FORECASTING

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Demand Management
and
FORECASTING
Operations Management
Dr. Ron Lembke
Demand Management
• Coordinate sources of demand for supply chain
to run efficiently, deliver on time
• Independent Demand
▫ Things demanded by end users
• Dependent Demand
▫ Demand known, once demand for end items is
known
Affecting Demand
• Increasing demand
▫ Marketing campaigns
▫ Sales force efforts, cut prices
• Changing Timing of demand
▫ Incentives for earlier or later delivery
▫ At capacity, don’t actively pursue more
Predicting the Future
We know the forecast will be wrong.
Try to make the best forecast we can,
▫ Given the time we want to invest
▫ Given the available data
• The “Rules” of Forecasting:
1. The forecast will always be wrong
2. The farther out you are, the worse your forecast
is likely to be.
3. Aggregate forecasts are more likely to accurate
than individual item ones
Time Horizons
Different decisions require projections about
different time periods:
• Short-range: who works when, what to make each
day (weeks to months)
• Medium-range: when to hire, lay off (months to
years)
• Long-range: where to build plants, enter new
markets, products (years to decades)
Forecast Impact
Finance & Accounting: budget planning
Human Resources: hiring, training, laying off
employees
Capacity: not enough, customers go away angry,
too much, costs are too high
Supply-Chain Management: bringing in new
vendors takes time, and rushing it can lead to
quality problems later
Qualitative Methods
• Sales force composite / Grass Roots
• Market Research / Consumer market surveys &
interviews
• Jury of Executive Opinion / Panel Consensus
• Delphi Method
• Historical Analogy - DVDs like VCRs
• Naïve approach
Quantitative Methods
Time Series Methods
0. All-Time Average
1. Simple Moving Average
2. Weighted Moving Average
3. Exponential Smoothing
4. Exponential smoothing with trend
5. Linear regression
Causal Methods
Linear Regression
Time Series Forecasting
Assume patterns in data will continue, including:
Trend (T)
Seasonality (S)
Cycles (C)
Random
Variations
All-Time Average
To forecast next period, take the average of all
previous periods
Advantages: Simple to use
Disadvantages: Ends up with a lot of data
Gives equal importance to very old data
4/7/2009
2009 Farm Angels:
Ty: 1.000, Jacob 0.833, Noah 0.667
(6 at bats)
End of 2008 season
Moving Average
Compute forecast using n most recent periods
Jan
Feb
Mar
Apr
May
Jun
Jul
3 month Moving Avg:
June forecast:
FJun = (AMar + AApr + AMay)/3
If no seasonality, freedom to choose n
If seasonality is N periods, must use N, 2N, 3N etc.
number of periods
Moving Average
Advantages:
▫
▫
▫
Ignores data that is “too” old
Requires less data than simple average
More responsive than simple average
Disadvantages:
▫
▫
▫
Still lacks behind trend like simple average,
(though not as badly)
The larger n is, more smoothing, but the more it
will lag
The smaller n is, the more over-reaction
Simple and Moving Averages
Period Demand All-Time
10
1
10
12
2
11.0
14
3
12.0
15
4
12.8
16
5
13.4
17
6
14.0
19
7
14.7
21
8
15.5
23
9
16.3
10
3MA
12.0
13.7
15.0
16.0
17.3
19.0
21.0
Centered MA
• CMA smoothes out
variability
• Plot the average of 5
periods: 2 previous, the
current, and the next two
• Obviously, this is only in
hindsight
• FRB Dalls graphs
Stability vs. Responsiveness
• Responsive
▫ Real-time accuracy
▫ Market conditions
• Stable
▫ Forecasts being used throughout the company
▫ Long-term decisions based on forecasts
▫ Don’t whipsaw those folks
Old Data
Comparison of simple, moving averages clearly
shows that getting rid of old data makes forecast
respond to trends faster
Moving average still lags the trend, but it suggests
to us we give newer data more weight, older data
less weight.
Weighted Moving Average
FJun = (AMar + AApr + AMay)/3
= (3AMar + 3AApr + 3AMay)/9
Why not consider:
FJun
= (2AMar + 3AApr + 4AMay)/9
FJun = 2/9 AMar + 3/9 AApr + 4/9 AMay
Ft = w1At-3 + w2At-2 + w3At-1
Complicated:
• Have to decide number of periods, and weights for each
• Weights have to add up to 1.0
• Most recent probably most relevant, gets most weight
• Carry around n periods of data to make new forecast
Weighted Moving Average
Period Demand 3WMA
1
10
2
12
3
14
4
15
12.6
5
16
14.1
6
17
15.3
7
19
16.3
8
21
17.8
9
23
19.6
10
21.6
Wts = 0.5, 0.3, 0.2
Setting Parameters
• Weighted Moving Average
▫ Number of Periods
▫ Individual weights
• Trial and Error
▫ Evaluate performance of forecast based on some
metric
Exponential Smoothing
Ft  Ft 1    At 1  Ft 1 
F10 = F9 + 0.2 (A9 - F9)
Ft  1   Ft 1   At 1
F10 = 0.8 F9 + 0.2 (A9 - F9)
At-1 Actual demand in period t-1
Ft-1 Forecast for period t-1

