompute a three-period moving average
forecast for period 6, given the demand below
21
33.413
414043
3
415
404
433
402
421
DemandPeriod
5436
FFFF
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LO 3
Weighted Moving Average - Example Compute a 4-period weighted moving average
forecast for period 6 using a weight of 0.4 for the most recent period, 0.3 for the next, 0.2 for the next, and 0.1 for the next.
22
414.03.02.01.0
4.03.02.01.0
0.4415
0.3404
0.2433
0.1402
421
WeightDemandPeriod
54326
FFFFF
The choice of weights may involve the use of trial and error to find a suitable weighting scheme
Weights must add up to 100%
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LO 3
Moving Average Example
23
(14 + 16 + 19)/3 = 16 1/3
(16 + 19 + 23)/3 = 19 1/3
91214
(9 + 12 + 14)/3 = 11 2/3 (12 + 14 + 16)/3 = 14
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LO 3
Graph of Moving Average
24
| | | | | | | | | | | |
1 2 3 4 5 6 7 8 9 10 11 12
Qu
an
tity
30 –28 –26 –24 –22 –20 –18 –16 –14 –12 –10 –
Actual Sales
Moving Average Forecast
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LO 3
Moving Average Example
25
1 92 123 144 165 196 237 26
Period Demand Forecast
Apply weights of .5 for most recent period, then .3, then .2
[(.5 x 16) + (.3 x 14) + (.2 x 12)] = 14.6
[(.5 x 19) + (.3 x 16) + (.2 x 14)] = 17.1
[(.5 x 23) + (.3 x 19) + (.2 x16)] = 20.4
91214
[(.5 x 14) + (.3 x 12) + (.2 x 9)] = 12.4
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LO 3
Moving Average And Weighted Moving Average
26
30 –
25 –
20 –
15 –
10 –
5 –
Qu
an
tity
| | | | | | | | | | | |
1 2 3 4 5 6 7 8 9 10 11 12
Actual sales
Moving average
Weighted moving average
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LO 3
Exponential Smoothing
sophisticated weighted moving averageweights decline exponentiallymost recent data weighted most
subjectively choose smoothing constant ranges from 0 to 1 (commonly .05 to .5)
widely used easy to use easy to alter weighting 27
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LO 3
Exponential Smoothing FormulaForecast = previous forecast plus a
percentage of the forecast errorActual - Forecast is the error term is the % feedback
28
Ft = Ft-1 + (At-1 - Ft-1)
F = forecast A = actual
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LO 3
Exponential Smoothing: Alternate FormulaForecast = previous forecast plus a
percentage of the forecast error is the weight on actual demand is the weight on previous
forecast
29
Ft = (1 - Ft-1 + (At-1)
F = forecast A = actual
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LO 3
Exponential Smoothing: ExampleForecasted demand = 142 video gamesActual demand = 153Smoothing constant = .20
30
New forecast = .2 (153) + (1 - .2)(142)
= 30.6 + 113.6
= 144.2 ≈ 144 games
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LO 3
Exponential Smoothing: ExampleForecasted demand = 142 video gamesActual demand = 153Smoothing constant = .20
31
New forecast = 142 + .2 (153 - 142)
= 30.6 + 113.6
= 144.2 ≈ 144 games
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LO 3
Exponential Smoothing: Example
32
72.5859.2-580.42.95FA0.4FF644
2.5962-550.462FA0.4FF583
6260-650.460FA0.4FF552
60651
nsCalculatioForecastActualPeriod
3334
2223
1112
Prepare a forecast using smoothing constant = 0.40.
What is the starting point? average of several periods of actual data subjective estimate (for this example, use 60) first actual value (naïve approach)
Prepare a forecast using smoothing constant = 0.40.
What is the starting point? average of several periods of actual data subjective estimate (for this example, use 60) first actual value (naïve approach)
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LO 3
Week Demand1 8202 7753 6804 6555
Exponential Smoothing: Your Turn!What are the exponential smoothing
forecasts for periods 2-5 using =0.5?Use naïve approach for 1st week
What are the exponential smoothing forecasts for periods 2-5 using =0.5?
Use naïve approach for 1st week
33
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LO 3
Week Demand 0.51 820 820.002 775 820.003 680 797.504 655 738.755 696.88
Exponential Smoothing: Your Turn!
