Forecasting in POM

1
(No Transcript)
2
Chapter 3

• Demand Forecasting

3
Overview

• Introduction
• Qualitative Forecasting Methods
• Quantitative Forecasting Models
• How to Have a Successful Forecasting System
• Computer Software for Forecasting
• Forecasting in Small Businesses and Start-Up
  Ventures
• Wrap-Up What World-Class Producers Do

4
Introduction

• Demand estimates for products and services are
  the starting point for all the other planning in
  operations management.
• Management teams develop sales forecasts based in
  part on demand estimates.
• The sales forecasts become inputs to both
  business strategy and production resource
  forecasts.

5
Forecasting is an Integral Part of Business
Planning
Demand Estimates
Inputs Market, Economic, Other
Forecast Method(s)
Sales Forecast
Management Team
Business Strategy
Production Resource Forecasts
6
Some Reasons WhyForecasting is Essential in OM

• New Facility Planning It can take 5 years to
  design and build a new factory or design and
  implement a new production process.
• Production Planning Demand for products vary
  from month to month and it can take several
  months to change the capacities of production
  processes.
• Workforce Scheduling Demand for services (and
  the necessary staffing) can vary from hour to
  hour and employees weekly work schedules must be
  developed in advance.

7
Examples of Production Resource Forecasts
Forecast Horizon
Time Span
Item Being Forecasted
Unit of Measure
Long Range
Years
Product Lines, Factory Capacities
Dollars, Tons
Medium Range
Months
Product Groups, Depart. Capacities
Units, Pounds
Short Range
Days, Weeks
Specific Products, Machine Capacities
Units, Hours
8
Forecasting Methods

• Qualitative Approaches
• Quantitative Approaches

9
Qualitative Approaches

• Usually based on judgments about causal factors
  that underlie the demand of particular products
  or services
• Do not require a demand history for the product
  or service, therefore are useful for new
  products/services
• Approaches vary in sophistication from
  scientifically conducted surveys to intuitive
  hunches about future events
• The approach/method that is appropriate depends
  on a products life cycle stage

10
Qualitative Methods

• Educated guess intuitive hunches
• Executive committee consensus
• Delphi method
• Survey of sales force
• Survey of customers
• Historical analogy
• Market research scientifically conducted
  surveys

11
Quantitative Forecasting Approaches

• Based on the assumption that the forces that
  generated the past demand will generate the
  future demand, i.e., history will tend to repeat
  itself
• Analysis of the past demand pattern provides a
  good basis for forecasting future demand
• Majority of quantitative approaches fall in the
  category of time series analysis

12
Time Series Analysis

• A time series is a set of numbers where the order
  or sequence of the numbers is important, e.g.,
  historical demand
• Analysis of the time series identifies patterns
• Once the patterns are identified, they can be
  used to develop a forecast

13
Components of a Time Series

• Trends are noted by an upward or downward sloping
  line.
• Cycle is a data pattern that may cover several
  years before it repeats itself.
• Seasonality is a data pattern that repeats itself
  over the period of one year or less.
• Random fluctuation (noise) results from random
  variation or unexplained causes.

14
Seasonal Patterns

• Length of Time Number of
• Before Pattern Length of
  Seasons
• Is Repeated Season in
  Pattern
• Year Quarter 4
• Year Month 12
• Year Week 52
• Month Day 28-31
• Week Day 7

15
Quantitative Forecasting Approaches

• Linear Regression
• Simple Moving Average
• Weighted Moving Average
• Exponential Smoothing (exponentially weighted
  moving average)
• Exponential Smoothing with Trend (double
  exponential smoothing)

16
Long-Range Forecasts

• Time spans usually greater than one year
• Necessary to support strategic decisions about
  planning products, processes, and facilities

17
Simple Linear Regression

• Linear regression analysis establishes a
  relationship between a dependent variable and one
  or more independent variables.
• In simple linear regression analysis there is
  only one independent variable.
• If the data is a time series, the independent
  variable is the time period.
• The dependent variable is whatever we wish to
  forecast.

18
Simple Linear Regression

• Regression Equation
• This model is of the form
• Y a bX
• Y dependent variable
• X independent variable
• a y-axis intercept
• b slope of regression line

19
Simple Linear Regression

• Constants a and b
• The constants a and b are computed using the
  following equations

20
Simple Linear Regression

• Once the a and b values are computed, a future
  value of X can be entered into the regression
  equation and a corresponding value of Y (the
  forecast) can be calculated.

