Chapter 3 Demand Forecasting

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

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.

Forecasting is an Integral Part of Business Planning Inputs: Market, Economic, Other Demand Estimates Forecast Method(s) Sales Forecast Management Team Business Strategy Production Resource Forecasts

Some Reasons Why Forecasting 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.

Examples of Production Resource Forecasts 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

Qualitative Approaches Quantitative Approaches Forecasting Methods Qualitative Approaches Quantitative Approaches

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 product’s life cycle stage

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

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

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

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.

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

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

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

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.

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

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

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.

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

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 Sx=21 Sy=18.1 Sx2=91 Sxy=66.5

Example: College Enrollment Simple Linear Regression Y = 2.387 + 0.180X

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.

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.

Example: Railroad Products Co. 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.

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

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

Example: Railroad Products Co. Simple Linear Regression – Causal Model Y = 0.528 + 0.0801X

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.

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 = firm’s annual sales ($millions) X1 = industry sales ($millions) X2 = regional per capita income ($thousands) X3 = regional per capita debt ($thousands)

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.

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

Coefficient of Correlation (r) r is computed by:

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:

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

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

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.

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.

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

Ranging Forecasts The standard error (deviation) of the forecast is computed as:

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.

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.

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.

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.

Example: Computer Products Corp. 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.

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

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

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

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

Example: Computer Products Corp. Seasonalized Times Series Regression Analysis Perform Regression on Deseasonalized Data Y = 8.357 + 0.199X

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.

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

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

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

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.

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

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)

Monitoring Accuracy Mean Absolute Deviation (MAD)

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)

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

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

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)

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

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.

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

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.

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.

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

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

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 13’s relatively low call volume carries almost twice as much weight in the WMA (.60) as it does in the MA (.33).

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

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.)

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

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.

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

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

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

Criteria for Selecting a 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

Criteria for Selecting a 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

Criteria for Selecting a 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.

Criteria for Selecting a 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.

Criteria for Selecting a 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?

Criteria for Selecting a 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

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

Monitoring and Controlling a 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.

Monitoring and Controlling a 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.

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

Forecasting in Small Businesses and 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

Sources of Forecasting Data and Help Government agencies at the local, regional, state, and federal levels Industry associations Consulting companies

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 Manager’s Index Retail Sales

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