Smoothing constant >0, <1
Forecast is old forecast plus a portion of the
error of the last forecast.
Formulas are equivalent, give same answer
Exponential Smoothing
• Smoothing Constant between 0.1-0.3
• Easier to compute than moving average
• Most widely used forecasting method, because of
its easy use
• F1 = 1,050,  = 0.05, A1 = 1,000
• F2 = F1 + (A1 - F1)
• = 1,050 + 0.05(1,000 – 1,050)
• = 1,050 + 0.05(-50) = 1,047.5 units
• BTW, we have to make a starting forecast to get
started. Often, use actual A1
Exponential Smoothing
Period Demand
1
10
2
12
3
14
4
15
5
16
6
17
7
19
8
21
9
23
10
Alpha = 0.3
ES
10.0
10.0
10.6
11.6
12.6
13.6
14.7
16.0
17.5
19.1
Exponential Smoothing
Period Demand
1
10
2
12
3
14
4
15
5
16
6
17
7
19
8
21
9
23
10
Alpha = 0.5
ES
10.0
10.0
11.0
12.5
13.8
14.9
15.9
17.5
19.2
21.1
Exponential Smoothing
F12   A11  1   F11
We take:
And substitute in
to get:
F11   A10  1   F10
F12   A11   1  A10  1   F10
2
and if we continue doing this, we get:
F12   A11   1   A10   1    A9   1   A8   1    A7  ...
2
3
Older demands get exponentially less weight
4
Choosing 
• Low : if demand is stable, we don’t want to get
thrown into a wild-goose chase, over-reacting to
“trends” that are really just short-term variation
• High : If demand really is changing rapidly, we
want to react as quickly as possible
Averaging Methods
•
•
•
•
Simple Average
Moving Average
Weighted Moving Average
Exponentially Weighted Moving Average
(Exponential Smoothing)
• They ALL take an average of the past
▫ With a trend, all do badly
▫ Average must be in-between
30
20
10
Trend-Adjusted Ex. Smoothing
St  exp.smoothedLevel,forecastas of t
Tt  exp.smoothedT rend
1. St  TAFt    At  TAFt 
 (1   )TAFt   At
2. T t  T t 1  TAFt  TAFt 1  Tt 1 
3. TAFt 1  St  Tt
where and  are smoothingconstants
Trend-Adjusted Ex. Smoothing
S1  100 T1  10 TAF1  100   0.20   0.30
Trend-Adjusted Forecast for period 2 was
TAF2  S1 T 1 100 10  110
Suppose actual demand is 115, A2=115


1. S2  TAF2    A2  TAF2  
 110 0.2 *(115 110)  110 1  111.0
2. T 2  T 1  TAF2  TAF1  T1 
 10  0.30* (110 100 10)  10  0.3 * 0  10
3. TAF3  S2 T 2 111 10  121
Trend-Adjusted Ex. Smoothing
S 2  100 T2  10 TAF3  121   0.20   0.30
Suppose actual demand is 120, A3=120
1. S3  TAF3    A3  TAF3  

 121 0.2 *(120 121)  121 0.2  120.8
2. T 3  T 2  TAF3  TAF2  T2 
 10  0.30* (121 110 10)  10  0.3 *1  10.3
3. TAF3  S2 T 2 120.8  10.3  131.1
TAF6=S5+T5
A5
S5
F6
Selecting  and β
• You could:
▫ Try an initial value for each parameter.
▫ Try lots of combinations and see what looks best.
▫ But how do we decide “what looks best?”
• Let’s measure the amount of forecast error.
• Then, try lots of combinations of parameters in a
methodical way.
▫ Let  = 0 to 1, increasing by 0.1
 For each  value, try  = 0 to 1, increasing by 0.1
Evaluating Forecasts
How far off is the forecast?
Forecasts
Demands
What do we do with this information?
Measuring the Errors
Period
A-F
Method 1
A-F
Method 2
1
100
10
2
-100
10
3
100
10
4
-100
10
5
100
10
6
-100
10
7
100
10
8
-100
10
9
100
10
10
-100
10
RSFE
0
100
• Method 1 forecasts are low,
high, etc.
• Method 2 forecasts always too
low.
• Running Sum of Forecast
Errors, RSFE
▫ Sum of all periods
▫ Also known as the Bias
n
RSFE   At  Ft
t 1
Evaluating Forecasts
n

