Demand

Management and FORECASTING

Operations ManagementDr. Ron Tibben-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

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 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 Methods

Time Series Methods0. All-Time Average 1. Simple Moving Average2. Weighted Moving Average3. Exponential Smoothing4. Exponential smoothing with trend5. Linear regressionCausal MethodsLinear 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 dataGives equal importance to very old data

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 cycles to demand, quite a bit of freedom to choose n

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 3MA

1 102 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 Moving Average• Take average of n periods,• Plot the average in the middle period• Not useful for forecasting• More stable than actuals• If seasonality, n = season length (4wks, 12 mo,

etc.)

CMA - # Periods to Average

•What if data has 12-month cycle?

Ja F M Ap My Jn Jl Au S O N D Ja F M Avg of Jan-Dec gives average of month 6.5: (1+2+3+4+5+6+7+8+9+10+11+12)/12=6.5Avg of Feb-Jan gives average of month 6.5: (2+3+4+5+6+7+8+9+10+11+12+13)/12=7.5How get a July average? Average of other two averages

Centered Moving Average

• To center even-number of periods• 12: take half each of 1 and 13, plus sum of

2-12.• F14 = 0.5 A1 + A2 + A3 + A4 + A5 + A6

+ A7 + A8 + A9 + A10 + A11 + A12 + 0.5A13

• This is exactly the same as what you get by taking the average of the averages from previous slide

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 + 3DApr + 3AMay)/9

Why 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 3WMA1 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

Exponential Smoothing

At-1 Actual demand in period t-1 Ft-1 Forecast for period t-1 Smoothing constant >0, <1Forecast is old forecast plus a portion of the

error of the last forecast.Formulas are equivalent, give same answer

11

111

1

ttt

tttt

AFF

FAFF

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

Weighted Moving Average

Period Demand ES1 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

Weighted Moving Average

Period Demand ES1 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

11 1 ttt FAF

221 1 ttt FAF

We take:

And substitute in

to get:

and if we continue doing this, we get:

Older demands get exponentially less weight

22

21 11 tttt FAAF

...1111 34

33

32

21 tttttt 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 IncludingForecast ttt TFFIT

Estimate Trend Smoothed Exp.

for forecast Smoothed Exp.

t

t

T

tF

11

11

111

)1(

tttt

tt

tttt

FITFTT

AFIT

FITAFITF

constants smoothing are and where

Trend-Adjusted Ex. Smoothing

3.103.010)110111(*30.010

121112

FITFTFITFTT ttt

F1 100

T1 10

0.20

0.30Forecast including trend for period 1 is

FIT1 F1 T1100 10 110

F2 FITt 1 At 1 FITt 1 FIT1 A1 FIT1 110 0.2 *(115 110) 110 1111.0

Suppose actual demand is 115, A1=115

FIT2 F2 T 211110.3 121.3

Trend-Adjusted Ex. Smoothing

22.10078.03.10)3.12104.121(*30.03.10

2323

FITFTT

0.1112 F 3.102 T

0.20

0.30Forecast including trend for period 1 is

3.1213.10111222 TFFIT

04.1213.1*2.03.121)3.121120(*2.03.121

2223

FITAFITF

Suppose actual demand is 120, A2=120

26.13122.1004.121333 TFFIT

Selecting and

•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?

What do we do with this information?

Forecasts

Demands

Evaluating Forecasts

Mean Absolute Deviation

Mean Squared Error

Mean Absolute Percent Error

MAD(1/n) At Fti1

n

MSE (1/n) At Ft 2

i1

n

MAPE (1/n)At FtDii1

n

100

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

MAD

RSFESignal Tracking

Monitoring Forecast Accuracy

•Monitor forecast error each period, to see if it becomes too great

0

-10

10

Fore

cast

Err

or

Forecast PeriodLower Limit

Upper Limit

Updating MAD

•Simplified calculation avoids keeping running total of all errors and demands:

•Standard Deviation can be estimated from MAD:

MAD 25.1

11 tttt MADForecastActualMADMAD

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

)(1

2

22

n

YyS

xbyn

xbya

xnx

yxnxyb

n

i iiyx

Linear Regression•Three methods

▫Type in formulas for trend, intercept▫Tools | Data Analysis | Regression▫Graph, and R click on data, add a trendline,

and display the equation.▫Use intercept(Y,X) and slope(Y,X) commands

•Fits a trend and intercept to the data.•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.

