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  1. Supply Chain Management (SCM) Forecasting 2 Dr. Husam Arman

  2. Today’s Outline • Seasonal forecasting • Choosing between times series methods • Calculating errors; • Cumulative forecast error (CFE) • Mean absolute deviation (MAD) • Mean squared error (MSE) • Mean absolute percent error (MAPE) • Quantitative methods – • Causal methods - Linear regression

  3. Time-Series MethodsSeasonal Influences

  4. Quarter Year 1 Year 2 Year 3 Year 4 1 45 70 100 100 2 335 370 585 725 3 520 590 830 1160 4 100 170 285 215 Total 1000 1200 1800 2200 Average 250 300 450 550 Time-Series MethodsSeasonal Influences Example 12.6

  5. Quarter Year 1 Year 2 Year 3 Year 4 1 45 70 100 100 2 335 370 585 725 3 520 590 830 1160 4 100 170 285 215 Total 1000 1200 1800 2200 Average 250 300 450 550 Actual Demand Average Demand Seasonal Index = Time-Series MethodsSeasonal Influences Example 12.6

  6. Quarter Year 1 Year 2 Year 3 Year 4 1 45 70 100 100 2 335 370 585 725 3 520 590 830 1160 4 100 170 285 215 Total 1000 1200 1800 2200 Average 250 300 450 550 45 250 Seasonal Index = = 0.18 Time-Series MethodsSeasonal Influences Example 12.6

  7. Quarter Year 1 Year 2 Year 3 Year 4 1 45/250 = 0.18 70 100 100 2 335 370 585 725 3 520 590 830 1160 4 100 170 285 215 Total 1000 1200 1800 2200 Average 250 300 450 550 45 250 Seasonal Index = = 0.18 Time-Series MethodsSeasonal Influences Example 12.6

  8. Quarter Year 1 Year 2 Year 3 Year 4 1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.18 2 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32 3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.11 4 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39 Time-Series MethodsSeasonal Influences Example 12.6

  9. Quarter Year 1 Year 2 Year 3 Year 4 1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.18 2 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32 3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.11 4 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39 Quarter Average Seasonal Index 1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20 2 3 4 Time-Series MethodsSeasonal Influences Example 12.6

  10. Quarter Year 1 Year 2 Year 3 Year 4 1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.18 2 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32 3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.11 4 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39 Quarter Average Seasonal Index 1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20 2 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.30 3 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.00 4 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50 Time-Series MethodsSeasonal Influences Example 12.6

  11. Quarter Year 1 Year 2 Year 3 Year 4 1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.18 2 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32 3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.11 4 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39 Projected Annual Demand = 2600 Average Quarterly Demand = 2600/4 = 650 Quarter Average Seasonal Index Forecast 1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20 2 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.30 3 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.00 4 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50 Time-Series MethodsSeasonal Influences Example 12.6

  12. Quarter Year 1 Year 2 Year 3 Year 4 1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.18 2 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32 3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.11 4 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39 Projected Annual Demand = 2600 Average Quarterly Demand = 2600/4 = 650 Quarter Average Seasonal Index Forecast 1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20 650(0.20) = 130 2 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.30 3 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.00 4 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50 Time-Series MethodsSeasonal Influences Example 12.6

  13. Quarter Year 1 Year 2 Year 3 Year 4 1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.18 2 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32 3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.11 4 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39 Quarter Average Seasonal Index Forecast 1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20 650(0.20) = 130 2 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.30 650(1.30) = 845 3 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.00 650(2.00) = 1300 4 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50 650(0.50) = 325 Time-Series MethodsSeasonal Influences Example 12.6

  14. Measures of Forecast Error Et = Dt – Ft Choosing a MethodForecast Error Example 12.7

  15. Measures of Forecast Error Et = Dt – Ft CFE = Et  = MSE = MAD = MAPE = (Et – E)2 n– 1 Et2 n [|Et | (100)]/Dt n |Et | n Choosing a MethodForecast Error Example 12.7