34
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LO 3
Selecting a Smoothing Constant
35
225 –
200 –
175 –
150 –| | | | | | | | |
1 2 3 4 5 6 7 8 9Period
Dem
an
d
a = .1
Actual deman
d
a = .5
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LO 3
Choosing When demand is fairly stable, use a lower
value for smoothes out random fluctuations
When demand increasing or decreasing, use a higher value for more responsive to real changes
Try to find balance trial and error can change over time.
36
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LO 3
True or False?
A moving average forecast tends to be more responsive to changes in the data series when more data points are included in the average.
False
As compared to a simple moving average, the weighted moving average is more reflective of the recent changes.
True
A smoothing constant of .1 will cause an exponential smoothing forecast to react more quickly to a sudden change than a value of .3 will.
False
37
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LO 3
Excel: Exponential Smoothing
38
Solved Problem 1: Excel Template
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LO 4
Techniques for Trend
39
– Develop an equation
that describes the trend
– Look at historical data
– Develop an equation
that describes the trend
– Look at historical data
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LO 4
Nonlinear Trends
40
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LO 4
Linear Trend Equation
– Fit a trend line to a series of historical data– Use regression to find the equation of the line
(called the Least Squares Line)
41
n
tbya
ttn
yttynb
btayt
:intercept-y
:Slope
:Equation
22
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LO 4
Linear Trend
42
Deviation
Deviation
Deviation
Deviation
Deviation
Deviation
Deviation
Time
Dem
and
Actual observation
Points on the line
btayt
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LO 4
Linear Trend: Example
43
tbtay
a
b
t
tytyt
tytyt
t 3.65.143
5.1435
153.6812
3.6225275
180,12495,12
225555
81215499,25
225
499,25581215
885251775
664161664
48691623
31441572
15011501
Salesweek
2
2
2
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LO 4
Excel - Linear Trend
44
Insert Chart
Scatter
Highlight data range
Right Click on a data point
Add TrendlineType: LinearOptions: Show equation on chart
Scatter with Trendline
y = 10.171x - 20242
0
20
40
60
80
100
120
140
160
1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
Sal
es
Or Insert Functions:
=SLOPE(Range of y's,Range of x's)
=INTERCEPT(Range of y's,Range of x's)
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LO 4
Excel - Linear Trend
45
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LO 4
Trend-Adjusted Exponential Smoothingselect values (usually through trial and
error) for = smoothing constant for average = smoothing constant for trend
estimate starting smoothed average and smoothed trend use most recent data
46
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LO 4
Trend-Adjusted Exponential Smoothing
47
TAFt+1 = St + Tt (3–6)
whereSt = smoothed average at the end of period tTt = smoothed trend at the end of period t
St = TAFt +α(At TAFt) (3–7)Tt = Tt-1 + ( St St-1 Tt-1)
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LO 4
Trend-Adjusted Forecast: Example
48
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LO 5
Techniques for SeasonalityAdditive or Multiplicative Model
quantity added to average or trendor proportion x average or trend
49time
Dem
and
Additive Model
Demand = Trend + Seasonality
Multiplicative Model
Demand = Trend x Seasonality
Multiplicative Model
Demand = Trend x Seasonality
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LO 5
Using Seasonal Relatives
Seasonal Relative (or index) = proportion of average or trend for a season in
the multiplicative modelseasonal relative of 1.2 = 20% above average
Deseasonalize remove seasonal component to more clearly see
other componentsdivide by seasonal relative
Reseasonalize adjust the forecast for seasonal componentmultiply by seasonal relative
Seasonal Relative (or index) = proportion of average or trend for a season in
the multiplicative modelseasonal relative of 1.2 = 20% above average
Deseasonalize remove seasonal component to more clearly see
other componentsdivide by seasonal relative
Reseasonalize adjust the forecast for seasonal componentmultiply by seasonal relative
50
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LO 5
Times Series Decomposition
51
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LO 5
Techniques for Seasonality - ExamplePredict quarterly demand for a certain loveseatThe series has both trend and seasonality. Quarterly relatives : Q1 = 1.20, Q2 = 1.10, Q3 = 0.75, Q4 = 0.95. Trend equation yt=124+7.5t (t = 1 in first quarter of 2003)
Predict demand for quarter 3 of 2006
52
38.17775.05.236
5.236155.7124
15 2006 of 3quarter for
15
15
F
y
t
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LO 6
Associative Forecasting
53
If I want to predict ridership originating from a If I want to predict ridership originating from a new train station, what data might I look at?new train station, what data might I look at?