Mean Absolute MAD  (1 / n)
At  Ft
Deviation
t 1
Mean Squared
Error
n
MSE  (1 / n)  At  Ft 
2
t 1
Mean Absolute

MAPE  (1 / n)
Percent Error

n

t 1
At  Ft
At

 100

MAD of examples
Period
|A-F|
Method 1
|A-F|
Method 2
1
100
10
2
100
10
3
100
10
4
100
10
5
100
10
6
100
10
7
100
10
8
100
10
9
100
10
10
100
10
MAD
100
10
• MAD shows that method 1 is
off by a larger amount
• Method 2 was biased
• However, overall, Method 2
seems preferable
n
MAD  (1 / n) At  Ft
t 1
Tracking Signal
• To monitor, compute tracking signal
RSFE
Tracking Signal 
MAD
n
RSFE   At  Ft
t 1
• If >4 or <-4 something is wrong
• Top should sum to 0 over time. If not, forecast is
biased.
Monitoring Forecast Accuracy
Forecast Error
• Monitor forecast error each period, to see if it
becomes too great
4
Upper Limit
0
-4
Forecast Period
Lower Limit
Techniques for Trend
• Determine how demand increases as a function
of time
yt  a  bt
t = periods since beginning of data
b = Slope of the line
a = Value of yt at t = 0
Computing Values
xy  n x  y