  16. Absolute Error Absolute Percent Month, Demand, Forecast, Error, Squared, Error, Error, tDtFtEt Et2 |Et| (|Et|/Dt)(100) 1 200 225 -25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7 Total –15 5275 195 81.3% Choosing a MethodForecast Error Example 12.7

  17. Measures of Error Absolute Error Absolute Percent Month, Demand, Forecast, Error, Squared, Error, Error, tDtFtEt Et2 |Et| (|Et|/Dt)(100) 1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7 Total –15 5275 195 81.3% Choosing a MethodForecast Error Example 12.7

  18. Measures of Error Absolute Error Absolute Percent Month, Demand, Forecast, Error, Squared, Error, Error, tDtFtEt Et2 |Et| (|Et|/Dt)(100) 1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7 Total –15 5275 195 81.3% CFE = – 15 Choosing a MethodForecast Error Example 12.7

  19. Measures of Error Absolute Error Absolute Percent Month, Demand, Forecast, Error, Squared, Error, Error, tDtFtEt Et2 |Et| (|Et|/Dt)(100) 1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7 Total –15 5275 195 81.3% CFE = – 15 –15 8 E = = – 1.875 Choosing a MethodForecast Error Example 12.7

  20. Measures of Error Absolute Error Absolute Percent Month, Demand, Forecast, Error, Squared, Error, Error, tDtFtEt Et2 |Et| (|Et|/Dt)(100) 1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7 Total –15 5275 195 81.3% CFE = – 15 – 15 8 E = = – 1.875 5275 8 MSE = = 659.4 Choosing a MethodForecast Error Example 12.7

  21. Measures of Error Absolute Error Absolute Percent Month, Demand, Forecast, Error, Squared, Error, Error, tDtFtEt Et2 |Et| (|Et|/Dt)(100) 1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7 Total –15 5275 195 81.3% CFE = – 15 – 15 8 E = = – 1.875 5275 8 MSE = = 659.4 s = 27.4 Choosing a MethodForecast Error Example 12.7

  22. Measures of Error Absolute Error Absolute Percent Month, Demand, Forecast, Error, Squared, Error, Error, tDtFtEt Et2 |Et| (|Et|/Dt)(100) 1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7 Total –15 5275 195 81.3% CFE = – 15 – 15 8 E = = – 1.875 5275 8 MSE = = 659.4 195 8 s = 27.4 MAD = = 24.4 Choosing a MethodForecast Error Example 12.7

  23. Measures of Error Absolute Error Absolute Percent Month, Demand, Forecast, Error, Squared, Error, Error, tDtFtEt Et2 |Et| (|Et|/Dt)(100) 1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7 Total –15 5275 195 81.3% CFE = – 15 – 15 8 E = = – 1.875 5275 8 MSE = = 659.4 195 8 s = 27.4 MAD = = 24.4 81.3% 8 MAPE = = 10.2% Choosing a MethodForecast Error Example 12.7

  24. Measures of Error Absolute Error Absolute Percent Month, Demand, Forecast, Error, Squared, Error, Error, tDtFtEt Et2 |Et| (|Et|/Dt)(100) 1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7 Total –15 5275 195 81.3% CFE = – 15 – 15 8 E = = – 1.875 5275 8 MSE = = 659.4 195 8 s = 27.4 MAD = = 24.4 81.3% 8 MAPE = = 10.2% Choosing a MethodForecast Error Example 12.7

  25. Choosing a MethodForecast Error

  26. Choosing between time series methods • Assuming we decided time series is the right technique in general !! • Stable demand Vs. Dynamic demand • Adjust parameters; , n and  • Combine techniques! • averaging forecasts results using different technique • evidences say better output

  27. Causal models • Examples of related variables for Causal models • Value of property owned and the income levelof owner • Number of days holiday spent from home and family income and family size • Annual retail sales of washing machines and price, per capita incomeand new house completion

