1. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Forecasting A. A. Elimam

2. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Components of Demand Quantity Time (a) Average: Data cluster about a horizontal line.

3. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Components of Demand Quantity Time (b) Linear trend: Data consistently increase or decrease.

4. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Components of Demand Quantity |||||||||||| JFMAMJJASOND Months (c) Seasonal influence: Data consistently show peaks and valleys. Year 1

5. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Components of Demand Quantity |||||||||||| JFMAMJJASOND Months (c) Seasonal influence: Data consistently show peaks and valleys. Year 1 Year 2

6. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Components of Demand Quantity |||||| 123456 Years (c) Cyclical movements: Gradual changes over extended periods of time.

7. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Forecasting Elements: Time Horizon Short-range: immediate future - 3 months Medium-range: several months to a year Long range: More than one year

8. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Forecasting Applications: Examples Short-range: Weekly staffing Medium-range: Production Planning Long range: Plant Capacity

9. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. 1. Identify the purpose of forecast 2. Collect historical data 3. Plot data and identify patterns 4. Select a forecast model 5. Develop/compute forecast 6. Check forecast accuracy (A):The Forecasting Process

10. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. (B): The Forecasting Process 10. Monitor results and measure accuracy 8b. Select new forecast model 9. Adjust forecast 7. Is accuracy acceptable? 8a. Forecast over planning horizon

11. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Data Patterns Flat Average: Up and Down Trend: Gradual up or down Seasonal Pattern: periodic, oscillating & repetitive Cyclic: Undulating, repetitive movement up and down

12. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression Dependent variable Independent variable X Y Actual value of Y Estimate of Y from regression equation Value of X used to estimate Y Regression equation: Y = a + bX

13. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression Dependent variable Independent variable X Y Actual value of Y Estimate of Y from regression equation Value of X used to estimate Y Deviation, or error { Regression equation: Y = a + bX

14. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 a = Y - b X b =  XY - n XY  X 2 - n X 2

15. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. a = Y - b X b =  XY - n XY  X 2 - n X 2 Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 12642.5660.06.25 21161.3150.81.69 31651.4231.01.96 41011.0101.01.00 52092.0418.04.00 Total8558.21560.814.90 Y = 171X = 1.64 Causal Methods Linear Regression

16. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression a = Y - b X b = 1560.8 - 5(1.64)(171) 14.90 - 5(1.64) 2 Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 12642.5660.06.25 21161.3150.81.69 31651.4231.01.96 41011.0101.01.00 52092.0418.04.00 Total8558.21560.814.90 Y = 171X = 1.64

17. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression a = Y - b X b = 109.229 Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 12642.5660.06.25 21161.3150.81.69 31651.4231.01.96 41011.0101.01.00 52092.0418.04.00 Total8558.21560.814.90 Y = 171X = 1.64

18. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression a = 171 - 109.229(1.64) b = 109.229 Sales, YAdvertising, Month(000 units)(000 $)XYX 2 12642.5660.06.25 21161.3150.81.69 31651.4231.01.96 41011.0101.01.00 52092.0418.04.00 Total8558.21560.814.90 Y = 171X = 1.64

19. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression a = - 8.136 b = 109.229 Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 12642.5660.06.25 21161.3150.81.69 31651.4231.01.96 41011.0101.01.00 52092.0418.04.00 Total8558.21560.814.90 Y = 171X = 1.64 Y = - 8.136 + 109.229(X)

20. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression 300 — 250 — 200 — 150 — 100 — 50 a = - 8.136 b = 109.229 Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 Y = - 8.136 + 109.229(X) Sales (000s) |||| 1.01.52.02.5 Advertising (000s)

21. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 12642.5660.06.25 21161.3150.81.69 31651.4231.01.96 41011.0101.01.00 52092.0418.04.00 Total8558.21560.814.90 Y = 171X = 1.64 r = 0.98 r 2 = 0.96  YX = 15.61

22. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y 2 12642.5660.06.2569,696 21161.3150.81.6913,456 31651.4231.01.9627,225 41011.0101.01.0010,201 52092.0418.04.0043,681 Total8558.21560.814.90164,259 Y = 171X = 1.64 r = 0.98 r 2 = 0.96  YX = 15.61 Forecast for Month 6: Advertising expenditure = $1750 Y = 183.015 or 183,015 hinges

23. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Simple Moving Averages Week 450 — 430 — 410 — 390 — 370 — Patient arrivals |||||| 051015202530 Actual patient arrivals

24. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Simple Moving Averages Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Patient WeekArrivals 1400 2380 3411

25. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Simple Moving Averages Week Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Patient arrivals |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 F 4 = 411 + 380 + 400 3

26. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Simple Moving Averages Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 F 4 = 397.0

27. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Simple Moving Averages Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 F 4 = 397.0

28. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Simple Moving Averages Week Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Patient arrivals |||||| 051015202530 Patient WeekArrivals 2380 3411 4415 F 5 = 415 + 411 + 380 3

29. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Simple Moving Averages Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Patient WeekArrivals 2380 3411 4415 F 5 = 402.0

30. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Simple Moving Averages 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Actual patient arrivals 3-week MA forecast

31. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Simple Moving Averages Week 450 — 430 — 410 — 390 — 370 — Patient arrivals |||||| 051015202530 Actual patient arrivals 3-week MA forecast 6-week MA forecast

32. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Weighted Moving Average Week 450 — 430 — 410 — 390 — 370 — Patient arrivals |||||| 051015202530 Actual patient arrivals 3-week MA forecast 6-week MA forecast Weighted Moving Average Assigned weights t 0.70 t -10.20 t -20.10

33. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Weighted Moving Average 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Actual patient arrivals 3-week MA forecast 6-week MA forecast Weighted Moving Average Assigned weights t 0.70 t -10.20 t -20.10 F 4 = 0.70(411) + 0.20(380) + 0.10(400)

34. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Weighted Moving Average 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Actual patient arrivals 3-week MA forecast 6-week MA forecast Weighted Moving Average Assigned weights t 0.70 t -10.20 t -20.10 F 4 = 403.7

35. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Weighted Moving Average 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Actual patient arrivals 3-week MA forecast 6-week MA forecast Weighted Moving Average Assigned weights t 0.70 t -10.20 t -20.10 F 4 = 403.7 F 5 = 410.7

36. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Weighted Moving Average 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Actual patient arrivals 3-week MA forecast 6-week MA forecast Weighted Moving Average Assigned weights t 0.70 t -10.20 t -20.10 F 4 = 403.7 F 5 = 410.7

37. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Exponential Smoothing 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Exponential Smoothing  = 0.10 F t = F t - 1 +  D t-1 - F t - 1 )

38. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Exponential Smoothing F t = F t-1 +  D t-1 - F t-1 ) F t = the forecast for next period D t-1 = actual demand for present period F t-1 = forecast for period t  = weighting factor - smoothing constant

39. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Exponential Smoothing 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Exponential Smoothing  = 0.10 F 4 = 390+ 0.10(411 - 390) F t - 1 = (400 + 380)/2 D 3 = 411 F t = F t - 1 +  D t-1 - F t - 1 )

40. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Exponential Smoothing 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 F 4 = 392.1 F 4 = 390+ 0.10(411 - 390) F t - 1 = (400 + 380)/2 D 3 = 411 F t = F t - 1 +  D t-1 - F t - 1 )

41. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Exponential Smoothing Week 450 — 430 — 410 — 390 — 370 — Patient arrivals |||||| 051015202530 F 4 = 392.1 D 4 = 415 Exponential Smoothing  = 0.10b F 4 = 392.1 F 5 = 394.4 F t = F t - 1 +  D t-1 - F t - 1 )

42. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Exponential Smoothing 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530

43. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Linear Regression Analysis ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Y n = a + bX n where X n = Week n

44. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Time Series Methods Linear Regression Analysis ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Y n = a + bX n where X n = Week n

45. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. QuarterYear 1Year 2Year 3Year 4 14570100100 2335370585725 35205908301160 4100170285215 Total1000120018002200 Average250300450550 Seasonal Index = Actual Demand Average Demand Time Series Methods Seasonal Influences

46. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. QuarterYear 1Year 2Year 3Year 4 145/250 = 0.1870100100 2335370585725 35205908301160 4100170285215 Total1000120018002200 Average250300450550 Seasonal Index = = 0.18 45 250 Time Series Methods Seasonal Influences

47. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Quarter Year 1 Year 2 Year 3 Year 4 145/250 = 0.1870/300 = 0.23100/450 = 0.22100/550 = 0.18 2335/250 = 1.34370/300 = 1.23585/450 = 1.30725/550 = 1.32 3520/250 = 2.08590/300 = 1.97830/450 = 1.841160/550 = 2.11 4100/250 = 0.40170/300 = 0.57285/450 = 0.63215/550 = 0.39 QuarterAverage 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 Methods Seasonal Influences

48. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Quarter Year 1 Year 2 Year 3 Year 4 145/250 = 0.1870/300 = 0.23100/450 = 0.22100/550 = 0.18 2335/250 = 1.34370/300 = 1.23585/450 = 1.30725/550 = 1.32 3520/250 = 2.08590/300 = 1.97830/450 = 1.841160/550 = 2.11 4100/250 = 0.40170/300 = 0.57285/450 = 0.63215/550 = 0.39 QuarterAverage Seasonal IndexForecast 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 Projected Annual Demand = 2600 Average Quarterly Demand = 2600/4 = 650 Time Series Methods Seasonal Influences

49. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Quarter Year 1 Year 2 Year 3 Year 4 145/250 = 0.1870/300 = 0.23100/450 = 0.22100/550 = 0.18 2335/250 = 1.34370/300 = 1.23585/450 = 1.30725/550 = 1.32 3520/250 = 2.08590/300 = 1.97830/450 = 1.841160/550 = 2.11 4100/250 = 0.40170/300 = 0.57285/450 = 0.63215/550 = 0.39 QuarterAverage Seasonal IndexForecast 1(0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20650(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 Projected Annual Demand = 2600 Average Quarterly Demand = 2600/4 = 650 Time Series Methods Seasonal Influences

50. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Quarter Year 1 Year 2 Year 3 Year 4 145/250 = 0.1870/300 = 0.23100/450 = 0.22100/550 = 0.18 2335/250 = 1.34370/300 = 1.23585/450 = 1.30725/550 = 1.32 3520/250 = 2.08590/300 = 1.97830/450 = 1.841160/550 = 2.11 4100/250 = 0.40170/300 = 0.57285/450 = 0.63215/550 = 0.39 QuarterAverage Seasonal IndexForecast 1(0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20650(0.20) =130 2(1.34 + 1.23 + 1.30 + 1.32)/4 = 1.30650(1.30) =845 3(2.08 + 1.97 + 1.84 + 2.11)/4 = 2.00650(2.00) =1300 4(0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50650(0.50) =325 Time Series Methods Seasonal Influences

51. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Et2nEt2n Bias CFE =  E t Mean Square Error MSE =  = MSE Measures of Forecast Error E t = D t - F t Choosing a Method Forecast Error

52. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Mean Absolute Deviation MAD = Mean Absolute Percent Error MAPE =  |E t | n  [ |E t | (100) ] / D t n Measures of Forecast Error E t = D t - F t Choosing a Method Forecast Error

53. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Bias: When Consistently over or under- forecasting. MSE: To avoid canceling out (+ve and -ve) Error. Penalizes large Errors MAD: To avoid canceling out (+ve and -ve) without Penalizing large Errors MAPE: To consider error relative to the order of magnitude of forecast value Selecting a Forecast Error Measurement

54. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) 1200225-25 625 2512.5% 224022020 400 208.3 330028515 225 155.0 4270290-20 400 207.4 5230250-20 400 208.7 626024020 400 207.7 7210250-40 1600 4019.0 827524035 1225 3512.7 Total-15 5275 19581.3% Choosing a Method Forecast Error

55. To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) 1200225-25 625 2512.5% 224022020 400 208.3 330028515 225 155.0 4270290-20 400 207.4 5230250-20 400 208.7 626024020 400 207.7 7210250-40 1600 4019.0 827524035 1225 3512.7 Total-15 5275 19581.3% MSE = = 659.4 5275 8 CFE = - 15 Measures of Error MAD = = 24.4 195 8 MAPE = = 10.2% 81.3% 8 Choosing a Method Forecast Error