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Outline – Continued

Outline – Continued. Time-Series Forecasting Decomposition of a Time Series Naive Approach Moving Averages Exponential Smoothing Exponential Smoothing with Trend Adjustment Trend Projections Seasonal Variations in Data Cyclical Variations in Data. Outline – Continued.

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Outline – Continued

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  1. Outline – Continued • Time-Series Forecasting • Decomposition of a Time Series • Naive Approach • Moving Averages • Exponential Smoothing • Exponential Smoothing with Trend Adjustment • Trend Projections • Seasonal Variations in Data • Cyclical Variations in Data

  2. Outline – Continued • Associative Forecasting Methods: Regression and Correlation Analysis • Using Regression Analysis for Forecasting • Standard Error of the Estimate • Correlation Coefficients for Regression Lines • Multiple-Regression Analysis

  3. Outline – Continued • Monitoring and Controlling Forecasts • Adaptive Smoothing • Focus Forecasting • Forecasting In The Service Sector

  4. Forecasting at Disney World • Global portfolio includes parks in Hong Kong, Paris, Tokyo, Orlando, and Anaheim • Revenues are derived from people – how many visitors and how they spend their money • Daily management report contains only the forecast and actual attendance at each park

  5. Forecasting at Disney World • Disney generates daily, weekly, monthly, annual, and 5-year forecasts • Forecast used by labor management, maintenance, operations, finance, and park scheduling • Forecast used to adjust opening times, rides, shows, staffing levels, and guests admitted

  6. Forecasting at Disney World • 20% of customers come from outside the USA • Economic model includes gross domestic product, cross-exchange rates, arrivals into the USA • A staff of 35 analysts and 70 field people survey 1 million park guests, employees, and travel professionals each year

  7. Forecasting at Disney World • Inputs to the forecasting model include airline specials, Federal Reserve policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world • Average forecast error for the 5-year forecast is 5% • Average forecast error for annual forecasts is between 0% and 3%

  8. ?? What is Forecasting? • Process of predicting a future event • Underlying basis of all business decisions • Production • Inventory • Personnel • Facilities

  9. Forecasting Time Horizons • Short-range forecast • Up to 1 year, generally less than 3 months • Purchasing, job scheduling, workforce levels, job assignments, production levels • Medium-range forecast • 3 months to 3 years • Sales and production planning, budgeting • Long-range forecast • 3+ years • New product planning, facility location, research and development

  10. Seven Steps in Forecasting • Determine the use of the forecast • Select the items to be forecasted • Determine the time horizon of the forecast • Select the forecasting model(s) • Gather the data • Make the forecast • Validate and implement results

  11. The Realities! • Forecasts are seldom perfect • Most techniques assume an underlying stability in the system • Product family and aggregated forecasts are more accurate than individual product forecasts

  12. Forecasting Approaches Quantitative Methods • Used when situation is ‘stable’ and historical data exist • Existing products • Current technology • Involves mathematical techniques • e.g., forecasting sales of color televisions

  13. Time-Series Models Associative Model Overview of Quantitative Approaches • Naive approach • Moving averages • Exponential smoothing • Trend projection • Linear regression

  14. Time Series Forecasting • Set of evenly spaced numerical data • Obtained by observing response variable at regular time periods • Forecast based only on past values, no other variables important • Assumes that factors influencing past and present will continue influence in future

  15. Trend Cyclical Seasonal Random Time Series Components

  16. Trend component Seasonal peaks Actual demand Demand for product or service Average demand over four years Random variation | | | | 1 2 3 4 Year Components of Demand Figure 4.1

  17. Trend Component • Persistent, overall upward or downward pattern • Changes due to population, technology, age, culture, etc. • Typically several years duration

  18. Number of Period Length Seasons Week Day 7 Month Week 4-4.5 Month Day 28-31 Year Quarter 4 Year Month 12 Year Week 52 Seasonal Component • Regular pattern of up and down fluctuations • Due to weather, customs, etc. • Occurs within a single year

