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Chapter 3

Chapter 3. Forecasting. Forecasting Demand. Why is demand forecasting important? What is bad about poor forecasting? What do these organizations forecast: Sony (consumer products division) Foley’s Dallas Area Rapid Transit (DART) UTA. Questions in Demand Forecasting.

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Chapter 3

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  1. Chapter 3 Forecasting

  2. Forecasting Demand Why is demand forecasting important? What is bad about poor forecasting? What do these organizations forecast: • Sony (consumer products division) • Foley’s • Dallas Area Rapid Transit (DART) • UTA

  3. Questions in Demand Forecasting For a particular product or service: • What exactly is to be forecasted? • What will the forecasts be used for? • What forecasting period is most useful? • What time horizon in the future is to be forecasted? • How many periods of past data should be used? • What patterns would you expect to see? • How do you select a forecasting model?

  4. Demand Management Recognizing and planning for all sources of demand Can demand be controlled or influenced? • appointment schedules • doctor’s office • attorney • SAM telephone registration • sales promotions • restaurant discounts before 6pm • video rental store discounts on Tuesdays • golf course discounts if you start playing after 4pm • theater matinee movie discounts

  5. Qualitative vs. QuantitativeForecasting Methods Some Qualitative Methods: • Experienced guess/judgement • Consensus of committee • Survey of sales force • Survey of all customers • Historical analogy • new products • Market research • survey a sample of customers • test market a product

  6. Steps for Quantitative Forecasting Methods • Collect past data—usually the more the better • Identify patterns in past data • Select one or more appropriate forecasting methods • Forecast part of past data with each method • Determine best parameters for each method • Compare forecasts with actual data • Select method that had smallest forecasting errors on past data • Forecast future time periods • Determine prediction interval (forecast range) • Monitor forecasting accuracy over time • Tracking signal

  7. Types of Quantitative Forecasting Methods Pattern Projection • time series regression • trend or seasonal models Data Smoothing • moving average • exponential smoothing Causal • multiple regression

  8. Sales Sales Sales Dec Dec Dec Time Time Time LEVEL TREND SEASONALITY Sales Sales 1980 1986 Time Time CYCLICALITY NOISE Data Pattern Components

  9. Identifying Data Patterns for Time Series Always Plot Data First • After plotting data, patterns are often obvious. Average or level • Use mean of all data Trend • Use time series regression – slope is trend – time period is independent variable Seasonality • Deseasonalize the data Cyclicality • Similar to deseasonalizing Random noise • No pattern – try to eliminate in forecasts

  10. Forecast Accuracy

  11. Forecast Accuracy

  12. Forecast Accuracy Example Period At Ft Et |Et| (Et)2 1 32 30 2 28 31 3 31 33 4 34 35 5 34 33 6 36 34 Totals:

  13. Forecast Accuracy Example Bias = MAD = MSE =

  14. Quantity of Electric Irons Shipped by U.S. Mfgs.

  15. Electric Irons Example -- Data Year QtyYear Qty 1979 12.079 1984 7.843 1980 11.478 1985 6.834 1981 11.013 1986 7.660 1982 6.616 1987 5.918 1983 7.279 1988 7.115 10-year average = Last-7-year average =

  16. Do time series regression analysis Y = a + bX Y = dependent variable (actual sales) X = independent variable (time period in this case) a = y-intercept (value of Y when X=0) b = slope or trend where N = number of periods of data

  17. Electric Irons Example X Y X2 XY 4 6.616 16 26.46 5 7.279 25 36.40 6 7.843 : : 7 6.834 : : 8 7.660 : : 9 5.918 : : 10 7.115 : : == ===== === ===== 49 49.265 371 343.45

  18. b = a = Y = Y11 = Y12 =

  19. Seasonality and Trend Patterns (Seasonalized Regression) Steps: 1. Deseasonalize the data to remove seasonality • divide by seasonal index (SI) 2. Use regression to model trend 3. Make initial forecasts to project trend 4. Seasonalize the forecast • multiply by SI

  20. Moving Company Example Spring Summer Fall Winter 1988 90 160 70 120 Overall Avg. 1989 130 200 90 100 2020/16 1990 80 170 130 140 = 126.25 1991 130210 80120 Total: 430 740 370 480 Avg: 107.5 185 92.5 120 SI:

  21. Deseasonalize the Data Spring Summer Fall Winter 1988 105.7* 109.2 95.5 126.3 1989 152.7 136.5 122.8 105.2 1990 94.0 116.0+ 177.4 147.3 1991 152.7 143.3 109.2 126.3 * Spring 1988: 90/.851 = 105.7 + Summer 1990: 170/1.465 = 116.0