  28. Causal models INPUTS THE MODEL OUTPUT Price X1 Per capita income X2 New house completion X3 Y Annual sales THE INDEPENDENT VARIABLES THE DEPENDENT VARIABLES

  29. Forecasting with Causal models How do we build a model Price X1 Per capita income X2 New house completion X3 Y Annual sales Set these values Generate a forecast Run the model

  30. The Causal forecasting process • Typically relates demand to explanatory variables • Input variables are the independent variables • The variable that we wish to predict is known as the dependent variable • Univariateproblems- one independent variable • Mulitvariate problems- more than one independent variable

  31. Model building • The problem is finding an ‘adequate’ relationship • If Causal processes are clearly understood we may be able to construct model • More commonly, use a ‘flexible’ form of relationship and employ statistical methods to define it explicitly - regression • The key issue is its predictive accuracy

  32. Y Dependent variable X Independent variable Causal MethodsLinear Regression Figure 12.2

  33. Simple Linear Regression Model Y The simple linear regression model seeks to fit a line through various data over time. a x Yt = a + bx Ytis the regressed forecast value or dependent variable in the model, a is the intercept value of the regression line, and b is similar to the slope of the regression line.

  34. Simple Linear Regression Formulas for Calculating “a” and “b”

  35. Y Dependent variable X Independent variable Causal MethodsLinear Regression Figure 12.2

  36. Regression equation: Y = a + bX Y Dependent variable X Independent variable Causal MethodsLinear Regression Figure 12.2

  37. Regression equation: Y = a + bX Y Actual value of Y Dependent variable Value of X used to estimate Y X Independent variable Causal MethodsLinear Regression Figure 12.2

  38. 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 Causal MethodsLinear Regression Figure 12.2

  39. 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 Causal MethodsLinear Regression Figure 12.2

  40. 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 Causal MethodsLinear Regression Example 12.1

  41. 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 Causal MethodsLinear Regression a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Example 12.1

  42. 300 — 250 — 200 — 150 — 100 — 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 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) | | | | 1.0 1.5 2.0 2.5 Advertising (thousands of dollars) Causal MethodsLinear Regression Figure 12.3

  43. 300 — 250 — 200 — 150 — 100 — 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 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) | | | | 1.0 1.5 2.0 2.5 Advertising (thousands of dollars) Causal MethodsLinear Regression Figure 12.3

  44. 300 — 250 — 200 — 150 — 100 — 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 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) Y = – 8.136 + 109.229X | | | | 1.0 1.5 2.0 2.5 Advertising (thousands of dollars) Causal MethodsLinear Regression Figure 12.3

  45. 300 — 250 — 200 — 150 — 100 — 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 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) Y = – 8.136 + 109.229X | | | | 1.0 1.5 2.0 2.5 Advertising (thousands of dollars) Causal MethodsLinear Regression Figure 12.3

  46. 300 — 250 — 200 — 150 — 100 — 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 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) Y = – 8.136 + 109.229X | | | | 1.0 1.5 2.0 2.5 Forecast for Month 6 X = $1750, Y = – 8.136 + 109.229(1.75) Advertising (thousands of dollars) Causal MethodsLinear Regression Figure 12.3

  47. 300 — 250 — 200 — 150 — 100 — 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 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) Y = – 8.136 + 109.229X | | | | 1.0 1.5 2.0 2.5 Forecast for Month 6 X = $1750, Y = 183.015, or 183,015 units Advertising (thousands of dollars) Causal MethodsLinear Regression Figure 12.3

  48. 300 — 250 — 200 — 150 — 100 — 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 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) Y = – 8.136 + 109.229X | | | | 1.0 1.5 2.0 2.5 Advertising (thousands of dollars) Causal MethodsLinear Regression Figure 12.3

  49. 300 — 250 — 200 — 150 — 100 — 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 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) Y = – 8.136 + 109.229X | | | | 1.0 1.5 2.0 2.5 Advertising (thousands of dollars) Causal MethodsLinear Regression Figure 12.3

  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 Causal MethodsLinear Regression Example 12.1