•R2 measures the percentage of change in y that can be explained by changes in x.

bxayc

Video sales of Shrek 2?

Box Office $ Millions

0100

200300400500

600700800

9001000

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

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 Factors

•Seasonal factor 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

Sales FactorSpring 200200/250 = 0.8Summer 350350/250 = 1.4Fall 300300/250 = 1.2Winter 150150/250 = 0.6

Total 1,000Avg 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

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 trend1. Calculate seasonal factors2. Deseasonalize the demand3. Find trend of deseasonalized line

• Project trend into the future4. Project trend line into future5. Multiply trend line by seasonal component.

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

2003Q3 - 2007Q3

2003Q2 - 2007Q3

2003-2007

Date Quarter Win

59 276,371

60 235,766

2004 61 240,221

62 259,350

63 279,758

64 245,811

2005 65 231,608

66 259,687

67 297,414

68 260,149

2006 69 245,775

70 269,670

71 294,839

72 257,015

2007 73 244,643

74 273,116

75 284,734

Q Avg Index

1 240,562 0.9168

2 265,456 1.0117

3 289,187 1.1022

4 254,325 0.9693

Total Avg. 262,382

For each Q:

Compute Indexes

Deseasonalize: Divide Win by Index276,371 / 1.1022 = 250,755

Compute Avg Win for each Q

Divide Avg by Total Avg to get Index:240,562/262,382 = 0.9168

2003-2007period Win Deseasonalized

59 276,371 250,755

60 235,766 243,236

2004 61 240,221 262,010

62 259,350 256,347

63 279,758 253,828

64 245,811 253,598

2005 65 231,608 252,616

66 259,687 256,681

67 297,414 269,847

68 260,149 268,391

2006 69 245,775 268,069

70 269,670 266,548

71 294,839 267,511

72 257,015 265,157

2007 73 244,643 266,834

74 273,116 269,954

75 284,734 258,343

Do LR on deseasonalized dataintercept 185,538.00 slope 1,119.91 rsq 0.497

Create Linear ForecastsInt + slope * period

Linear 251,613 252,733 253,853 254,972 256,092 257,212 258,332 259,452 260,572 261,692 262,812 263,932 265,052 266,172 267,291 268,411 269,531 270,651 271,771 272,891 274,011

Seasonal Forecast58 257,062 Deseasonalized Linear Forecast59 276,371 250,755 251,613 277,317 60 235,766 243,236 252,733 244,972

2004 61 240,221 262,010 253,853 232,741 62 259,350 256,347 254,972 257,959 63 279,758 253,828 256,092 282,254 64 245,811 253,598 257,212 249,314

2005 65 231,608 252,616 258,332 236,848 66 259,687 256,681 259,452 262,491 67 297,414 269,847 260,572 287,191 68 260,149 268,391 261,692 253,656

2006 69 245,775 268,069 262,812 240,956 70 269,670 266,548 263,932 267,023 71 294,839 267,511 265,052 292,129 72 257,015 265,157 266,172 257,998

2007 73 244,643 266,834 267,291 245,063 74 273,116 269,954 268,411 271,556 75 284,734 258,343 269,531 297,066 76 270,651 262,340

2008 77 271,771 263,425 78 272,891 264,511 79 274,011 265,596

Multiply Linear forecast by indexes251,613 * 1.1022= 277,317

267,291 * 0.9168 = 245,063

Q Index1 0.91682 1.01173 1.10224 0.9693