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CHAPTER 13 FORECASTING

CHAPTER 13 FORECASTING. Outline Forecasting and Choice of a Forecasting Methods Methods for Stationary Series: Simple and Weighted Moving Average Exponential smoothing Trend-Based Methods Regression Double Exponential Smoothing: Holt’s Method A Method for Seasonality and Trend.

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CHAPTER 13 FORECASTING

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  1. CHAPTER 13FORECASTING Outline • Forecasting and Choice of a Forecasting Methods • Methods for Stationary Series: • Simple and Weighted Moving Average • Exponential smoothing • Trend-Based Methods • Regression • Double Exponential Smoothing: Holt’s Method • A Method for Seasonality and Trend

  2. Forecasting

  3. Production Aggregate planning, inventory control, scheduling Marketing New product introduction, sales-force allocation, promotions Finance Plant/equipment investment, budgetary planning Personnel Workforce planning, hiring, layoff Decisions Based on Forecasts

  4. Forecasts are always wrong; so consider both expected value and a measure of forecast error Long-term forecasts are less accurate than short-term forecasts Aggregate forecasts are more accurate than disaggregate forecasts Characteristics of Forecasts

  5. Forecasting • Components of demand • Evaluation of forecasts • Time series: stationary series • Time series: trend • Linear regression • Double exponential smoothing • Time series: seasonality

  6. Components of Demand • Average demand • Trend • Gradual shift in average demand • Seasonal pattern • Periodic oscillation in demand which repeats • Cycle • Similar to seasonal patterns, length and magnitude of the cycle may vary • Random movements • Auto-correlation

  7. Components of Demand Qantity Time (a) Average: Data cluster about a horizontal line.

  8. Components of Demand Quantity Time (b) Linear trend: Data consistently increase or decrease.

  9. Components of Demand Year 1 Quantity | | | | | | | | | | | | J F M A M J J A S O N D Months (c) Seasonal influence: Data consistently show peaks and valleys.

  10. Components of Demand Year 1 Quantity Year 2 | | | | | | | | | | | | J F M A M J J A S O N D Months (c) Seasonal influence: Data consistently show peaks and valleys.

  11. Components of Demand

  12. Components of Demand Quantity | | | | | | 1 2 3 4 5 6 Years (c) Cyclical movements: Gradual changes over extended periods of time.

  13. Components of Demand

  14. Components of Demand Trend Demand Random movement Time Demand Trend with seasonal pattern Time

  15. Snow Skiing Seasonal Long term growth trend Demand for skiing products increased sharply after the Nagano Olympics

  16. Measures of Forecast Error Et = At - Ft RSFE = Et MAD = MSE = MAPE =  = MSE |Et | n Et2 n [|Et | (100)]/At n Choosing a MethodForecast Error

  17. Absolute Error Absolute Percent Month, Demand, Forecast, Error, Squared, Error, Error, tAtFtEt Et2 |Et| (|Et|/At)(100) 1 200 225 2 240 220 3 300 285 4 270 290 5 230 250 6 260 240 7 210 250 8 275 240 - Total Choosing a MethodForecast Error

  18. MSE = = MAD = = MAPE = = Choosing a MethodForecast Error Measures of Error RSFE =

  19. Running Sum Mean Absolute of Forecast Errors Deviation Method (RSFE - bias) (MAD) Simple moving average Three-week (n = 3) 23.1 17.1 Six-week (n = 6) 69.8 15.5 Weighted moving average 0.70, 0.20, 0.10 14.0 18.4 Exponential smoothing  = 0.1 65.6 14.8  = 0.2 41.0 15.3 Choosing a MethodForecast Error

  20. RSFE MAD Tracking signal = +2.0 — +1.5 — +1.0 — +0.5 — 0 — - 0.5 — - 1.0 — - 1.5 — Control limit Tracking signal Control limit | | | | | 0 5 10 15 20 25 Observation number Choosing a MethodTracking Signals

  21. RSFE MAD Tracking signal = +2.0 — +1.5 — +1.0 — +0.5 — 0 — - 0.5 — - 1.0 — - 1.5 — Out of control Control limit Tracking signal Control limit | | | | | 0 5 10 15 20 25 Observation number Choosing a MethodTracking Signals

  22. Choosing a MethodTracking Signals

  23. Problem 13-2: Historical demand for a product is: Month Jan Feb Mar Apr May Jun Demand 12 11 15 12 16 15 a. Using a weighted moving average with weights of 0.60, 0.30, and 0.10, find the July forecast. b. Using a simple three-month moving average, find the July forecast. c. Using single exponential smoothing with =0.20 and a June forecast =13, find the July forecast. d. Using simple regression analysis, calculate the regression equation for the preceding demand data e. Using regression equation in d, calculate the forecast in July

  24. Problem 13-15: In this problem, you are to test the validity of your forecasting model. Here are the forecasts for a model you have been using and the actual demands that occurred: Week 1 2 3 4 5 6 Forecast 800 850 950 950 1,000 975 Actual 900 1,000 1,050 900 900 1,100 Compute MAD and tracking signal. Then decide whether the forecasting model you have been using is giving reasonable results.

