chapter 9 forecasting. forecasting demand why is demand forecasting important? what is bad about...
TRANSCRIPT
Chapter 9
Forecasting
Forecasting Demand
Why is demand forecasting important?
What is bad about poor forecasting?
What do these organizations forecast:• Sony (consumer products division)• Foley’s• Dallas Area Rapid Transit (DART)• UTA
Questions in Demand Forecasting
For a particular product or service:• What exactly is to be forecasted?• What will the forecasts be used for?• What forecasting period is most useful?• What time horizon in the future is to be
forecasted?• How many periods of past data should be used?• What patterns would you expect to see?• How do you select a forecasting model?
Demand Management
Recognizing and planning for all sources of demandCan demand be controlled or influenced?• appointment schedules
– doctor’s office– attorney– SAM telephone registration
• sales promotions– restaurant discounts before 6pm– video rental store discounts on Tuesdays– golf course discounts if you start playing after 4pm– theater matinee movie discounts
Qualitative vs. QuantitativeForecasting Methods
Some Qualitative Methods:• Experienced guess/judgement• Consensus of committee• Survey of sales force• Survey of all customers• Historical analogy
– new products• Market research
– survey a sample of customers– test market a product
Steps for Quantitative Forecasting Methods
1. Collect past data—usually the more the better
2. Identify patterns in past data
3. Select one or more appropriate forecasting methods
4. Forecast part of past data with each method– Determine best parameters for each method– Compare forecasts with actual data
5. Select method that had smallest forecasting errors on past data
6. Forecast future time periods
7. Determine prediction interval (forecast range)
8. Monitor forecasting accuracy over time– Tracking signal
Types of Quantitative Forecasting Methods
Pattern Projection– time series regression– trend or seasonal models
Data Smoothing– moving average– exponential smoothing
Causal– multiple regression
Data Pattern Components
Sales
Time
LEVEL
Sales
Time
TREND
Sales
Time
SEASONALITY
Sales
Time
CYCLICALITY
Sales
Time
NOISE
De
c
De
c
De
c
19
80
19
86
Identifying Data Patterns for Time Series
Always Plot Data First– After plotting data, patterns are often obvious.
Average or level– Use mean of all data
Trend– Use time series regression – slope is trend – time period is
independent variableSeasonality
– Deseasonalize the dataCyclicality
– Similar to deseasonalizingRandom noise
– No pattern – try to eliminate in forecasts
Forecast Accuracy
n
EMAD
n
tt
1 Deviation AbsoluteMean
tperiodfor forecast
tperiodfor demand actual or
tperiodfor error forecast
t
ttttt
t
F
ADFDE
E
Forecast Accuracy
n
EME
n
EMSE
n
tt
n
tt
1
1
2
(Bias)Error Mean
Error SquaredMean
Forecast Accuracy Example
Period At Ft Et |Et| (Et)2
1 32 30
2 28 31
3 31 33
4 34 35
5 34 33
6 36 34
Totals:
Forecast Accuracy Example
Bias =
MAD =
MSE =
Quantity of Electric Irons Shipped by U.S. Mfgs.
0
2
4
6
8
10
12
14
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
mill
ion
un
its
Electric Irons Example -- Data
Year Qty Year Qty
1979 12.079 1984 7.843
1980 11.478 1985 6.834
1981 11.013 1986 7.660
1982 6.616 1987 5.918
1983 7.279 1988 7.115
10-year average =
Last-7-year average =
Do time series regression analysis
Y = a + bX
Y = dependent variable (actual sales)
X = independent variable (time period in this case)
a = y-intercept (value of Y when X=0)
b = slope or trend
where N = number of periods of data
N
Xb
N
Ya
XXN
YXXYNb 22
Electric Irons Example
X Y X2 XY
4 6.616 16 26.46
5 7.279 25 36.40
6 7.843 : :
7 6.834 : :
8 7.660 : :
9 5.918 : :
10 7.115 : :
== ===== === =====
49 49.265 371 343.45
b =
a =
Y =
Y11 =
Y12 =
Moving Company Sales
0
50
100
150
200
250
Sp 19
88Sum Fall W
in
Sp 19
89Sum Fall W
in
Sp 19
90Sum Fall W
in
Sp 19
91Sum Fall W
in
Nu
mb
er
of
Tru
ck
s L
ea
se
d
Overlay the Years
0
50
100
150
200
250
Spring Summer Fall Winter
Nu
mb
er
of
Tru
cks
Le
ase
d
1988
1989
1990
1991
Seasonality and Trend Patterns (Seasonalized Regression)
Steps:
1. Deseasonalize the data to remove seasonality– divide by seasonal index (SI)
2. Use regression to model trend
3. Make initial forecasts to project trend
4. Seasonalize the forecast– multiply by SI
Moving Company Example
Spring Summer Fall Winter
1988 90 160 70 120 Overall Avg.