  19. 0 5 10 15 20 Cyclical Component • Repeating up and down movements • Affected by business cycle, political, and economic factors • Multiple years duration • Often causal or associative relationships

  20. M T W T F Random Component • Erratic, unsystematic, ‘residual’ fluctuations • Due to random variation or unforeseen events • Short duration and nonrepeating

  21. Naive Approach • Assumes demand in next period is the same as demand in most recent period • e.g., If January sales were 68, then February sales will be 68 • Sometimes cost effective and efficient • Can be good starting point

  22. ∑ demand in previous n periods n Moving average = Moving Average Method • MA is a series of arithmetic means • Used if little or no trend • Used often for smoothing • Provides overall impression of data over time

  23. Actual 3-Month Month Shed Sales Moving Average January 10 February 12 March 13 April 16 May 19 June 23 July 26 10 12 13 (10 + 12 + 13)/3 = 11 2/3 Moving Average Example (12 + 13 + 16)/3 = 13 2/3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1/3

  24. Moving Average Forecast 30 – 28 – 26 – 24 – 22 – 20 – 18 – 16 – 14 – 12 – 10 – Actual Sales Shed Sales | | | | | | | | | | | | J F M A M J J A S O N D Graph of Moving Average

  25. Potential Problems With Moving Average • Increasing n smooths the forecast but makes it less sensitive to changes • Do not forecast trends well • Require extensive historical data

  26. Exponential Smoothing • Form of weighted moving average • Weights decline exponentially • Most recent data weighted most • Requires smoothing constant () • Ranges from 0 to 1 • Subjectively chosen • Involves little record keeping of past data

  27. Exponential Smoothing New forecast = Last period’s forecast + a(Last period’s actual demand – Last period’s forecast) Ft = Ft – 1 +a(At – 1 - Ft – 1) where Ft = new forecast Ft – 1 = previous forecast a = smoothing (or weighting) constant (0 ≤a≤ 1)

  28. Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20

  29. New forecast = 142 + .2(153 – 142) Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20

  30. Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = 142 + .2(153 – 142) = 142 + 2.2 = 144.2 ≈ 144 cars

  31. Weight Assigned to Most 2nd Most 3rd Most 4th Most 5th Most Recent Recent Recent Recent Recent Smoothing Period Period Period Period Period Constant (a) a(1 - a) a(1 - a)2a(1 - a)3a(1 - a)4 a = .1 .1 .09 .081 .073 .066 a = .5 .5 .25 .125 .063 .031 Effect of Smoothing Constants

  32. 225 – 200 – 175 – 150 – Actual demand a = .5 Demand a = .1 | | | | | | | | | 1 2 3 4 5 6 7 8 9 Quarter Impact of Different 

  33. 225 – 200 – 175 – 150 – • Chose high values of  when underlying average is likely to change • Choose low values of  when underlying average is stable Actual demand a = .5 Demand a = .1 | | | | | | | | | 1 2 3 4 5 6 7 8 9 Quarter Impact of Different 

  34. Choosing  The objective is to obtain the most accurate forecast no matter the technique We generally do this by selecting the model that gives us the lowest forecast error Forecast error = Actual demand - Forecast value = At - Ft

  35. Mean Absolute Deviation (MAD) Mean Squared Error (MSE) MAD = ∑ |Actual - Forecast| n ∑(Forecast Errors)2 n MSE = Common Measures of Error

  36. Mean Absolute Percent Error (MAPE) n i = 1 ∑100|Actuali - Forecasti|/Actuali n MAPE = Common Measures of Error

  37. Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloadeda = .10 a = .10 a = .50 a = .50 1 180 175 5.00 175 5.00 2 168 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 175 173.18 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62 Comparison of Forecast Error