b
 x  nx
y  b x

a
 y  bx
2
2
n
S yx 

n
(
y

Y
)
i
i
i 1
n2
2
Linear Regression
• Four methods
1. Type in formulas for trend, intercept
2. Tools | Data Analysis | Regression
3. Graph, and R click on data, add a trendline, and
display the equation.
4. Use intercept(Y,X), slope(Y,X) and RSQ(Y,X)
commands
• Fits a trend and intercept to the data.
• R2 measures the percentage of change in y that
can be explained by changes in x.
• Gives all data equal weight.
• Exp. smoothing with a trend gives more weight
to recent, less to old.
Causal Forecasting
• Linear regression seeks a linear relationship
between the input variable and the output
quantity.
yc  a  bx
• For example, furniture sales correlates to
housing sales
• Not easy, multiple sources of error:
▫ Understand and quantify relationship
▫ Someone else has to forecast the x values for you
Video sales of Shrek 2?
• Shrek did $500m at the box office, and sold
almost 50 million DVDs & videos
• Shrek2 did $920m at the box office
Box Office $ Millions
1000
900
800
700
600
500
400
300
200
100
0
Shrek
Shrek2
Video sales of Shrek 2?
• Assume 1-1 ratio:
•
•
•
•
▫ 920/500 = 1.84
▫ 1.84 * 50 million = 92 million videos?
▫ Fortunately, not that dumb.
January 3, 2005: 37 million sold!
March analyst call: 40m by end Q1
March SEC filing: 33.7 million sold. Oops.
May 10 Announcement:
▫ In 2nd public Q, missed earnings targets by 25%.
▫ May 9, word started leaking
▫ Stock dropped 16.7%
Lessons Learned
• Flooded market with DVDs
• Guaranteed Sales
▫ Promised the retailer they would sell them, or else the
retailer could return them
▫ Didn’t know how many would come back
• 5 years ago
▫ Typical movie 30% of sales in first week
▫ Animated movies even lower than that
• 2004/5 50-70% in first week
▫ Shrek 2: 12.1m in first 3 days
▫ American Idol ending, had to vote in first week
The Human Element
• Colbert says you have more nerve endings in
your gut than in your brain
• Limited ability to include factors
▫ Can’t include everything
• If it feels really wrong to your gut, maybe your
gut is right
Washoe Gaming Win, 1993-96
300
What did they
mean when they
said it was down
three quarters
in a row?
280
260
240
220
200
180
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1993
1994
1995
1996
Seasonality
• Seasonality is regular up or down
movements in the data
• Can be hourly, daily, weekly, yearly
• Naïve method
▫ N1: Assume January sales will be same as
December
▫ N2: Assume this Friday’s ticket sales will be
same as last
Seasonal Relatives
• Seasonal relative for May is 1.20, means May
sales are typically 20% above the average
• Factor for July is 0.90, meaning July sales are
typically 10% below the average
Seasonality & No Trend
Spring
Summer
Fall
Winter
Sales
200
350
300
150
Relative
200/250 = 0.8
350/250 = 1.4
300/250 = 1.2
150/250 = 0.6
Total
Avg
1,000
1,000/4=250
Seasonality & No Trend
If we expected total demand for the next year to be
1,100, the average per quarter would be
1,100/4=275
Forecast
Spring
275 * 0.8 = 220
Summer
275 * 1.4 = 385
Fall
275 * 1.2 = 330
Winter
275 * 0.6 = 165
Total
1,100
Trend & Seasonality
•
Deseasonalize to find the trend
1. Calculate seasonal relatives
2. Deseasonalize the demand
3. Find trend of deseasonalized line
•
Project trend into the future
4. Project trend line into future
5. Multiply trend line by seasonal relatives.
Washoe Gaming Win, 1993-96
300
Looks like a
downhill slide
-Silver Legacy
opened 95Q3
-Otherwise,
upward trend
280
260
240
220
200
180
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1993
1994
1995
1996
Source: Comstock Bank, Survey of Nevada Business & Economics
Washoe Win 1989-1996
290000
270000
250000
230000
210000
190000
170000
150000
1989
1990
1991
1992
1993
1994
1995
1996
Definitely a general upward trend, slowed 93-94
1989-2007
1989-2007
1998-2007
Cache
Creek
9/11
Thunder CC
Valley
Expands
2003-2010
350,000,000
300,000,000
250,000,000
200,000,000
150,000,000
Washoe Win
Deseas
100,000,000
50,000,000
2003
2004
2005
2006
2007
2008
2009
2010
2003-2011
350,000,000
300,000,000
250,000,000
200,000,000
150,000,000
100,000,000
50,000,000
Washoe Win
R² = 0.5807
Deseas
R² = 0.7377
2003
2004
2005
2006
2007
2008
2009
2010
2011
2011 Forecast using 2003-10 SR
350,000,000
300,000,000
250,000,000
200,000,000
150,000,000
Washoe Win
100,000,000
Data for LR
Linear
Forecast
50,000,000
2003
2004
2005
2006
2007
2008
2009
2010
2011
Seasonal Relatives calculated using 2003-10 data
How Good Was It?
350,000,000
300,000,000
250,000,000
200,000,000
150,000,000
Washoe Win
100,000,000
Linear
Forecast
50,000,000
2003
2004
2005
2006
2007
2008
2009
2010
2011
350,000,000
2003
300,000,000
1.Compute
Seasonal Relatives
2004
250,000,000
2005
200,000,000
2006
150,000,000
2007
100,000,000
2008
50,000,000
2009
1
Q1
avg
SR
Q2
Q3
2
240,114,703
259,349,602
279,784,440
246,068,018
2004
231,607,546
259,849,383
297,401,507
259,617,607
2005
245,793,646
269,238,341
294,810,396
257,014,585
2006
245,775,176
269,670,481
294,839,349
257,155,338
2007
244,648,019
273,460,685
284,733,890
246,352,794
2008
227,915,101
237,045,466
258,990,669
206,203,166
2009
190,098,500
211,913,667
217,227,445
185,971,111
2010
187,016,132
198,330,968
209,608,491
175,601,589
2011
174,138,905
192,122,889
203,912,214
175,510,911
220,789,748
241,220,165
260,145,378
223,277,235
1.021
1.101
4
2010
Q4
2003
0.934
3
0.945
236,358,131
2.Deseasonalize
Year Quarter Gaming Win
Seasonal Deseas
2003
2004
1
240,114,703
0.934
257,045,733
2
259,349,602
1.021
254,122,152
3
279,784,440
1.101
254,201,431
4
246,068,018
0.945
260,484,132
1
231,607,546
0.934
247,938,717
2
259,849,383
1.021
254,611,859
3
297,401,507
1.101
270,207,624
4
259,617,607
0.945
274,827,536
3.LR on Deseasonalized data 2008
Q4-2011Q4
Period
1
2
3
4
5
6
7
8
9
10
11
12
13
Deseasonalized
218,283,762
203,502,775
207,642,335
197,364,541
196,866,394
200,203,062
194,333,409
190,442,251
185,889,365
186,417,833
188,250,460
185,266,831
185,793,374
250,000,000
200,000,000
150,000,000
Deseasonalized
100,000,000
Linear
50,000,000
2009
2010
2011
Intercept = 211,875,992
Slope =
-2,352,992
R-squared =
0.83
4.Project trend line into future
300,000,000
250,000,000
200,000,000
150,000,000
Deseasonalized
100,000,000
Straight Line
50,000,000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Period Number
Intercept = 211,875,992
Slope =
-2,352,992
5.Multiply by Seasonal Relatives
Linear Trend
Period Q Line
Seasonal Seasonalized
Relative Forecast
37 1 178,933,394
0.934 167,147,450
38 2 176,580,402
1.021 180,212,770
39 3 174,227,410
1.101 191,761,778
40 4 171,874,418
0.945 162,362,279
350000000
300000000
250000000
200000000
150000000
100000000
Gaming Win
Deseasonalized
50000000
Straight Line
Seasonal Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Summary
1. Calculate seasonal relatives
2. Deseasonalize
1. Divide actual demands by seasonal relatives
3. Do a LR
4. Project the LR into the future
5. Seasonalize
1. Multiply straight-line forecast by relatives
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