Demand Management and FORECASTING
Operations ManagementDr. 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 FutureWe 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 wrong2. 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 HorizonsDifferent 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 ImpactFinance & Accounting: budget planningHuman Resources: hiring, training, laying
off employeesCapacity: not enough, customers go away
angry, too much, costs are too highSupply-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 MethodsTime Series Methods
0. All-Time Average 1. Simple Moving Average2. Weighted Moving Average3. Exponential Smoothing4. Exponential smoothing with trend5. Linear regression
Causal MethodsLinear Regression
Time Series ForecastingAssume patterns in data will continue,
including:
Trend (T)Seasonality (S)Cycles (C)Random Variations
All-Time AverageTo forecast next period, take the average of
all previous periods
Advantages: Simple to use
Disadvantages: Ends up with a lot of dataGives 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 AverageCompute forecast using n most recent
periods
Jan Feb Mar Apr May Jun Jul
3 month Moving Avg:June forecast: FJun = (AMar + AApr + AMay)/3If no seasonality, freedom to choose nIf seasonality is N periods, must use N, 2N,
3N etc. number of periods
Moving AverageAdvantages:
▫ 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 3MA1 102 12 103 14 11.04 15 12.0 12.05 16 12.8 13.76 17 13.4 15.07 19 14.0 16.08 21 14.7 17.39 23 15.5 19.0
10 16.3 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 DataComparison 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 AverageFJun = (AMar + AApr + AMay)/3
= (3AMar + 3AApr + 3AMay)/9Why not consider:FJun = (2AMar + 3AApr + 4AMay)/9FJun = 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
1 102 123 144 15 12.65 16 14.16 17 15.37 19 16.38 21 17.89 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
At-1 Actual demand in period t-1 Ft-1 Forecast for period t-1Smoothing constant >0, <1Forecast is old forecast plus a portion of the
error of the last forecast.Formulas are equivalent, give same answer
111 tttt FAFF F10 = F9 + 0.2 (A9 - F9)
111 ttt AFF F10 = 0.8 F9 + 0.2 (A9 - F9)
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 ES
1 10 10.02 12 10.03 14 10.64 15 11.65 16 12.66 17 13.67 19 14.78 21 16.09 23 17.5
10 19.1
Alpha = 0.3
Exponential Smoothing Period Demand ES
1 10 10.02 12 10.03 14 11.04 15 12.55 16 13.86 17 14.97 19 15.98 21 17.59 23 19.2
10 21.1
Alpha = 0.5
Exponential Smoothing
111112 1 FAF
101011 1 FAF
We take:
And substitute in
to get:
and if we continue doing this, we get:
Older demands get exponentially less weight
102
101112 11 FAAF
...1111 74
83
92
101112 AAAAAF
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
2010
Trend-Adjusted Ex. Smoothing
Trend smoothed exp. of asforecast Level, smoothed exp.
t
t
TtS
ttt
ttttt
tt
tttt
TSTAFTTAFTAFTT
ATAFTAFATAFS
1
111
.3
.2)1(
.1
constants smoothing are and where
Trend-Adjusted Ex. Smoothing
100*3.010)10100110(*30.010
.2 11212
TTAFTAFTT
Trend-Adjusted Forecast for period 2 was 11010100112 TSTAF
0.1111110)110115(*2.0110
.1 2222
TAFATAFS
Suppose actual demand is 115, A2=115
12110111.3 223 TSTAF
1001 S
T1 10
0.20 30.01001 TAF
Trend-Adjusted Ex. Smoothing
Suppose actual demand is 120, A3=120
1002 S 102 T
0.20 30.01213 TAF
3.101*3.010)10110121(*30.010
.2 22323
TTAFTAFTT
8.1202.0121)121120(*2.0121
.1 3333
TAFATAFS
1.1313.108.120.3 223 TSTAF
S5
TAF6=S5+T5
A5F6
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 ForecastsHow far off is the forecast?
What do we do with this information?
Forecasts
Demands
Measuring the ErrorsPeriod A-F
Method 1
A-FMethod 2
1 100 102 -100 103 100 104 -100 105 100 106 -100 107 100 108 -100 109 100 1010 -100 10RSFE 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
ttt FARSFE
1
Evaluating Forecasts
Mean Absolute DeviationMean Squared ErrorMean Absolute Percent Error
100)/1(
)/1(
)/1(
1
1
2
1
n
t t
tt
n
ttt
n
ttt
AFAnMAPE
FAnMSE
FAnMAD
MAD of examplesPeriod |A-F|
Method 1
|A-F|Method 2
1 100 102 100 103 100 104 100 105 100 106 100 107 100 108 100 109 100 1010 100 10MAD 100 10
• MAD shows that method 1 is off by a larger amount
• Method 2 was biased• However, overall, Method
2 seems preferable
n
ttt FAnMAD
1
)/1(
Tracking Signal•To monitor, compute tracking signal
•If >4 or <-4 something is wrong•Top should sum to 0 over time. If not,
forecast is biased.
n
ttt FARSFE
1
MADRSFE
Signal Tracking
Monitoring Forecast Accuracy•Monitor forecast error each period, to
see if it becomes too great
0
-4
4
Fore
cast
Erro
r
Forecast PeriodLower Limit
Upper Limit
Techniques for Trend•Determine how demand increases as a
function of time
t = periods since beginning of datab = Slope of the linea = Value of yt at t = 0
btayt
Computing Values
2)(
12
22
nYy
S
xbyn
xbya
xnx
yxnxyb
n
i iiyx
Linear Regression•Four methods
1. Type in formulas for trend, intercept2. Tools | Data Analysis | Regression3. 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.
