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Chapter 10 Forecasting

• Overview of Forecasting Techniques • The Time-Series Forecasting Methods in Perspective• Case Study: Applying Time-Series Forecasting to The

Computer Club Warehouse Problem

Problem 1

• You are working for Fortress, an electronic outlet.

• Your assignment:– Determine the number of units of a new heater to

stock for the coming winter.

• How would you approach this problem?

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Problem 2

• You are working for Hoixe Cake Shop

• Your assignment:– Determine the number of loaves of bread to

produce for tomorrow’s sales

• How would you approach this problem?

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Problem 3

• You are working for a large production firm

• Your assignment:– Forecast the employee turnover rate

• How would you approach this problem?

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Problem 4

• You are working for an investment firm

• Your assignment:– forecast the interest rate movement

• How would you approach this problem?

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Forecasting Issues

• What is forecasting?

• Why do we forecast?

• How do we forecast?

• What is a good forecast?

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What is a forecast?

• A statement about the future value of a variable of interest such as interest rate, unemployment rate, demand, supply, cost, rainfall, etc.

• Observed measurement = systematic part + random part

• Forecasting tries to isolate the systematic part• The random part determines the forecast accuracy

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• Forecasts rarely perfect because of randomness (natural or assignable)

• Forecasts more accurate for groups vs. individuals• Forecast accuracy decreases as time horizon increases

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Characteristics of forecasts

Forecasting is hard:Some famous forecasts

• This 'telephone' has too many shortcomings to be seriously considered as a means of communication. The device is inherently of no value to us.– Western Union internal memo, 1876

• 640K memory ought to be enough for anybody.– Bill Gates, 1981

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Forecasting is hard:Some famous forecasts

• I think there is a world market for may be five computers.– Thomas Watson, chairman of IBM, 1943

• There is no reason anyone would want a computer in their home.– Ken Olson, president, chairman and founder of

DEC, 1977

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Why do we forecast?

• To make better decisions

• Forecasting is vital to every functional area– Finance and accounting:

budgetary planning and cost control

– Marketing: new product demand– Human resources: recruiting– Production and operations:

capacity planning, process selection, inventory control.

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Steps in the forecasting process

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How do we forecastTypes of forecasts

• Qualitative (Judgmental)- uses subjective inputs

• Time Series Analysis - uses historical data assuming the future will be like the past

• Causal Relationship - uses explanatory variables to predict the future (Covered in BUS102)

How do we forecast?

ForecastingMethods

Qualitative methods

Time series analysis

Causal Relationship

Last valueRegression

analysis

Manager’sjudgement

Jury of Executive Opinion

Consumer MarketSurvey

Salesforce Composite

DelphiMethod

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Exponentialsmoothing

Simple movingaverage

Averaging

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Qualitative Forecasting Methods

• Manager’s Opinion: A single manager uses his or her best judgment.• Jury of Executive Opinion: A small group of high-level managers

pool their best judgment to collectively make the forecast.• Salesforce Composite: A bottom-up approach where each

salesperson provides an estimate of what sales will be in his or her region. These estimates are then aggregated into a corporate sales forecast.

• Consumer Market Survey: A grass-roots approach that surveys customers and potential customers regarding their future purchasing plans and how they would respond to various new features in products.

• Delphi Method: A panel of experts in different locations who independently fill out a series of questionnaires. The results from each questionnaire are provided with the next one, so each expert can evaluate the group information in adjusting his or her responses next time.

Time Series AnalysisTime series data: data collected over different time periods (Hourly, Daily, Weekly, Monthly, or Annually).

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Time Series Analysis

• Four components of a time series― Trend - long-term movement in data― Seasonality - short-term regular variations in data― Cycle – wavelike variations of more than one year’s

duration― Irregular /Random variations - caused by unusual

circumstances/ chance• Multiplicative model: Y = T * S * C * I

• Additive model: Y = T + S + C + I

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A typical time-series of past demands

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Components of A Time Series

Irregularvariation

Seasonal variations

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Cycles

RandomvariationTrend

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Forecasting at Fastchips

• Fastchips is a leading producer of microprocessors.• Six months ago, it launched the sales of its latest

microprocessor.• Month-by-month sales (in thousands) over the initial six

months have been

17 25 24 26 30 28

Question: What is the forecast for next month’s sales?

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The Last-Value (Naïve) Forecasting Method

The last-value forecasting method ignores all data points in a time series except the last one.

