1 Chapter 3 Demand Forecasting

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

3 Forecasting is an Integral Part of Business Planning ForecastMethod(s) DemandEstimates SalesForecastManagementTeam Inputs:Market,Economic,Other BusinessStrategy Production Resource Forecasts

4 Some Reasons Why Forecasting is Essential in OM l New Facility Planning – It can take 5 years to design and build a new factory or design and implement a new production process. l Production Planning – Demand for products vary from month to month and it can take several months to change the capacities of production processes. l 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.

5 Examples of Production Resource Forecasts LongRange MediumRange ShortRange Years Months Days,Weeks Product Lines, Factory Capacities ForecastHorizonTimeSpan Item Being Forecasted Unit of Measure Product Groups, Depart. Capacities Specific Products, Machine Capacities Dollars,Tons Units,Pounds Units,Hours

6 Forecasting Methods l Qualitative Approaches l Quantitative Approaches

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

8 Qualitative Methods l Educated guessintuitive hunches l Executive committee consensus l Delphi method l Survey of sales force l Survey of customers l Historical analogy l Market research scientifically conducted surveys

9 Quantitative Forecasting Approaches l 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 l Analysis of the past demand pattern provides a good basis for forecasting future demand l Majority of quantitative approaches fall in the category of time series analysis

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

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

12 Seasonal Patterns Length of Time Number of Length of Time Number of Before Pattern Length of Seasons Before Pattern Length of Seasons Is Repeated Season in Pattern Is Repeated Season in Pattern YearQuarter 4 YearQuarter 4 Year Month12 Year Month12 Year Week52 Year Week52 Month Day Month Day Week Day 7 Week Day 7

13 Quantitative Forecasting Approaches l Linear Regression l Simple Moving Average l Weighted Moving Average l Exponential Smoothing (exponentially weighted moving average) l Exponential Smoothing with Trend (double exponential smoothing)

14 Long-Range Forecasts l Time spans usually greater than one year l Necessary to support strategic decisions about planning products, processes, and facilities

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

16 Simple Linear Regression l Regression Equation This model is of the form: Y = a + bX Y = a + bX Y = dependent variable Y = dependent variable X = independent variable X = independent variable a = y-axis intercept a = y-axis intercept b = slope of regression line b = slope of regression line

17 Simple Linear Regression l Constants a and b The constants a and b are computed using the following equations:

18 Simple Linear Regression l 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.

19 Example: College Enrollment l 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. StudentsStudents Year Enrolled (1000s) Year Enrolled (1000s)

20 Example: College Enrollment l Simple Linear Regression xyx 2 xy  x=21  y=18.1  x 2 =91  xy=66.5  x=21  y=18.1  x 2 =91  xy=66.5

21 Example: College Enrollment l Simple Linear Regression Y = X Y = X

22 Example: College Enrollment l Simple Linear Regression Y 7 = (7) = 3.65 or 3,650 students Y 8 = (8) = 3.83 or 3,830 students Y 8 = (8) = 3.83 or 3,830 students Y 9 = (9) = 4.01 or 4,010 students Note: Enrollment is expected to increase by 180 students per year. students per year.

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

24 Example: Railroad Products Co. l Simple Linear Regression – Causal Model The manager of RPC wants to project the firm’s sales for the next 3 years. He knows that RPC’s 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.

25 Example: Railroad Products Co. l Simple Linear Regression – Causal Model RPC SalesCar Loadings Year($millions)(millions)

26 Example: Railroad Products Co. l Simple Linear Regression – Causal Model xyx 2 xy ,4001, ,2251, ,9001, ,5001, ,9002, ,1003, ,4003,960 1, ,42515,440

27 Example: Railroad Products Co. l Simple Linear Regression – Causal Model Y = X Y = X

28 Example: Railroad Products Co. l Simple Linear Regression – Causal Model Y 8 = (250) = $20.55 million Y 8 = (250) = $20.55 million Y 9 = (270) = $22.16 million Y 9 = (270) = $22.16 million Y 10 = (300) = $24.56 million Note: RPC sales are expected to increase by $80,100 for each additional million national freight car loadings.