•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
bxayc
Video sales of Shrek 2?
Box Office $ Millions
0100200300400500600700800900
1000
Shrek Shrek2
•Shrek did $500m at the box office, and sold almost 50 million DVDs & videos
•Shrek2 did $920m at the box office
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
180
200
220
240
260
280
300
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
What did they mean when they said it was down three quartersin a row?
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 TrendSales Relative
Spring 200 200/250 = 0.8Summer 350 350/250 = 1.4Fall 300 300/250 = 1.2Winter 150 150/250 = 0.6
Total 1,000Avg 1,000/4=250
Seasonality & No TrendIf we expected total demand for the next
year to be 1,100, the average per quarter would be 1,100/4=275
ForecastSpring 275 * 0.8 = 220Summer 275 * 1.4 = 385Fall 275 * 1.2 = 330Winter 275 * 0.6 = 165Total 1,100
Trend & Seasonality• Deseasonalize to find the trend
1. Calculate seasonal relatives2. Deseasonalize the demand3. Find trend of deseasonalized line
• Project trend into the future4. Project trend line into future5. Multiply trend line by seasonal relatives.
Washoe Gaming Win, 1993-96
180
200
220
240
260
280
300
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
Looks like a downhill slide- Silver Legacy
opened 95Q3- Otherwise,
upward trend
1993 1994 1995 1996
Source: Comstock Bank, Survey of Nevada Business & Economics
Washoe Win 1989-1996
150000
170000
190000
210000
230000
250000
270000
290000
1989 1990 1991 1992 1993 1994 1995 1996
Definitely a general upward trend, slowed 93-94
1989-2007
1989-2007
1998-2007
CacheCreek
ThunderValley
CCExpands
9/11
2003 2004 2005 2006 2007 2008 2009 2010 -
50,000,000
100,000,000
150,000,000
200,000,000
250,000,000
300,000,000
350,000,000
Washoe Win
Deseas
2003-2010
2003-2011
2003 2004 2005 2006 2007 2008 2009 2010 2011 -
50,000,000
100,000,000
150,000,000
200,000,000
250,000,000
300,000,000
350,000,000
R² = 0.58074452310794R² = 0.73774638194945
Washoe WinLinear (Washoe Win)Deseas
2003 2004 2005 2006 2007 2008 2009 2010 2011 -
50,000,000
100,000,000
150,000,000
200,000,000
250,000,000
300,000,000
350,000,000
Washoe Win
Linear
Forecast
2011 Forecast using 2003-10 SR
Data for LR
Seasonal Relatives calculated using 2003-10 data
How Good Was It?
2003 2004 2005 2006 2007 2008 2009 2010 2011 -
50,000,000
100,000,000
150,000,000
200,000,000
250,000,000
300,000,000
350,000,000
Washoe Win
Linear
Forecast
1 2 3 4 -
50,000,000
100,000,000
150,000,000
200,000,000
250,000,000
300,000,000
350,000,000 200320042005200620072008200920102011
1.Compute Seasonal Relatives
Q1 Q2 Q3 Q4
2003 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
avg 220,789,748 241,220,165 260,145,378 223,277,235 236,358,131
SR
0.934
1.021
1.101
0.945
2.DeseasonalizeYear Quarter Gaming Win Seasonal Deseas
2003 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
2004 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 Deseasonalized1 218,283,762 2 203,502,775 3 207,642,335 4 197,364,541 5 196,866,394 6 200,203,062 7 194,333,409 8 190,442,251 9 185,889,365
10 186,417,833 11 188,250,460 12 185,266,831 13 185,793,374
Intercept = 211,875,992Slope = -2,352,992R-squared =0.83
2009 2010 2011 -
50,000,000
100,000,000
150,000,000
200,000,000
250,000,000
DeseasonalizedLinear
4.Project trend line into future
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536 -
50,000,000
100,000,000
150,000,000
200,000,000
250,000,000
300,000,000
Deseasonalized
Straight Line
Period Number
Intercept = 211,875,992Slope = -2,352,992
5.Multiply by Seasonal RelativesPeriod Q
Linear Trend Line
Seasonal Relative
Seasonalized 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
1 2 3 4 5 6 7 8 9 100
50000000
100000000
150000000
200000000
250000000
300000000
350000000
Gaming Win
Deseasonalized
Straight Line
Seasonal Forecast
Summary1. Calculate seasonal relatives2. Deseasonalize
1. Divide actual demands by seasonal relatives
3. Do a LR4. Project the LR into the future5. Seasonalize
1. Multiply straight-line forecast by relatives
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