Forecast = Last valueFastchips: Month-by-month sales (in thousands) over the initial six months:

17 25 24 26 30 28Forecast = 28

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The Averaging Forecasting Method

The averaging forecasting method uses all the data points in the time series and simply averages these points.Forecast = Average of all data to dateFastchips: Month-by-month sales (in thousands) over the initial six months:

17 25 24 26 30 28Forecast = (17+25+24+26+30+28) / 6 = 25

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The Moving-Average Forecasting Method

The moving-average forecasting method averages the data for only the most recent time periods.n = Number of recent periods to consider as relevant for forecastingForecast = Average of last n valuesFastchips: Month-by-month sales (in thousands) over the initial six months:

17 25 24 26 30 28Forecast (n=3) = (26+30+28) / 3 = 28

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The Exponential Smoothing Forecasting Method

• The exponential smoothing forecasting method provides a more sophisticated version of the moving-average method.

• It gives the greatest weight to the last month and then progressively smaller weights to the older months.

Forecast = a (Last value) + (1 – a) (Last forecast)

a is the smoothing constant between 0 and 1.

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Measuring the Forecast Error

• The mean absolute deviation (called MAD) measures the average absolute forecasting error.MAD = (Sum of absolute forecasting errors) / (Number of forecasts)

• The mean square error (often abbreviated MSE) measures the average of the square of the forecasting error.MSE = (Sum of square of forecasting errors) / (Number of forecasts).

• The MSE increases the weight of large errors relative to the weight of small errors.

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The Computer Club Warehouse (CCW)• The Computer Club Warehouse (CCW) sells computer products at bargain

prices by taking telephone orders (as well as website and fax orders) directly from customers.

• Products include computers, peripherals, supplies, software, and computer furniture.

• The CCW call center is never closed. It is staffed by dozens of agents to take and process customer orders.

• A large number of telephone trunks are provided for incoming calls. If an agent is not free when a call arrives, it is placed on hold. If all the trunks are in use (called saturation), the call receives a busy signal.

• An accurate forecast of the demand for agents is needed.

Question: How should the demand for agents be forecasted?

Which model is most superior for predicting the demand?

Case Study

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Average Daily Call Volume (3 Years of Data)

CCW's Average Daily Call Volume

Year Quarter Call Volume1 1 6,8091 2 6,4651 3 6,5691 4 8,2662 1 7,2572 2 7,0642 3 7,7842 4 8,7243 1 6,9923 2 6,8223 3 7,9493 4 9,650

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25 Percent Rule (Current Forecasting Method)

Since sales are relatively stable through the year except for a substantial increase during the Christmas season, assume that each quarter’s call volume will be the same as the preceding quarter, except for adding 25 percent for Quarter 4.Forecast for Quarter 2 = Call volume for Quarter 1Forecast for Quarter 3 = Call volume for Quarter 2Forecast for Quarter 4 = 1.25(Call volume for Quarter 3)Forecast for next Quarter 1 = (Call volume for Quarter 4) / 1.25

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Applying the 25-Percent RuleCurrent Forecasting Method for CCW's Average Daily Call Volume

Absolute Squared Forecasting Forecasting

Year Quarter Data Forecast Error Error Mean Absolute Deviation1 1 6,809 MAD = 4241 2 6,465 6,809 344 118,3361 3 6,569 6,465 104 10,816 Mean Square Error1 4 8,266 8,211 55 2,998 MSE = 317,8152 1 7,257 6,613 644 414,9942 2 7,064 7,257 193 37,2492 3 7,784 7,064 720 518,4002 4 8,724 9,730 1,006 1,012,0363 1 6,992 6,979 13 1643 2 6,822 6,992 170 28,9003 3 7,949 6,822 1,127 1,270,1293 4 9,650 9,936 286 81,9394 1 7,7204 24 34 4

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Considering Seasonal Effects

• When there are seasonal patterns in the data, they can be addressed by forecasting methods that use seasonal factors.

• The seasonal factor for any period of a year (a quarter, a month, etc.) measures how that period compares to the overall average for an entire year.