29 Multiple Regression Analysis l Multiple regression analysis is used when there are two or more independent variables. l An example of a multiple regression equation is: Y = X X 2 – 0.03X 3 Y = X X 2 – 0.03X 3 where: Y = firm’s annual sales ($millions) X 1 = industry sales ($millions) X 1 = industry sales ($millions) X 2 = regional per capita income ($thousands) X 2 = regional per capita income ($thousands) X 3 = regional per capita debt ($thousands) X 3 = regional per capita debt ($thousands)

30 Coefficient of Correlation (r) l The coefficient of correlation, r, explains the relative importance of the relationship between x and y. l The sign of r shows the direction of the relationship. l The absolute value of r shows the strength of the relationship. l The sign of r is always the same as the sign of b. l r can take on any value between –1 and +1.

31 Coefficient of Correlation (r) l 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 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) +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 no relationship exists between x and y +0.3 a weak positive relationship +0.3 a weak positive relationship -0.8 a strong negative relationship -0.8 a strong negative relationship

32 Coefficient of Correlation (r) l r is computed by:

33 Coefficient of Determination (r 2 ) l The coefficient of determination, r 2, is the square of the coefficient of correlation. l The modification of r to r 2 allows us to shift from subjective measures of relationship to a more specific measure. l r 2 is determined by the ratio of explained variation to total variation:

34 Example: Railroad Products Co. l Coefficient of Correlation xyx 2 xyy ,4001, ,2251, ,9001, ,5001, ,9002, ,1003, ,4003, , ,42515,4401,287.50

35 Example: Railroad Products Co. l Coefficient of Correlation r =.9829 r =.9829

36 Example: Railroad Products Co. l Coefficient of Determination r 2 = (.9829) 2 =.966 r 2 = (.9829) 2 = % of the variation in RPC sales is explained by national freight car loadings.

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

38 Seasonalized Time Series Regression Analysis l Select a representative historical data set. l Develop a seasonal index for each season. l Use the seasonal indexes to deseasonalize the data. l Perform lin. regr. analysis on the deseasonalized data. l Use the regression equation to compute the forecasts. l Use the seas. indexes to reapply the seasonal patterns to the forecasts.

39 Example: Computer Products Corp. l Seasonalized Times Series Regression Analysis An analyst at CPC wants to develop next year’s quarterly forecasts of sales revenue for CPC’s line of Epsilon Computers. She believes that the most recent 8 quarters of sales (shown on the next slide) are representative of next year’s sales.

40 Example: Computer Products Corp. l Seasonalized Times Series Regression Analysis l Representative Historical Data Set YearQtr.($mil.)YearQtr.($mil.)

41 Example: Computer Products Corp. l Seasonalized Times Series Regression Analysis l Compute the Seasonal Indexes Quarterly Sales Quarterly Sales YearQ1Q2Q3Q4Total Totals Totals Qtr. Avg Qtr. Avg Seas.Ind Seas.Ind

42 Example: Computer Products Corp. l Seasonalized Times Series Regression Analysis l Deseasonalize the Data Quarterly Sales Quarterly Sales YearQ1Q2Q3Q

43 Example: Computer Products Corp. l Seasonalized Times Series Regression Analysis l Perform Regression on Deseasonalized Data Yr.Qtr.xyx 2 xy Totals

44 Example: Computer Products Corp. l Seasonalized Times Series Regression Analysis l Perform Regression on Deseasonalized Data Y = X Y = X

45 Example: Computer Products Corp. l Seasonalized Times Series Regression Analysis l Compute the Deseasonalized Forecasts Y 9 = (9) = Y 9 = (9) = Y 10 = (10) = Y 10 = (10) = Y 11 = (11) = Y 11 = (11) = Y 12 = (12) = Y 12 = (12) = Note: Average sales are expected to increase by.199 million (about $200,000) per quarter..199 million (about $200,000) per quarter.