21
Example College Enrollment

• Simple Linear Regression
• At a small regional college enrollments have
  grown steadily over the past six years, as
  evidenced below. Use time series regression to
  forecast the student enrollments for the next
  three years.
• Students Students
• Year Enrolled (1000s) Year Enrolled
  (1000s)
• 1 2.5 4 3.2
• 2 2.8 5 3.3
• 3 2.9 6 3.4

22
Example College Enrollment

• Simple Linear Regression
• x y x2 xy
• 1 2.5 1 2.5
• 2 2.8 4 5.6
• 3 2.9 9 8.7
• 4 3.2 16 12.8
• 5 3.3 25 16.5
• 6 3.4 36 20.4
• Sx21 Sy18.1 Sx291 Sxy66.5

23
Example College Enrollment

• Simple Linear Regression
• Y 2.387 0.180X

24
Example College Enrollment

• Simple Linear Regression
• Y7 2.387 0.180(7) 3.65 or 3,650 students
• Y8 2.387 0.180(8) 3.83 or 3,830 students
• Y9 2.387 0.180(9) 4.01 or 4,010 students
• Note Enrollment is expected to increase by 180
• students per year.

25
Simple Linear Regression

• Simple linear regression can also be used when
  the independent variable X represents a variable
  other than time.
• In this case, linear regression is representative
  of a class of forecasting models called causal
  forecasting models.

26
Example Railroad Products Co.

• Simple Linear Regression Causal Model
• The manager of RPC wants to project the firms
  sales for the next 3 years. He knows that RPCs
  long-range sales are tied very closely to
  national freight car loadings. On the next slide
  are 7 years of relevant historical data.
• Develop a simple linear regression model
  between RPC sales and national freight car
  loadings. Forecast RPC sales for the next 3
  years, given that the rail industry estimates car
  loadings of 250, 270, and 300 million.

27
Example Railroad Products Co.

• Simple Linear Regression Causal Model
• RPC Sales Car Loadings
• Year (millions) (millions)
• 1 9.5 120
• 2 11.0 135
• 3 12.0 130
• 4 12.5 150
• 5 14.0 170
• 6 16.0 190
• 7 18.0 220

28
Example Railroad Products Co.

• Simple Linear Regression Causal Model
• x y x2 xy
• 120 9.5 14,400 1,140
• 135 11.0 18,225 1,485
• 130 12.0 16,900 1,560
• 150 12.5 22,500 1,875
• 170 14.0 28,900 2,380
• 190 16.0 36,100 3,040
• 220 18.0 48,400 3,960
• 1,115 93.0 185,425 15,440

29
Example Railroad Products Co.

• Simple Linear Regression Causal Model
• Y 0.528 0.0801X

30
Example Railroad Products Co.

• Simple Linear Regression Causal Model
• Y8 0.528 0.0801(250) 20.55 million
• Y9 0.528 0.0801(270) 22.16 million
• Y10 0.528 0.0801(300) 24.56 million
• Note RPC sales are expected to increase by
  80,100 for each additional million national
  freight car loadings.

31
Multiple Regression Analysis

• Multiple regression analysis is used when there
  are two or more independent variables.
• An example of a multiple regression equation is
• Y 50.0 0.05X1 0.10X2 0.03X3
• where Y firms annual sales (millions)
• X1 industry sales (millions)
• X2 regional per capita income
  (thousands)
• X3 regional per capita debt (thousands)

32
Coefficient of Correlation (r)

• The coefficient of correlation, r, explains the
  relative importance of the relationship between x
  and y.
• The sign of r shows the direction of the
  relationship.
• The absolute value of r shows the strength of the
  relationship.
• The sign of r is always the same as the sign of
  b.
• r can take on any value between 1 and 1.