1989 130 200 90 100 2020/16
1990 80 170 130 140 = 126.25
1991 130 210 80 120
Total: 430 740 370 480
Avg: 107.5 185 92.5 120
SI:
Deseasonalize the Data
Spring Summer Fall Winter
1988 105.7* 109.2 95.5 126.3
1989 152.7 136.5 122.8 105.2
1990 94.0 116.0+ 177.4 147.3
1991 152.7 143.3 109.2 126.3
* Spring 1988: 90/.851 = 105.7+ Summer 1990: 170/1.465 = 116.0
Perform Time Series Regression
X Y X2 XY
1 105.7 1 105.7
2 109.2 4 218.4
3 95.5 9 286.6
4 : : :
: : : :
16 126.3 256 2020.0
=== ====== ===== =======
136 2,020.0 1,496 17,773.5 Totals
b =
a =
Y =
N
Xb
N
Ya
XXN
YXXYNb 22
Make initial forecasts:
Y17 =
Y18 =
Y19 =
Y20 =
Make final forecasts: (Seasonalize F = Y x SI)
F17 =
F18 =
F19 =
F20 =
Gasoline Service Station Monthly Sales
6
7
8
9
10
11
12
13
0 6 12 18 24 30 36 42 48 54 60 66 72 78
month
bill
ion
$
Gasoline Service Station Monthly Sales
6
7
8
9
10
11
12
13
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
month
bill
ion
$
1985
1986
1987
1988
1989
1990
Deseasonalized Sales
6
7
8
9
10
11
12
13
0 6 12 18 24 30 36 42 48 54 60 66 72 78
month
bill
ion
$
Regression Line
6
7
8
9
10
11
12
13
0 6 12 18 24 30 36 42 48 54 60 66 72 78
month
bill
ion
$
Final Forecasts
6
7
8
9
10
11
12
13
0 6 12 18 24 30 36 42 48 54 60 66 72 78
month
bill
ion
$
Actual Sales
6
7
8
9
10
11
12
13
0 6 12 18 24 30 36 42 48 54 60 66 72 78
month
bill
ion
$
Past Sales Forecasts Actuals
Forecast Ranging
Forecasts are rarely perfect!
A forecast range reflects the degree of confidence that you have in your forecasts.
Forecast ranging allows you to estimate a prediction interval for actual demand
“There is a ___% probability that actual demand will be within the upper and lower limits of the forecast range.”
Standard Error of the Forecast(a measure of dispersion of the forecast errors)
Upper Limit = Fi + t(syx)
Lower Limit = Fi - t(syx)
Need desired level of significance (α) and degrees of freedom (df) to look up t in table
2n
xybyays
2
yx
Forecast Confidence Intervals(Forecast Ranging)
LowerLimit
UpperLimit
Ft
t(Syx)α/2 α/2
(1 – α)
Actual Salesin Future
t-statistic and degrees of freedom
For a confidence interval of 95%,α = .05 (.025 in each tail), and df=16
From table, t =
Why does df = n-2 for simple regression?
If the forecast was from a multiple regression model with 3 independent variables, what would be the degrees of freedom? df = n - __
Example: Judy manages a large used car dealership that has experienced a steady growth in sales during the last few years. Using time series regression and sales data for the last 20 quarters, Judy obtained a forecast of 800 car sales for next quarter. With her model and the past data the standard error of the forecast was 50 cars. What are the limits for a 95% forecast range? for an 80% forecast range?
Example: A manager’s forecast of next month’s sales of product Q was 1500 units using time series regression based on the last 24 months of sales, which had a standard forecast error of 29 units. Her boss asked how sure she was that actual sales would be within 50 units of her forecast.
Short Range Forecasting
• A few days to a few months• Assumes there are no patterns in the data• Random noise has a greater impact in the short
term• These approaches try to eliminate some of the
random noise• Random walk, moving average, weighted
moving average, exponential smoothing
Random Walk
The next forecast is equal to the last period’s actual value
Period Sales Forecast
1 21
2 30
3 27
4 ?
Moving Average Method
The next forecast is equal to an average of the last AP periods of actual data
Period Sales AP=4 AP=3 AP=2
1 21
2 28
3 35
4 30
5 ?
Impulse Response – how fast the forecasts react to changes in the data
The higher the value of AP, the less the forecast will react to changes in the data, so the lower the impulse response is.
Noise Dampening – how much the forecasts are smoothed
Noise dampening is the opposite of impulse response.
A moving average model with AP=1 has high impulse response and low noise dampening characteristics.