  38. ∑ |deviations| n MAD = For a = .10 = 82.45/8 = 10.31 For a = .50 = 98.62/8 = 12.33 Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloadeda = .10 a = .10 a = .50 a = .50 1 180 175 5.00 175 5.00 2 168 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 175 173.18 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62

  39. For a = .10 = 1,526.54/8 = 190.82 For a = .50 = 1,561.91/8 = 195.24 ∑(forecast errors)2 n MSE = Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloadeda = .10 a = .10 a = .50 a = .50 1 180 175 5.00 175 5.00 2 168 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 175 173.18 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62 MAD 10.31 12.33

  40. n i = 1 ∑100|deviationi|/actuali n MAPE = For a = .10 = 44.75/8 = 5.59% For a = .50 = 54.05/8 = 6.76% Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloadeda = .10 a = .10 a = .50 a = .50 1 180 175 5.00 175 5.00 2 168 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 175 173.18 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62 MAD 10.31 12.33 MSE 190.82 195.24

  41. Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloadeda = .10 a = .10 a = .50 a = .50 1 180 175 5.00 175 5.00 2 168 175.5 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4 175 173.18 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8 182 178.22 3.78 186.30 4.30 82.45 98.62 MAD 10.31 12.33 MSE 190.82 195.24 MAPE 5.59% 6.76%

  42. ^ y = a + bx ^ where y = computed value of the variable to be predicted (dependent variable) a = y-axis intercept b = slope of the regression line x = the independent variable Trend Projections Fitting a trend line to historical data points to project into the medium to long-range Linear trends can be found using the least squares technique

  43. Actual observation (y value) Deviation7 Deviation5 Deviation6 Deviation3 Values of Dependent Variable Deviation4 Deviation1 (error) Deviation2 ^ Trend line, y = a + bx Time period Least Squares Method Figure 4.4

  44. Actual observation (y value) Deviation7 Deviation5 Deviation6 Deviation3 Values of Dependent Variable Deviation4 Deviation1 Deviation2 ^ Trend line, y = a + bx Time period Least Squares Method Least squares method minimizes the sum of the squared errors (deviations) Figure 4.4

  45. Sxy - nxy Sx2 - nx2 b = ^ y = a + bx a = y - bx Least Squares Method Equations to calculate the regression variables

  46. Time Electrical Power Year Period (x) Demand x2 xy 2001 1 74 1 74 2002 2 79 4 158 2003 3 80 9 240 2004 4 90 16 360 2005 5 105 25 525 2005 6 142 36 852 2007 7 122 49 854 ∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063 x = 4 y = 98.86 3,063 - (7)(4)(98.86) 140 - (7)(42) a = y - bx = 98.86 - 10.54(4) = 56.70 ∑xy - nxy ∑x2 - nx2 b = = = 10.54 Least Squares Example

  47. Time Electrical Power Year Period (x) Demand x2 xy 1999 1 74 1 74 2000 2 79 4 158 2001 3 80 9 240 2002 4 90 16 360 2003 5 105 25 525 2004 6 142 36 852 2005 7 122 49 854 Sx = 28 Sy = 692 Sx2 = 140 Sxy = 3,063 x = 4 y = 98.86 The trend line is ^ y = 56.70 + 10.54x 3,063 - (7)(4)(98.86) 140 - (7)(42) a = y - bx = 98.86 - 10.54(4) = 56.70 Sxy - nxy Sx2 - nx2 b = = = 10.54 Least Squares Example

  48. Trend line, y = 56.70 + 10.54x 160 – 150 – 140 – 130 – 120 – 110 – 100 – 90 – 80 – 70 – 60 – 50 – ^ Power demand | | | | | | | | | 2001 2002 2003 2004 2005 2006 2007 2008 2009 Year Least Squares Example

  49. Seasonal Variations In Data The multiplicative seasonal model can adjust trend data for seasonal variations in demand

  50. Seasonal Variations In Data Steps in the process: Find average historical demand for each season Compute the average demand over all seasons Compute a seasonal index for each season Estimate next year’s total demand Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season

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