Seasonal factor = (Average for the period) / (Overall average)• It is easier to analyze data and detect new trends if the data are

first adjusted to remove the seasonal patterns.Seasonally adjusted data = (Actual call volume) / (Seasonal factor)

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Calculation of Seasonal Factors for CCWYear Q1 Q2 Q3 Q4

1 6,809 6,465 6,569 8,2662 7,257 7,064 7,784 8,7243 6,992 6,822 7,949 9,650

7,019 6,784 7,434 8,880 7,529S.F. 93.23% 90.10% 98.73% 117.94%

QuarterThree-Year

AverageSeasonal

Factor

1 7,019 7,019 / 7,529 = 0.93

2 6,784 6,784 / 7,529 = 0.90

3 7,434 7,434 / 7,529 = 0.99

4 8,880 8,880 / 7,529 = 1.18

Total = 30,117

Average = 30,117 / 4

= 7,529

QuarterThree-Year

AverageSeasonal

Factor

1 7,019 7,019 / 7,529 = 0.93

2 6,784 6,784 / 7,529 = 0.90

3 7,434 7,434 / 7,529 = 0.99

4 8,880 8,880 / 7,529 = 1.18

Total = 30,117

Average = 30,117 / 4

= 7,529

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Excel Template for Calculating Seasonal Factors

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A B C D E F G

Estimating Seasonal Factors for CCW

True Year Quarter Value Type of Seasonality

1 1 6,809 Quarterly1 2 6,4651 3 6,5691 4 8,266 Estimate for2 1 7,257 Quarter Seasonal Factor2 2 7,064 1 0.93232 3 7,784 2 0.90102 4 8,724 3 0.98733 1 6,992 4 1.17943 2 6,8223 3 7,9493 4 9,650

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Seasonally Adjusted Time Series for CCW

12345678910111213141516

A B C D E F

Seasonally Adjusted Time Series for CCW

Seasonal Actual Seasonally AdjustedYear Quarter Factor Call Volume Call Volume

1 1 0.93 6,809 7,3221 2 0.90 6,465 7,1831 3 0.99 6,569 6,6351 4 1.18 8,266 7,0052 1 0.93 7,257 7,8032 2 0.90 7,064 7,8492 3 0.99 7,784 7,8632 4 1.18 8,724 7,3933 1 0.93 6,992 7,5183 2 0.90 6,822 7,5803 3 0.99 7,949 8,0293 4 1.18 9,650 8,178

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Outline for Forecasting Call Volume

1. Select a time-series forecasting method.2. Apply this method to the seasonally adjusted time series to

obtain a forecast of the seasonally adjusted call volume for the next time period.

3. Multiply this forecast by the corresponding seasonal factor to obtain a forecast of the actual call volume (without seasonal adjustment).

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The Last-Value (Naïve) Forecasting Method

• The last-value forecasting method ignores all data points in a time series except the last one.Forecast = Last value

• The last-value forecasting method is sometimes called the naïve method, because statisticians consider it naïve to use just a sample size of one when other data are available.

• However, when conditions are changing rapidly, it may be that the last value is the only relevant data point.

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The Last-Value Method Applied to CCW’s ProblemLast-Value Forecasting Method with Seasonality for CCW

Seasonally Seasonally Absolute Squared True Adjusted Adjusted Actual Forecasting Forecasting

Year Quarter Value Value Forecast Forecast Error Error Type of Seasonality1 1 6,809 7,322 Quarterly1 2 6,465 7,183 7,322 6,589 124 15,4641 3 6,569 6,635 7,183 7,112 543 294,306 Quarter Seasonal Factor1 4 8,266 7,005 6,635 7,830 436 190,343 1 0.932 1 7,257 7,803 7,005 6,515 742 550,967 2 0.902 2 7,064 7,849 7,803 7,023 41 1,689 3 0.992 3 7,784 7,863 7,849 7,770 14 185 4 1.182 4 8,724 7,393 7,863 9,278 554 306,8043 1 6,992 7,518 7,393 6,876 116 13,5273 2 6,822 7,580 7,518 6,766 56 3,0863 3 7,949 8,029 7,580 7,504 445 197,8473 4 9,650 8,178 8,029 9,475 175 30,7774 1 8,178 7,6064 24 34 45 1 Mean Absolute Deviation5 2 MAD = 2955 35 4 Mean Square Error6 1 MSE = 145,909

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The Averaging Forecasting Method

• The averaging forecasting method uses all the data points in the time series and simply averages these points.Forecast = Average of all data to date

• The averaging forecasting method is a good one to use when conditions are very stable.

• However, the averaging method is very slow to respond to changing conditions. It places the same weight on all the data, even though the older values may be less representative of current conditions than the last value observed.