33
Coefficient of Correlation (r)

• Meanings of several values of r
• -1 a perfect negative relationship (as x
  goes up, y goes down by one unit, and vice
  versa)
• 1 a perfect positive relationship (as x
  goes up, y goes up by one unit, and vice
  versa)
• 0 no relationship exists between x and y
• 0.3 a weak positive relationship
• -0.8 a strong negative relationship

34
Coefficient of Correlation (r)

• r is computed by

35
Coefficient of Determination (r2)

• The coefficient of determination, r2, is the
  square of the coefficient of correlation.
• The modification of r to r2 allows us to shift
  from subjective measures of relationship to a
  more specific measure.
• r2 is determined by the ratio of explained
  variation to total variation

36
Example Railroad Products Co.

• Coefficient of Correlation
• x y x2 xy y2
• 120 9.5 14,400 1,140 90.25
• 135 11.0 18,225 1,485 121.00
• 130 12.0 16,900 1,560 144.00
• 150 12.5 22,500 1,875 156.25
• 170 14.0 28,900 2,380 196.00
• 190 16.0 36,100 3,040 256.00
• 220 18.0 48,400 3,960 324.00
• 1,115 93.0 185,425 15,440 1,287.50

37
Example Railroad Products Co.

• Coefficient of Correlation
• r .9829

38
Example Railroad Products Co.

• Coefficient of Determination
• r2 (.9829)2 .966
• 96.6 of the variation in RPC sales is explained
  by national freight car loadings.

39
Ranging Forecasts

• Forecasts for future periods are only estimates
  and are subject to error.
• One way to deal with uncertainty is to develop
  best-estimate forecasts and the ranges within
  which the actual data are likely to fall.
• The ranges of a forecast are defined by the upper
  and lower limits of a confidence interval.

40
Ranging Forecasts

• The ranges or limits of a forecast are estimated
  by
• Upper limit Y t(syx)
• Lower limit Y - t(syx)
• where
• Y best-estimate forecast
• t number of standard deviations from the
  mean of the distribution to provide a
  given proba- bility of exceeding the limits
  through chance
• syx standard error of the forecast

41
Ranging Forecasts

• The standard error (deviation) of the forecast is
  computed as

42
Example Railroad Products Co.

• Ranging Forecasts
• Recall that linear regression analysis provided
  a forecast of annual sales for RPC in year 8
  equal to 20.55 million.
• Set the limits (ranges) of the forecast so that
  there is only a 5 percent probability of
  exceeding the limits by chance.

43
Example Railroad Products Co.

• Ranging Forecasts
• Step 1 Compute the standard error of the
  forecasts, syx.
• Step 2 Determine the appropriate value for t.
• n 7, so degrees of freedom n 2 5.
• Area in upper tail .05/2 .025
• Appendix B, Table 2 shows t 2.571.

44
Example Railroad Products Co.

• Ranging Forecasts
• Step 3 Compute upper and lower limits.
• Upper limit 20.55 2.571(.5748)
• 20.55 1.478
• 22.028
• Lower limit 20.55 - 2.571(.5748)
• 20.55 - 1.478
• 19.072
• We are 95 confident the actual sales for year 8
  will be between 19.072 and 22.028 million.

45
Seasonalized Time Series Regression Analysis

• Select a representative historical data set.
• Develop a seasonal index for each season.
• Use the seasonal indexes to deseasonalize the
  data.
• Perform lin. regr. analysis on the deseasonalized
  data.
• Use the regression equation to compute the
  forecasts.
• Use the seas. indexes to reapply the seasonal
  patterns to the forecasts.

46
Example Computer Products Corp.

• Seasonalized Times Series Regression Analysis
• An analyst at CPC wants to develop next years
  quarterly forecasts of sales revenue for CPCs
  line of Epsilon Computers. She believes that the
  most recent 8 quarters of sales (shown on the
  next slide) are representative of next years
  sales.

47
Example Computer Products Corp.

• Seasonalized Times Series Regression Analysis
• Representative Historical Data Set
• Year Qtr. (mil.) Year Qtr. (mil.)
• 1 1 7.4 2 1 8.3
• 1 2 6.5 2 2 7.4
• 1 3 4.9 2 3 5.4
• 1 4 16.1 2 4 18.0

48
Example Computer Products Corp.

• Seasonalized Times Series Regression Analysis
• Compute the Seasonal Indexes
• Quarterly Sales
• Year Q1 Q2 Q3 Q4 Total
• 1 7.4 6.5 4.9 16.1 34.9
• 2 8.3 7.4 5.4 18.0 39.1
• Totals 15.7 13.9 10.3 34.1 74.0
• Qtr. Avg. 7.85 6.95 5.15 17.05 9.25
• Seas.Ind. .849 .751 .557 1.843 4.000