1. Find (predictor) variables that are associated with ridership at other stations.
2. Associated = correlated = as one moves the other moves
3. Create a model that shows the relationship between the predictor variables and the predicted variable (e.g. ridership)
4. Technique is regression analysis• Simple linear regression with one variable• Multiple regression (can be non-linear)
5. Test the model to see which variables most useful in predicting ridership (look at r2)
6. Use the model to predict ridership, given values of the predictor variables.
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LO 6
Associative ModelsPredictor variables (x): used to predict values of
the variable of interest (y)(also called independent variables)
Predictor variables (x): used to predict values of the variable of interest (y)(also called independent variables)
54
Linear regression: process of finding a straight line that best fits a set of points on a graph (use the Least Squares Equation)
Linear regression: process of finding a straight line that best fits a set of points on a graph (use the Least Squares Equation)
Multiple regression: models with more than one predictor variable (computations complex, created with computer)
Multiple regression: models with more than one predictor variable (computations complex, created with computer)
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LO 6
Simple Linear Regression
would a linear model be reasonable?55
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
Computed relationship
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LO 6
Excel: Simple Linear Regression
56
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LO 6
Correlation and ExcelCorrelation coefficient (r): measure of the strength
of relationship between two variablesranges from -1 to +1
-1 = two variables move together in same direction+1 = two variables move together in opposite direction
=CORREL(Range of y values, Range of x values)
r2 measures proportion of variation in the values of y that is “explained” by the predictor variables in the regression modelranges from 0 to 1
higher values = more useful predictors=RSQ(Range of y values, Range of x values)
57
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LO 6
Linear Regression AssumptionsPredictions are being made only within the
range of observed valuesrelationship may be non-linear outside that rangey-intercept often not meaningful
Variations around the line are random and normally distributed
For best results:Always plot the data to verify linearitySmall correlation may imply that
other variables are important
58
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LO 7
Accuracy and Control of ForecastsError = Actual value - Forecast value
+ve = forecast too low, -ve = too highThree measures of forecasts are used:
Mean absolute deviation (MAD)Mean squared error (MSE)Mean absolute percent error (MAPE)
Control chartsplot errors to see if within pre-set control limits
Tracking signalRatio of cumulative error and MAD
Error = Actual value - Forecast value+ve = forecast too low, -ve = too high
Three measures of forecasts are used:Mean absolute deviation (MAD)Mean squared error (MSE)Mean absolute percent error (MAPE)
Control chartsplot errors to see if within pre-set control limits
Tracking signalRatio of cumulative error and MAD
59
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LO 7
Error, MAD, MSE and MAPE
60
nMAD
ForecastActual
n
MSE
2ForecastActual
%100n
Actual
Forecast Actual
MAPE
tt FAe ForecastActualError
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LO 7
MAD, MSE and MAPE
61
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LO 7
Error, MAD, MSE and MAPE: ExampleCompute MAD, MSE, and MAPE for the following data.
62
%69.43010
%90.11644214
%46.0111215
%41.1933216
%92.0422215
2104
2163
2132
2171
100A
eeeeForecastActualPeriod 2
%17.1
100
5.7
5.2
2
n
A
e
MAPE
n
eMSE
n
eMAD
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LO 7
Forecast Errors
bias = the sum of the forecast errors+ve bias = frequent underestimation-ve bias = frequent overestimation
bias = the sum of the forecast errors+ve bias = frequent underestimation-ve bias = frequent overestimation
63
possible sources of error include:Model may be inadequate (things have
changed)Incorrect use of forecasting techniqueIrregular variations
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LO 7
Controlling the Forecasting ProcessControl chart
A visual tool for monitoring forecast errorsUsed to detect non-randomness in errorsSet limits that are multiples of the √MSE
Control chartA visual tool for monitoring forecast errorsUsed to detect non-randomness in errorsSet limits that are multiples of the √MSE
64
Forecasting errors are “in control” when only random errors, no errors from identifiable causes“in control” if
All errors are within control limitsNo patterns (e.g. trends or cycles) are present
errors outside limit = need corrective action
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LO 7
Control Chart
65
0
Upper limit
Lower limit
Range of acceptable variation
Time
Err
or
Need for corrective action
Need for corrective action
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LO 7
Controlling Forecasts: Control Limits
66
Standard deviation of error
=
Control Limits = 0 ± 2 (or 3) s
s MSEe
n
2
95% of all errors should be within 2s95% of all errors should be within 2s
97.7% of all errors should be within 3s97.7% of all errors should be within 3s
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LO 7
Control Chart Example
67
s 1575
6262 5 16 2. .