  25. Methods for Stationary Series

  26. 450 — 430 — 410 — 390 — 370 — Patient arrivals Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Time Series MethodsSimple Moving Averages Week

  27. Time Series MethodsSimple Moving Averages 450 — 430 — 410 — 390 — 370 — Patient Week Arrivals 1 400 2 380 3 411 Patient arrivals Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week

  28. Time Series MethodsSimple Moving Averages 450 — 430 — 410 — 390 — 370 — Patient Week Arrivals 1 400 2 380 3 411 Patient arrivals F4 = Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week

  29. Time Series MethodsSimple Moving Averages 450 — 430 — 410 — 390 — 370 — Patient Week Arrivals 2 380 3 411 4 415 Patient arrivals F5 = Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week

  30. 450 — 430 — 410 — 390 — 370 — 3-week MA forecast Patient arrivals Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week Time Series MethodsSimple Moving Averages

  31. 450 — 430 — 410 — 390 — 370 — 6-week MA forecast 3-week MA forecast Patient arrivals Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Time Series MethodsSimple Moving Averages Week

  32. Taco Bell determined that the demand for each 15-minute interval can be estimated from a 6-week simple moving average of sales. The forecast was used to determine the number of employees needed.

  33. Assigned weights t-1 0.70 t-2 0.20 t-3 0.10 Time Series MethodsWeighted Moving Average 450 — 430 — 410 — 390 — 370 — 3-week MA forecast Weighted Moving Average Patient arrivals F4 = Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week

  34. Assigned weights t-1 0.70 t-2 0.20 t-3 0.10 Time Series MethodsWeighted Moving Average 450 — 430 — 410 — 390 — 370 — 3-week MA forecast Weighted Moving Average Patient arrivals F5 = Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week

  35. Time Series MethodsExponential Smoothing 450 — 430 — 410 — 390 — 370 — Exponential Smoothing  = 0.10 Ft = At-1 + (1 - )Ft - 1 Patient arrivals | | | | | | 0 5 10 15 20 25 30 Week

  36. Time Series MethodsExponential Smoothing 450 — 430 — 410 — 390 — 370 — Exponential Smoothing  = 0.10 Ft = At-1 + (1 - )Ft - 1 F3 = (400 + 380)/2=390 A3 = 411 Patient arrivals | | | | | | 0 5 10 15 20 25 30 Week

  37. Time Series MethodsExponential Smoothing 450 — 430 — 410 — 390 — 370 — Exponential Smoothing  = 0.10 Ft = At-1 + (1 - )Ft - 1 F3 = (400 + 380)/2=390 A3 = 411 Patient arrivals F4 = | | | | | | 0 5 10 15 20 25 30 Week

  38. Time Series MethodsExponential Smoothing 450 — 430 — 410 — 390 — 370 — Exponential Smoothing  = 0.10 Ft = At + (1 - )Ft - 1 F4 = A4 = 415 Patient arrivals F5 = | | | | | | 0 5 10 15 20 25 30 Week

  39. 450 — 430 — 410 — 390 — 370 — Patient arrivals | | | | | | 0 5 10 15 20 25 30 Week Time Series MethodsExponential Smoothing

  40. Comparison of Exponential Smoothing and Simple Moving Average • Both Methods • Are designed for stationary demand • Require a single parameter • Lag behind a trend, if one exists • Have the same distribution of forecast error if

  41. Comparison of Exponential Smoothing and Simple Moving Average • Moving average uses only the last N periods data, exponential smoothing uses all data • Exponential smoothing uses less memory and requires fewer steps of computation; store only the most recent forecast!

  42. Problem 13-20: Your manager is trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecast and specify what procedure you would utilize: Month 1 2 3 4 5 6 7 8 9 10 11 12 Actual demand 62 65 67 68 71 73 76 78 78 80 84 85 a. Calculate the three-month SMA forecast for periods 4-12 b. Calculate the weighted three-month MA using weights of 0.50, 0.30, and 0.20 for periods 4-12. c. Calculate the single exponential smoothing forecast for periods 2-12 using an initial forecast, F1=61 and =0.30 d. Calculate the exponential smoothing with trend component forecast for periods 2-12 using T1=1.8,F1=60,=0.30,=0.30 e. Calculate MAD for the forecasts made by each technique in periods 4-12. Which forecasting method do you prefer?

  43. Trend-Based Methods

  44. Turkeys have a long-term trend for increasing demand with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January.

  45. Y Dependent variable X Independent variable Linear Regression

  46. Regression equation: Y = a + bX Y Dependent variable X Independent variable Linear Regression

  47. Regression equation: Y = a + bX Y Actual value of Y Dependent variable Value of X used to estimate Y X Independent variable Linear Regression

  48. Regression equation: Y = a + bX Y Estimate of Y from regression equation Actual value of Y Dependent variable Value of X used to estimate Y X Independent variable Linear Regression

  49. Deviation, or error Regression equation: Y = a + bX Y Estimate of Y from regression equation { Actual value of Y Dependent variable Value of X used to estimate Y X Independent variable Linear Regression

  50. Sales Advertising Month (000 units) (000 $) 1 264 2.5 2 116 1.3 3 165 1.4 4 101 1.0 5 209 2.0 Linear Regression

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