49
Example Computer Products Corp.

• Seasonalized Times Series Regression Analysis
• Deseasonalize the Data
• Quarterly Sales
• Year Q1 Q2 Q3 Q4
• 1 8.72 8.66 8.80 8.74
• 2 9.78 9.85 9.69 9.77

50
Example Computer Products Corp.

• Seasonalized Times Series Regression Analysis
• Perform Regression on Deseasonalized Data
• Yr. Qtr. x y x2 xy
• 1 1 1 8.72 1 8.72
• 1 2 2 8.66 4 17.32
• 1 3 3 8.80 9 26.40
• 1 4 4 8.74 16 34.96
• 2 1 5 9.78 25 48.90
• 2 2 6 9.85 36 59.10
• 2 3 7 9.69 49 67.83
• 2 4 8 9.77 64 78.16
• Totals 36 74.01 204 341.39

51
Example Computer Products Corp.

• Seasonalized Times Series Regression Analysis
• Perform Regression on Deseasonalized Data
• Y 8.357 0.199X

52
Example Computer Products Corp.

• Seasonalized Times Series Regression Analysis
• Compute the Deseasonalized Forecasts
• Y9 8.357 0.199(9) 10.148
• Y10 8.357 0.199(10) 10.347
• Y11 8.357 0.199(11) 10.546
• Y12 8.357 0.199(12) 10.745
• Note Average sales are expected to increase by
• .199 million (about 200,000) per quarter.

53
Example Computer Products Corp.

• Seasonalized Times Series Regression Analysis
• Seasonalize the Forecasts
• Seas. Deseas. Seas.
• Yr. Qtr. Index Forecast Forecast
• 3 1 .849 10.148 8.62
• 3 2 .751 10.347 7.77
• 3 3 .557 10.546 5.87
• 3 4 1.843 10.745 19.80

54
Short-Range Forecasts

• Time spans ranging from a few days to a few weeks
  
• Cycles, seasonality, and trend may have little
  effect
• Random fluctuation is main data component

55
Evaluating Forecast-Model Performance

• Short-range forecasting models are evaluated on
  the basis of three characteristics
• Impulse response
• Noise-dampening ability
• Accuracy

56
Evaluating Forecast-Model Performance

• Impulse Response and Noise-Dampening Ability
• If forecasts have little period-to-period
  fluctuation, they are said to be noise dampening.
• Forecasts that respond quickly to changes in data
  are said to have a high impulse response.
• A forecast system that responds quickly to data
  changes necessarily picks up a great deal of
  random fluctuation (noise).
• Hence, there is a trade-off between high impulse
  response and high noise dampening.

57
Evaluating Forecast-Model Performance

• Accuracy
• Accuracy is the typical criterion for judging the
  performance of a forecasting approach
• Accuracy is how well the forecasted values match
  the actual values

58
Monitoring Accuracy

• Accuracy of a forecasting approach needs to be
  monitored to assess the confidence you can have
  in its forecasts and changes in the market may
  require reevaluation of the approach
• Accuracy can be measured in several ways
• Standard error of the forecast (covered earlier)
• Mean absolute deviation (MAD)
• Mean squared error (MSE)

59
Monitoring Accuracy

• Mean Absolute Deviation (MAD)

60
Monitoring Accuracy

• Mean Squared Error (MSE)
• MSE (Syx)2
• A small value for Syx means data points are
  tightly grouped around the line and error range
  is small.
• When the forecast errors are normally
  distributed, the values of MAD and syx are
  related
• MSE 1.25(MAD)

61
Short-Range Forecasting Methods

• (Simple) Moving Average
• Weighted Moving Average
• Exponential Smoothing
• Exponential Smoothing with Trend

62
Simple Moving Average

• An averaging period (AP) is given or selected
• The forecast for the next period is the
  arithmetic average of the AP most recent actual
  demands
• It is called a simple average because each
  period used to compute the average is equally
  weighted
• . . . more

63
Simple Moving Average

• It is called moving because as new demand data
  becomes available, the oldest data is not used
• By increasing the AP, the forecast is less
  responsive to fluctuations in demand (low impulse
  response and high noise dampening)
• By decreasing the AP, the forecast is more
  responsive to fluctuations in demand (high
  impulse response and low noise dampening)

64
Weighted Moving Average

• This is a variation on the simple moving average
  where the weights used to compute the average are
  not equal.
• This allows more recent demand data to have a
  greater effect on the moving average, therefore
  the forecast.
• . . . more

65
Weighted Moving Average

• The weights must add to 1.0 and generally
  decrease in value with the age of the data.
• The distribution of the weights determine the
  impulse response of the forecast.