Errors should be within ± 2(16.2).
Lower limit = -32.4 Upper limit = 32.4
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LO 7
Control Chart Example
68
-32
-24
-16
-8
0
8
16
24
32
0 1 2 3 4 5 6 7
All the errors are within the control limits
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LO 7
Below is a pharmacy’s actual sales and forecasted demand for a certain prescription drug for 5 months. How accurate is their forecast? Calculate MAD and MSE and create a control chart.
Below is a pharmacy’s actual sales and forecasted demand for a certain prescription drug for 5 months. How accurate is their forecast? Calculate MAD and MSE and create a control chart.
Pharmacy Forecast Control: Your Turn!
69
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LO 7
10=4
40=
n
F-A
=MADtt
10=4
40=
n
F-A
=MADtt
137.5=4
550=
n
F-A
=MSE
2
tt 137.5=
4
550=
n
F-A
=MSE
2
tt
Pharmacy Forecast Control: Your Turn!
70
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LO 7
Pharmacy Forecast Control: Your Turn!
71-23.4
-15.6
-7.8
0
7.8
15.6
23.4
0 1 2 3 4 5
All the errors are within the control limits
550137.5 11.7
4s
Errors should be within ± 2(11.7).Lower limit = -23.4 Upper limit = 23.4
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LO 7
Tracking SignalTracking signal
ratio of cumulative error to MAD can be plotted on a control chart investigate if TS > 4
72
Tracking signal = (Actual -forecast)
MAD
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LO 7
True or False?
When error values fall outside the limits of a control chart, this signals a need for corrective action
Ans: TrueWhen all errors plotted on a control chart are
either all positive, or all negative, this shows that the forecasting technique is performing adequately.
Ans: FalseA random pattern of errors within the limits of
a control chart signals a need for corrective action.
Ans: False
73
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LO 8
Choosing a Forecasting TechniqueNo single technique works in every
situationTwo most important factors
CostAccuracy
Other factors include availability of:Historical dataComputersTime needed to gather and analyze the dataForecast horizon
74
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LO 8
Choosing a Forecast Technique
75Source: J. Holton Wilson and D. Allison-Koerber, “Combining Subjective and Objective Forecasts Improves Results,” Journal of Business Forecasting Methods & Systems, 11(3) Fall 1992, p. 4.
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LO 8
Choosing a Forecast TechniqueSource: C. L. Jain, “Benchmarking Forecasting Models,” Journal of Business Forecasting Methods & Systems, Fall 2002, pp. 18–20,
30.
76
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LO 8
Which technique?Sales for a product have been fairly consistent over
several years, although showing a steady upward trend. The company wants to understand what drives sales. The best forecasting technique would be:A) trend modelsB) judgmental methodsC) moving averagesD) regression modelsE) exponential smoothing techniques
Ans: D
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Learning Checklist
Describe at least three judgmental forecasting methods.
Describe the components of a time series model, and explain averaging techniques and solve typical problems.
Describe trend forecasting and solve typical problems.
Describe seasonality forecasting and solve typical problems.
Describe associative models and solve typical problems.
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Learning Checklist Identify uses of demand forecasts Distinguish between forecasting time frames Describe common features of forecasts List the elements of a good forecast and steps
of forecasting process, Contrast different forecasting approaches. Describe three measures of forecast
accuracy, and two ways of controlling forecasts, and solve typical problems.
Identify the major factors to consider when choosing a forecasting technique.
79