Weighted Moving Average method
Like the moving average method except that each of the AP periods can have a different weight
Actual AP=4Period Sales Weight 1 21 .1 2 28 .15 3 35 .25 4 30 .5 5 ?
Usually the recent periods have more weight
Exponential Smoothing
Most common short-term quantitative forecasting method (especially for forecasting inventory levels)
Why?– surprisingly accurate– easy to understand– simple to use– very little data is stored
Need 3 pieces of data to make forecast1. most recent forecast2. actual sales for that period3. smoothing constant (α)
Exponential Smoothing method
– gives a different weight to each period
Ft = Ft-1 + α(At-1 – Ft-1)
α is the smoothing parameter and is between 0 and 1
Interpretation: the next forecast equals last period’s forecast plus a percentage of last period’s forecasting error.
Alternative formula:
Ft = αAt-1 + (1 - α)Ft-1(rearranging terms)
Example: assume α = 0.3
We must assume a forecast for an earlier period
Period Sales Forecast
1 21
2 24
3 23
4 19
5 22
6 ?
Find best value for α by trial and error
The larger α is, the more weight that is placed on the more recent periods’ actual values, so the higher the impulse and the lower the noise dampening.
Tracking Signal
After a forecasting method has been selected, tracking signal is used to monitor accuracy of the method as time passes
Particularly good at identifying underforecasting or overforecasting trends
Tracking Signal =
Ideal value for tracking signal is ___
MAD
)(E Errors of Sum t
Guidelines would be used if the value exceeds specified limits
Example: Suppose exponential smoothing is used (α = .2)
If |TS| < 2.3 then do not change α
If |TS| > 2.3 then increase α by .1
If |TS| > 3.0 then increase α by .3
If |TS| > 3.6 then increase α by .5
After tracking signal goes back down, restore original value of α or calculate new α
Double Exponential Smoothing(Exponential Smoothing with Trend)
Two smoothing constants are used:
α smoothes out random variations
β smoothes out trends
An alternative to time series regression
Especially useful if there is much random variation
Winter’s Exponential Smoothing
Accounts for trend and seasonality
Three smoothing constants are usedα smoothes out random variationsβ smoothes out trendsγ smoothes out seasonality
There are many other variations of exponential smoothing
Box-Jenkins Forecasting Approach
Relatively accurate, but complex and time consuming to use
Needs at least 60 points
Good choice if there are not many time series to forecast, and accuracy is very important
Works best when random variation is a small component
Example: monthly automobile registrations in U.S.
Forecast = Dt + Dt-11 – Dt-12 – 0.21Et – 0.21Et-1
– 0.85Et-11 + 0.18Et-12 + 0.22Et-13
where Dt = Actual demand for time period t
Et = Error term for time period t
Focus Forecasting(Forecasting Simulation)
Bernard Smith at American Hardware Supply developed this method to make forecasts for 100,000 items
Based on 2 principles:– sophisticated methods don’t always work better– no single method works best for all items
Buyers tended not to use the previous exponential smoothing model because they did not trust or understand it. Instead, they were making up their own simple rule-of-thumb approaches.
Smith selected 7 forecasting methods to use, such as 1. sales = last month’s sales plus a percentage2. sales = sales for same month last year plus a %3. 2-month moving average4. exponential smoothingetc. (most were relatively simple)
All methods were used to forecast each product.Whichever method worked best for the previous month,
that method was used to forecast the next month.
Approach worked very well, and people understood and used it. Smith wrote a popular book describing his approach and success.
Multiple Regression ForecastingSales = f($advertising, #salespeople, $price)
Sales Adv People Price
5200 350 18 53
5600 520 18 52
5100 400 15 54
3800 320 13 64
5200 410 16 51
4900 290 17 60
5200 390 17 54
5400 470 20 55
4700 450 14 61
5000 500 15 58
5100 470 18 60
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.952
R Square 0.907
Adjusted R Square 0.867
Standard Error 170.988
Observations 11
ANOVA
df SS MS F Significance F
Regression 3 1991704.974 663901.7 22.708 0.00055
Residual 7 204658.662 29236.95
Total 10 2196363.636
Coefficients Standard Error t Stat P-value
Intercept 5839.347 1236.003 4.724 0.002
Adv 1.742 0.765 2.277 0.057
People 100.207 30.723 3.262 0.014
Price -56.478 14.999 -3.765 0.007
Multiple Regression Example
Suppose the manager wants to
forecast sales if $430 in advertising,
19 salespeople, and a price of $64
per unit are planned.
Forecasting equation:
Sales = 5839.347 + 1.742(adv) + 100.207(people) – 56.478(price)
Sales =
Sales =
Coefficients
Intercept 5839.347
Adv 1.742
People 100.207
Price -56.478