demand management and forecasting

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