66
Exponential Smoothing

• The weights used to compute the forecast (moving
  average) are exponentially distributed.
• The forecast is the sum of the old forecast and a
  portion (a) of the forecast error (A t-1 - Ft-1).
• Ft Ft-1 a(A t-1 - Ft-1)
• . . . more

67
Exponential Smoothing

• The smoothing constant, ?, must be between 0.0
  and 1.0.
• A large ? provides a high impulse response
  forecast.
• A small ? provides a low impulse response
  forecast.

68
Example Central Call Center

• Moving Average
• CCC wishes to forecast the number of incoming
  calls it receives in a day from the customers of
  one of its clients, BMI. CCC schedules the
  appropriate number of telephone operators based
  on projected call volumes.
• CCC believes that the most recent 12 days of
  call volumes (shown on the next slide) are
  representative of the near future call volumes.

69
Example Central Call Center

• Moving Average
• Representative Historical Data
• Day Calls Day Calls
• 1 159 7 203
• 2 217 8 195
• 3 186 9 188
• 4 161 10 168
• 5 173 11 198
• 6 157 12 159

70
Example Central Call Center

• Moving Average
• Use the moving average method with an AP 3
  days to develop a forecast of the call volume in
  Day 13.
• F13 (168 198 159)/3 175.0 calls

71
Example Central Call Center

• Weighted Moving Average
• Use the weighted moving average method with an
  AP 3 days and weights of .1 (for oldest datum),
  .3, and .6 to develop a forecast of the call
  volume in Day 13.
• F13 .1(168) .3(198) .6(159) 171.6
  calls
• Note The WMA forecast is lower than the MA
  forecast because Day 13s relatively low call
  volume carries almost twice as much weight in the
  WMA (.60) as it does in the MA (.33).

72
Example Central Call Center

• Exponential Smoothing
• If a smoothing constant value of .25 is used
  and the exponential smoothing forecast for Day 11
  was 180.76 calls, what is the exponential
  smoothing forecast for Day 13?
• F12 180.76 .25(198 180.76) 185.07
• F13 185.07 .25(159 185.07) 178.55

73
Example Central Call Center

• Forecast Accuracy - MAD
• Which forecasting method (the AP 3 moving
  average or the a .25 exponential smoothing) is
  preferred, based on the MAD over the most recent
  9 days? (Assume that the exponential smoothing
  forecast for Day 3 is the same as the actual call
  volume.)

74
Example Central Call Center

• AP 3 a .25
• Day Calls Forec. Error Forec. Error
• 4 161 187.3 26.3 186.0 25.0
• 5 173 188.0 15.0 179.8 6.8
• 6 157 173.3 16.3 178.1 21.1
• 7 203 163.7 39.3 172.8 30.2
• 8 195 177.7 17.3 180.4 14.6
• 9 188 185.0 3.0 184.0 4.0
• 10 168 195.3 27.3 185.0 17.0
• 11 198 183.7 14.3 180.8 17.2
• 12 159 184.7 25.7 185.1 26.1
• MAD 20.5 18.0

75
Exponential Smoothing with Trend

• As we move toward medium-range forecasts, trend
  becomes more important.
• Incorporating a trend component into
  exponentially smoothed forecasts is called double
  exponential smoothing.
• The estimate for the average and the estimate for
  the trend are both smoothed.