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The Averaging Method Applied to CCW’s ProblemAveraging Forecasting Method with Seasonality for CCW

Seasonally Seasonally Absolute Squared True Adjusted Adjusted Actual Forecasting Forecasting

Year Quarter Value Value Forecast Forecast Error Error Type of Seasonality1 1 6,809 7,322 Quarterly1 2 6,465 7,183 7,322 6,589 124 15,4641 3 6,569 6,635 7,252 7,180 611 373,193 Quarter Seasonal Factor1 4 8,266 7,005 7,047 8,315 49 2,415 1 0.932 1 7,257 7,803 7,036 6,544 713 508,687 2 0.902 2 7,064 7,849 7,190 6,471 593 351,969 3 0.992 3 7,784 7,863 7,300 7,227 557 310,729 4 1.182 4 8,724 7,393 7,380 8,708 16 2433 1 6,992 7,518 7,382 6,865 127 16,1453 2 6,822 7,580 7,397 6,657 165 27,1753 3 7,949 8,029 7,415 7,341 608 369,6643 4 9,650 8,178 7,471 8,816 834 695,9574 1 7,530 7,0034 24 34 45 1 Mean Absolute Deviation5 2 MAD = 4005 35 4 Mean Square Error6 1 MSE = 242,876

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The Moving-Average Forecasting Method• The moving-average forecasting method averages the data for

only the most recent time periods.n = Number of recent periods to consider as relevant for forecasting

Forecast = Average of last n values• The moving-average forecasting method is a good one to use

when conditions don’t change much over the number of time periods included in the average.

• However, the moving-average method is slow to respond to changing conditions. It places the same weight on each of the last n values even though the older values may be less representative of current conditions than the last value observed.

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The Moving-Average Method Applied to CCWMoving Average Forecasting Method with Seasonality for CCW

Seasonally Seasonally Absolute Squared True Adjusted Adjusted Actual Forecasting Forecasting Number of previous

Year Quarter Value Value Forecast Forecast Error Error periods to consider1 1 6,809 7,322 n = 41 2 6,465 7,1831 3 6,569 6,635 Type of Seasonality1 4 8,266 7,005 Quarterly2 1 7,257 7,803 7,036 6,544 713 508,6872 2 7,064 7,849 7,157 6,441 623 388,036 Quarter Seasonal Factor2 3 7,784 7,863 7,323 7,250 534 285,255 1 0.932 4 8,724 7,393 7,630 9,003 279 78,036 2 0.903 1 6,992 7,518 7,727 7,186 194 37,675 3 0.993 2 6,822 7,580 7,656 6,890 68 4,648 4 1.183 3 7,949 8,029 7,589 7,513 436 190,4053 4 9,650 8,178 7,630 9,004 646 417,7894 1 7,826 7,2794 24 34 45 15 25 35 4 Mean Absolute Deviation6 1 MAD = 4376 26 3 Mean Square Error6 4 MSE = 238,816

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The Exponential Smoothing Forecasting Method• The exponential smoothing forecasting method places the

greatest weight on the last value in the time series and then progressively smaller weights on the older values.

Forecast = a (Last value) + (1 – a) (Last forecast)

a is the smoothing constant between 0 and 1.

• This method places a weight of a on the last value, a(1–a) on the next-to-last value, a(1–a)2 on the next prior value, etc.– For example, when a = 0.5, the method places a weight

of 0.5 on the last value, 0.25 on the next-to-last, 0.125 on the next prior, etc.

– A larger value of a places more emphasis on the more recent values, a smaller value places more emphasis on the older values.

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The Exponential Smoothing Forecasting Method

• The choice of the value of the smoothing constant a has a substantial effect on the forecast.– A small value (say, a = 0.1) is appropriate if conditions are

relatively stable.– A larger value (say, a = 0.5) is appropriate if significant

changes occur frequently.

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The Exponential Smoothing Method Applied to CCW with = a 0.1

Exponential-Smoothing Forecasting Method with Seasonality for CCW

Seasonally Seasonally Absolute Squred True Adjusted Adjusted Actual Forecasting Forecasting Smoothing Constant

Year Quarter Value Value Forecast Forecast Error Error a = 0.11 1 6,809 7,322 7,500 6,975 166 27,5561 2 6,465 7,183 7,482 6,734 269 72,326 Initial Estimate1 3 6,569 6,635 7,452 7,378 809 654,070 Average = 7,5001 4 8,266 7,005 7,371 8,697 431 186,0032 1 7,257 7,803 7,334 6,821 436 190,405 Type of Seasonality2 2 7,064 7,849 7,381 6,643 421 177,365 Quarterly2 3 7,784 7,863 7,428 7,353 431 185,3612 4 8,724 7,393 7,471 8,816 92 8,474 Quarter Seasonal Factor3 1 6,992 7,518 7,463 6,941 51 2,602 1 0.933 2 6,822 7,580 7,469 6,722 100 9,995 2 0.903 3 7,949 8,029 7,480 7,405 544 295,694 3 0.993 4 9,650 8,178 7,535 8,891 759 575,715 4 1.184 1 7,599 7,0674 24 34 45 15 25 35 46 16 2 Mean Absolute Deviation6 3 MAD = 3766 47 1 Mean Square Error