46 Example: Computer Products Corp. l Seasonalized Times Series Regression Analysis l Seasonalize the Forecasts Seas.Deseas.Seas. Yr.Qtr.IndexForecastForecast

47 Short-Range Forecasts l Time spans ranging from a few days to a few weeks l Cycles, seasonality, and trend may have little effect l Random fluctuation is main data component

48 Evaluating Forecast-Model Performance Short-range forecasting models are evaluated on the basis of three characteristics: l Impulse response l Noise-dampening ability l Accuracy

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

50 Evaluating Forecast-Model Performance l Accuracy l Accuracy is the typical criterion for judging the performance of a forecasting approach l Accuracy is how well the forecasted values match the actual values

51 Monitoring Accuracy l 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 l Accuracy can be measured in several ways l Standard error of the forecast (covered earlier) l Mean absolute deviation (MAD) l Mean squared error (MSE)

52 Monitoring Accuracy l Mean Absolute Deviation (MAD)

53 l Mean Squared Error (MSE) MSE = (S yx ) 2 A small value for S yx 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 s yx are related: MSE = 1.25(MAD) MSE = 1.25(MAD) Monitoring Accuracy

54 Short-Range Forecasting Methods l (Simple) Moving Average l Weighted Moving Average l Exponential Smoothing l Exponential Smoothing with Trend

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

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

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

58 Weighted Moving Average l The weights must add to 1.0 and generally decrease in value with the age of the data. l The distribution of the weights determine the impulse response of the forecast.

59 l The weights used to compute the forecast (moving average) are exponentially distributed. The forecast is the sum of the old forecast and a portion (  ) of the forecast error (A t-1  -  F t-1 ). The forecast is the sum of the old forecast and a portion (  ) of the forecast error (A t-1  -  F t-1 ). F t = F t-1 +  (A t-1  -  F t-1 ) F t = F t-1 +  (A t-1  -  F t-1 ) l... more Exponential Smoothing

60 Exponential Smoothing The smoothing constant, , must be between 0.0 and 1.0. The smoothing constant, , must be between 0.0 and 1.0. A large  provides a high impulse response forecast. A large  provides a high impulse response forecast. A small  provides a low impulse response forecast. A small  provides a low impulse response forecast.

61 Example: Central Call Center l 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.

62 Example: Central Call Center l Moving Average l Representative Historical Data DayCallsDayCalls

63 Example: Central Call Center l Moving Average Use the moving average method with an AP = 3 days to develop a forecast of the call volume in Day 13. F 13 = ( )/3 = calls F 13 = ( )/3 = calls

64 Example: Central Call Center l 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. F 13 =.1(168) +.3(198) +.6(159) = calls F 13 =.1(168) +.3(198) +.6(159) = calls Note: The WMA forecast is lower than the MA forecast because Day 13’s relatively low call volume carries almost twice as much weight in the WMA (.60) as it does in the MA (.33).

65 Example: Central Call Center l Exponential Smoothing If a smoothing constant value of.25 is used and the exponential smoothing forecast for Day 11 was calls, what is the exponential smoothing forecast for Day 13? F 12 = (198 – ) = F 13 = (159 – ) =

66 Example: Central Call Center l Forecast Accuracy - MAD Which forecasting method (the AP = 3 moving average or the  =.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.)

67 Example: Central Call Center AP = 3  =.25 AP = 3  =.25 DayCallsForec.|Error|Forec.|Error| MAD

68 Criteria for Selecting a Forecasting Method l Cost l Accuracy l Data available l Time span l Nature of products and services l Impulse response and noise dampening

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

70 Criteria for Selecting a Forecasting Method l Cost and Accuracy l Low/Moderate-Cost Approaches – statistical models, historical analogies, executive-committee consensus l High-Cost Approaches – complex econometric models, Delphi, and market research

71 Criteria for Selecting a Forecasting Method l Data Available l Is the necessary data available or can it be economically obtained? l 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.

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

73 Criteria for Selecting a Forecasting Method l Nature of Products and Services l Is the product/service high cost or high volume? l Where is the product/service in its life cycle? l Does the product/service have seasonal demand fluctuations?

74 Criteria for Selecting a Forecasting Method l Impulse Response and Noise Dampening l An appropriate balance must be achieved between: l How responsive we want the forecasting model to be to changes in the actual demand data l Our desire to suppress undesirable chance variation or noise in the demand data

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

76 Computer Software for Forecasting l Examples of computer software with forecasting capabilities l Forecast Pro l Autobox l SmartForecasts for Windows l SAS l SPSS l SAP l POM Software Libary Primarily for forecasting HaveForecastingmodules