  22. Perform Time Series Regression X Y X2 XY 1 105.7 1 105.7 2 109.2 4 218.4 3 95.5 9 286.6 4 : : : : : : : 16 126.3 256 2020.0 === ====== ===== ======= 136 2,020.0 1,496 17,773.5 Totals

  23. b = a = Y =

  24. Make initial forecasts: Y17 = Y18 = Y19 = Y20 = Make final forecasts: (Seasonalize F = Y x SI) F17 = F18 = F19 = F20 =

  25. Forecast Ranging Forecasts are rarely perfect! A forecast range reflects the degree of confidence that you have in your forecasts. Forecast ranging allows you to estimate a prediction interval for actual demand “There is a ___% probability that actual demand will be within the upper and lower limits of the forecast range.”

  26. Standard Error of the Forecast(a measure of dispersion of the forecast errors) Upper Limit = Fi + t(syx) Lower Limit = Fi - t(syx) Need desired level of significance (α) and degrees of freedom (df) to look up t in table

  27. Forecast Confidence Intervals (Forecast Ranging) (1 – α) α/2 α/2 t(Syx) Actual Sales in Future Ft Lower Limit Upper Limit

  28. t-statistic and degrees of freedom For a confidence interval of 95%,α = .05 (.025 in each tail), and df=16 From table, t = Why does df = n-2 for simple regression? If the forecast was from a multiple regression model with 3 independent variables, what would be the degrees of freedom? df = n - __

  29. Example: Judy manages a large used car dealership that has experienced a steady growth in sales during the last few years. Using time series regression and sales data for the last 20 quarters, Judy obtained a forecast of 800 car sales for next quarter. With her model and the past data the standard error of the forecast was 50 cars. What are the limits for a 95% forecast range? for an 80% forecast range?

  30. Example: A manager’s forecast of next month’s sales of product Q was 1500 units using time series regression based on the last 24 months of sales, which had a standard forecast error of 29 units. Her boss asked how sure she was that actual sales would be within 50 units of her forecast.

  31. Short Range Forecasting • A few days to a few months • Assumes there are no patterns in the data • Random noise has a greater impact in the short term • These approaches try to eliminate some of the random noise • Random walk, moving average, weighted moving average, exponential smoothing

  32. Random Walk The next forecast is equal to the last period’s actual value PeriodSalesForecast 1 21 2 30 3 27 4 ?

  33. Moving Average Method The next forecast is equal to an average of the last AP periods of actual data PeriodSalesAP=4AP=3AP=2 1 21 2 28 3 35 4 30 5 ?

  34. Impulse Response – how fast the forecasts react to changes in the data The higher the value of AP, the less the forecast will react to changes in the data, so the lower the impulse response is. Noise Dampening – how much the forecasts are smoothed Noise dampening is the opposite of impulse response. A moving average model with AP=1 has high impulse response and low noise dampening characteristics.

  35. Weighted Moving Average method Like the moving average method except that each of the AP periods can have a different weight Actual AP=4 PeriodSales Weight 1 21 .1 2 28 .15 3 35 .25 4 30 .5 5 ? Usually the recent periods have more weight

  36. Exponential Smoothing Most common short-term quantitative forecasting method (especially for forecasting inventory levels) Why? • surprisingly accurate • easy to understand • simple to use • very little data is stored Need 3 pieces of data to make forecast 1. most recent forecast 2. actual sales for that period 3. smoothing constant (α)

  37. Exponential Smoothing method • gives a different weight to each period Ft = Ft-1 + α(At-1 – Ft-1) α is the smoothing parameter and is between 0 and 1 Interpretation: the next forecast equals last period’s forecast plus a percentage of last period’s forecasting error. Alternative formula: Ft = αAt-1 + (1 - α)Ft-1 (rearranging terms)

  38. Example: assume α = 0.3 We must assume a forecast for an earlier period PeriodSalesForecast 1 21 2 24 3 23 4 19 5 22 6 ?

  39. Find best value for α by trial and error The larger α is, the more weight that is placed on the more recent periods’ actual values, so the higher the impulse and the lower the noise dampening.

  40. Tracking Signal After a forecasting method has been selected, tracking signal is used to monitor accuracy of the method as time passes Particularly good at identifying underforecasting or overforecasting trends Tracking Signal = Ideal value for tracking signal is ___

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