MSE = 198,797

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The Exponential Smoothing Method Applied to CCW with = a 0.5

Exponential-Smoothing Forecasting Method with Seasonality for CCW

Seasonally Seasonally Absolute Squred True Adjusted Adjusted Actual Forecasting Forecasting Smoothing Constant

Year Quarter Value Value Forecast Forecast Error Error a = 0.51 1 6,809 7,322 7,500 6,975 166 27,5561 2 6,465 7,183 7,411 6,670 205 41,893 Initial Estimate1 3 6,569 6,635 7,297 7,224 655 429,120 Average = 7,5001 4 8,266 7,005 6,966 8,220 46 2,1062 1 7,257 7,803 6,986 6,497 760 578,137 Type of Seasonality2 2 7,064 7,849 7,394 6,655 409 167,289 Quarterly2 3 7,784 7,863 7,622 7,545 239 56,9092 4 8,724 7,393 7,742 9,136 412 169,521 Quarter Seasonal Factor3 1 6,992 7,518 7,568 7,038 46 2,111 1 0.933 2 6,822 7,580 7,543 6,789 33 1,110 2 0.903 3 7,949 8,029 7,561 7,486 463 214,484 3 0.993 4 9,650 8,178 7,795 9,199 451 203,796 4 1.184 1 7,987 7,4284 24 34 45 15 25 35 46 16 2 Mean Absolute Deviation6 3 MAD = 3246 47 1 Mean Square Error

MSE = 157,836

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The Exponential Smoothing Method Applied to CCW with = a 0.9

Exponential-Smoothing Forecasting Method with Seasonality for CCW

Seasonally Seasonally Absolute Squred True Adjusted Adjusted Actual Forecasting Forecasting Smoothing Constant

Year Quarter Value Value Forecast Forecast Error Error a = 0.91 1 6,809 7,322 7,500 6,975 166 27,5561 2 6,465 7,183 7,339 6,605 140 19,718 Initial Estimate1 3 6,569 6,635 7,199 7,127 558 311,304 Average = 7,5001 4 8,266 7,005 6,692 7,896 370 136,7372 1 7,257 7,803 6,974 6,486 771 595,081 Type of Seasonality2 2 7,064 7,849 7,720 6,948 116 13,398 Quarterly2 3 7,784 7,863 7,836 7,758 26 6932 4 8,724 7,393 7,860 9,275 551 303,337 Quarter Seasonal Factor3 1 6,992 7,518 7,440 6,919 73 5,314 1 0.933 2 6,822 7,580 7,510 6,759 63 3,919 2 0.903 3 7,949 8,029 7,573 7,497 452 204,021 3 0.993 4 9,650 8,178 7,984 9,421 229 52,566 4 1.184 1 8,159 7,5874 24 34 45 15 25 35 46 16 2 Mean Absolute Deviation6 3 MAD = 2936 47 1 Mean Square Error

MSE = 139,470

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MAD and MSE for the Various Forecasting Method

Forecasting Method MAD MSE

CCW’s 25 percent rule 424 317,815

Last-value method 295 145,909

Averaging method 400 242,876

Moving-average method 437 238,816

Exponential smoothing =0.5a 324 157,836

Exponential smoothing =0.9a 293 139,470

Forecast

7,720

7,606

7,003

7,279

7,428

7,587

Since the exponential smoothing method with a = 0.9 gives the smallest MAD/MSE, it is the most superior method to make the forecast for the CCW problem.

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Comparison of the Forecasting Methods

• Last value method: Suitable for a time series that is so unstable that even the next-to-last value is not considered relevant for forecasting the next value.

• Averaging method: Suitable for a very stable time series where even its first few values are considered relevant for forecasting the next value.

• Moving-average method: Suitable for a moderately stable time series where the last few values are considered relevant for forecasting the next value.

• Exponential smoothing method: Suitable for a time series in the range from somewhat unstable to rather stable, where the value of the smoothing constant needs to be adjusted to fit the anticipated degree of stability.