76
Exponential Smoothing with Trend

• Model Form
• FTt St-1 Tt-1
• where
• FTt forecast with trend in period t
• St-1 smoothed forecast (average) in period
  t-1
• Tt-1 smoothed trend estimate in period t-1

77
Exponential Smoothing with Trend

• Smoothing the Average
• St FTt a (At FTt)
• Smoothing the Trend
• Tt Tt-1 b (FTt FTt-1 - Tt-1)
• where a smoothing constant for the
  average
• b smoothing constant for the trend

78
Criteria for Selectinga Forecasting Method

• Cost
• Accuracy
• Data available
• Time span
• Nature of products and services
• Impulse response and noise dampening

79
Criteria for Selectinga Forecasting Method

• Cost and Accuracy
• There is a trade-off between cost and accuracy
  generally, more forecast accuracy can be obtained
  at a cost.
• High-accuracy approaches have disadvantages
• Use more data
• Data are ordinarily more difficult to obtain
• The models are more costly to design, implement,
  and operate
• Take longer to use

80
Criteria for Selectinga Forecasting Method

• Cost and Accuracy
• Low/Moderate-Cost Approaches statistical
  models, historical analogies, executive-committee
  consensus
• High-Cost Approaches complex econometric
  models, Delphi, and market research

81
Criteria for Selectinga Forecasting Method

• Data Available
• Is the necessary data available or can it be
  economically obtained?
• If the need is to forecast sales of a new
  product, then a customer survey may not be
  practical instead, historical analogy or market
  research may have to be used.

82
Criteria for Selectinga Forecasting Method

• Time Span
• What operations resource is being forecast and
  for what purpose?
• Short-term staffing needs might best be forecast
  with moving average or exponential smoothing
  models.
• Long-term factory capacity needs might best be
  predicted with regression or executive-committee
  consensus methods.

83
Criteria for Selectinga Forecasting Method

• Nature of Products and Services
• Is the product/service high cost or high volume?
• Where is the product/service in its life cycle?
• Does the product/service have seasonal demand
  fluctuations?

84
Criteria for Selectinga Forecasting Method

• Impulse Response and Noise Dampening
• An appropriate balance must be achieved between
• How responsive we want the forecasting model to
  be to changes in the actual demand data
• Our desire to suppress undesirable chance
  variation or noise in the demand data

85
Reasons for Ineffective Forecasting

• Not involving a broad cross section of people
• Not recognizing that forecasting is integral to
  business planning
• Not recognizing that forecasts will always be
  wrong
• Not forecasting the right things
• Not selecting an appropriate forecasting method
• Not tracking the accuracy of the forecasting
  models

86
Monitoring and Controllinga Forecasting Model

• Tracking Signal (TS)
• The TS measures the cumulative forecast error
  over n periods in terms of MAD
• If the forecasting model is performing well, the
  TS should be around zero
• The TS indicates the direction of the forecasting
  error if the TS is positive -- increase the
  forecasts, if the TS is negative -- decrease the
  forecasts.

87
Monitoring and Controllinga Forecasting Model

• Tracking Signal
• The value of the TS can be used to automatically
  trigger new parameter values of a model, thereby
  correcting model performance.
• If the limits are set too narrow, the parameter
  values will be changed too often.
• If the limits are set too wide, the parameter
  values will not be changed often enough and
  accuracy will suffer.

88
Computer Software for Forecasting

• Examples of computer software with forecasting
  capabilities
• Forecast Pro
• Autobox
• SmartForecasts for Windows
• SAS
• SPSS
• SAP
• POM Software Libary

Primarily for forecasting
Have Forecasting modules
89
Forecasting in Small Businessesand Start-Up
Ventures

• Forecasting for these businesses can be difficult
  for the following reasons
• Not enough personnel with the time to forecast
• Personnel lack the necessary skills to develop
  good forecasts
• Such businesses are not data-rich environments
• Forecasting for new products/services is always
  difficult, even for the experienced forecaster

90
Sources of Forecasting Data and Help

• Government agencies at the local, regional,
  state, and federal levels
• Industry associations
• Consulting companies

91
Some Specific Forecasting Data

• Consumer Confidence Index
• Consumer Price Index (CPI)
• Gross Domestic Product (GDP)
• Housing Starts
• Index of Leading Economic Indicators
• Personal Income and Consumption
• Producer Price Index (PPI)
• Purchasing Managers Index
• Retail Sales

92
Wrap-Up World-Class Practice

• Predisposed to have effective methods of
  forecasting because they have exceptional
  long-range business planning
• Formal forecasting effort
• Develop methods to monitor the performance of
  their forecasting models
• Do not overlook the short run.... excellent short
  range forecasts as well