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## Chapter 3

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**Chapter 3**Demand Forecasting**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 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.**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**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 YearEnrolled (1000s)YearEnrolled (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.**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