1. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Chapter 12 - Forecasting

2. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Patterns of Demand

3. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Patterns of Demand Quantity Time Figure 12.1

4. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Patterns of Demand Quantity Time (a) Horizontal: Data cluster about a horizontal line. Figure 12.1

5. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Patterns of Demand Quantity Time (b) Trend: Data consistently increase or decrease. Figure 12.1

6. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Patterns of Demand Quantity |||||||||||| JFMAMJJASOND Months (c) Seasonal: Data consistently show peaks and valleys. Year 1 Figure 12.1

7. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Patterns of Demand Quantity |||||||||||| JFMAMJJASOND Months Year 1 Year 2 (c) Seasonal: Data consistently show peaks and valleys. Figure 12.1

8. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Patterns of Demand Quantity |||||| 123456 Years (c) Cyclical: Data reveal gradual increases and decreases over extended periods. Figure 12.1

9. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Demand Forecast Applications

10. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Demand Forecast Applications Table 12.1 Time Horizon Medium TermLong Term Short Term (3 months–(more than Application(0–3 months) 2 years) 2 years) Forecast quantity Decision area Forecasting technique

11. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Demand Forecast Applications Table 12.1 Time Horizon Medium TermLong Term Short Term (3 months–(more than Application(0–3 months) 2 years) 2 years) Forecast quantityIndividual products or services Decision areaInventory management Final assembly scheduling Workforce scheduling Master production scheduling ForecastingTime series techniqueCausal Judgment

12. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Demand Forecast Applications Table 12.1 Time Horizon Medium TermLong Term Short Term (3 months–(more than Application(0–3 months) 2 years) 2 years) Forecast quantityIndividualTotal sales products orGroups or families servicesof products or services Decision areaInventoryStaff planning managementProduction Final assemblyplanning schedulingMaster production Workforcescheduling schedulingPurchasing Master productionDistribution scheduling ForecastingTime seriesCausal techniqueCausalJudgment Judgment

13. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Demand Forecast Applications Time Horizon Medium TermLong Term Short Term (3 months–(more than Application(0–3 months) 2 years) 2 years) Forecast quantityIndividualTotal salesTotal sales products orGroups or families servicesof products or services Decision areaInventoryStaff planningFacility location managementProductionCapacity Final assemblyplanningplanning schedulingMaster productionProcess Workforceschedulingmanagement schedulingPurchasing Master productionDistribution scheduling ForecastingTime seriesCausalCausal techniqueCausalJudgmentJudgment Judgment Table 12.1

14. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression

15. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Dependent variable Independent variable X Y Figure 12.2

16. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Dependent variable Independent variable X Y Figure 12.2

17. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Dependent variable Independent variable X Y Regression equation: Y = a + bX Figure 12.2

18. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.2 Dependent variable Independent variable X Y Actual value of Y Value of X used to estimate Y Regression equation: Y = a + bX

19. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Figure 12.2

20. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Figure 12.2

21. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression

22. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 Example 12.1

23. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 Example 12.1 a = – 8.136 b = 109.229 X r = 0.98 r 2 = 0.96 s yx = 15.61

24. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.3 SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 a = – 8.136 b = 109.229 X r = 0.98 r 2 = 0.96 s yx = 15.61 |||| 1.01.52.02.5 Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Sales (thousands of units)

25. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.3 SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 a = – 8.136 b = 109.229 X r = 0.98 r 2 = 0.96 s yx = 15.61 |||| 1.01.52.02.5 Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Sales (thousands of units)

26. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.3 SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 a = – 8.136 b = 109.229 X r = 0.98 r 2 = 0.96 s yx = 15.61 |||| 1.01.52.02.5 Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – 8.136 + 109.229 X Sales (thousands of units)

27. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.3 SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 a = – 8.136 b = 109.229 X r = 0.98 r 2 = 0.96 s yx = 15.61 |||| 1.01.52.02.5 Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – 8.136 + 109.229 X Sales (thousands of units)

28. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.3 SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 a = – 8.136 b = 109.229 X r = 0.98 r 2 = 0.96 s yx = 15.61 |||| 1.01.52.02.5 Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – 8.136 + 109.229 X Sales (thousands of units) Forecast for Month 6 X = $1750, Y = – 8.136 + 109.229(1.75)

29. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.3 SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 a = – 8.136 b = 109.229 X r = 0.98 r 2 = 0.96 s yx = 15.61 |||| 1.01.52.02.5 Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – 8.136 + 109.229 X Sales (thousands of units) Forecast for Month 6 X = $1750, Y = 183.015, or 183,015 units

30. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.3 SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 a = – 8.136 b = 109.229 X r = 0.98 r 2 = 0.96 s yx = 15.61 |||| 1.01.52.02.5 Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – 8.136 + 109.229 X Sales (thousands of units)

31. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.3 SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 a = – 8.136 b = 109.229 X r = 0.98 r 2 = 0.96 s yx = 15.61 |||| 1.01.52.02.5 Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – 8.136 + 109.229 X Sales (thousands of units) If current stock = 62,500 units, Production = 183,015 – 62,500 = 120,015 units

32. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.4

33. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.4

34. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression SalesAdvertising Month(000 units)(000 $) 12642.5 21161.3 31651.4 41011.0 52092.0 Example 12.1

35. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.1

36. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 a = Y – b X b =  XY – n XY  X 2 – n X 2 Example 12.1

37. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 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 Causal Methods Linear Regression Example 12.1

38. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 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 Example 12.1

39. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression a = Y – b X 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 Example 12.1

40. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression a = 171 – 109.229(1.64) 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 Example 12.1

41. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression 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 Example 12.1

42. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression 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) Example 12.1

43. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression 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) Figure 12.3 Advertising (thousands of dollars) |||| 1.01.52.02.5 300 — 250 — 200 — 150 — 100 — 50 Sales (thousands of units)

44. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 12.3 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) |||| 1.01.52.02.5 Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Sales (thousands of units)

45. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression 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 (thousands of units) |||| 1.01.52.02.5 Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Figure 12.3

46. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.1

47. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 n  XY –  X  Y [ n  X 2 – (  X) 2 ][ n  Y 2 – (  Y) 2 ] r = Example 12.1

48. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.1

49. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.1

50. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 = - 8.136 + 109.229(1.75) Example 12.1

51. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.1

52. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages

53. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Week 450 — 430 — 410 — 390 — 370 — Patient arrivals |||||| 051015202530 Example 12.2 Patient arrivals

54. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Figure 12.5 Week 450 — 430 — 410 — 390 — 370 — |||||| 051015202530 Actual patient arrivals Patient arrivals

55. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 12.2 Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Week |||||| 051015202530 Patient arrivals

56. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 12.2 Actual patient arrivals Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Week |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 Patient arrivals

57. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 12.2 Actual patient arrivals Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Week |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 Patient arrivals

58. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Actual patient arrivals Week 450 — 430 — 410 — 390 — 370 — |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 F 4 = 411 + 380 + 400 3 Example 12.2 Patient arrivals

59. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 12.2 Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Week |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 F 4 = 397.0 Patient arrivals

60. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 12.2 Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Week |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 F 4 = 397.0 Patient arrivals

61. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 12.2 Actual patient arrivals Week 450 — 430 — 410 — 390 — 370 — |||||| 051015202530 Patient WeekArrivals 2380 3411 4415 F 5 = 415 + 411 + 380 3 Patient arrivals

62. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 12.2 Actual patient arrivals 450 — 430 — 410 — 390 — 370 — Week |||||| 051015202530 Patient WeekArrivals 2380 3411 4415 F 5 = 402.0 Patient arrivals

63. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 12.2 450 — 430 — 410 — 390 — 370 — Week |||||| 051015202530 Actual patient arrivals Patient arrivals

64. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages 450 — 430 — 410 — 390 — 370 — Week |||||| 051015202530 Actual patient arrivals 3-week MA forecast Figure 12.5 Patient arrivals

65. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Week 450 — 430 — 410 — 390 — 370 — |||||| 051015202530 Actual patient arrivals 3-week MA forecast 6-week MA forecast Figure 12.6 Patient arrivals

66. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Weighted Moving Average Week 450 — 430 — 410 — 390 — 370 — |||||| 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 Example 12.3 Patient arrivals

67. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Weighted Moving Average 450 — 430 — 410 — 390 — 370 — 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) Example 12.3 Patient arrivals

68. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Weighted Moving Average 450 — 430 — 410 — 390 — 370 — 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 Example 12.3 Patient arrivals

69. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Weighted Moving Average 450 — 430 — 410 — 390 — 370 — 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 = 404 F 5 = 410.7 Example 12.3 Patient arrivals

70. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Weighted Moving Average 450 — 430 — 410 — 390 — 370 — 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 = 404 F 5 = 411 Example 12.3 Patient arrivals

71. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing 450 — 430 — 410 — 390 — 370 — Week |||||| 051015202530 Exponential Smoothing  = 0.10 F t +1 = F t +  (D t – F t ) Example 12.4 Patient arrivals

72. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing 450 — 430 — 410 — 390 — 370 — Week |||||| 051015202530 Exponential Smoothing  = 0.10 F 4 = 0.10(411) + 0.90(390) F 3 = (400 + 380)/2 D 3 = 411 F t +1 = F t +  (D t – F t ) Example 12.4 Patient arrivals

73. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing Example 12.4 450 — 430 — 410 — 390 — 370 — Week |||||| 051015202530 F 4 = 392.1 Exponential Smoothing  = 0.10 F 3 = (400 + 380)/2 D 3 = 411 F t +1 = F t +  (D t – F t ) Patient arrivals

74. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing Example 12.4 Week 450 — 430 — 410 — 390 — 370 — |||||| 051015202530 F 4 = 392.1 D 4 = 415 Exponential Smoothing  = 0.10 F 4 = 392.1 F 5 = 394.4 F t +1 = F t +  (D t – F t ) Patient arrivals

75. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing Week 450 — 430 — 410 — 390 — 370 — |||||| 051015202530 Example 12.4 Patient arrivals

76. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 Example 12.4 Exponential smoothing  = 0.10

77. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing Example 12.4 450 — 430 — 410 — 390 — 370 — Patient arrivals Week |||||| 051015202530 3-week MA forecast 6-week MA forecast Exponential smoothing  = 0.10

78. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing

79. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Example 12.5 Actual blood test requests

80. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Medanalysis, Inc. Demand for blood analysis A t =  D t + (1 –  )(A t-1 + T t-1 ) T t =  (A t – A t-1 ) + (1 –  )T t-1 Example 12.5

81. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week A 1 = 0.2(27) + 0.80(28 + 3) T 1 = 0.2(30.2 - 28) + 0.80(3) Medanalysis, Inc. Demand for blood analysis A 0 = 28 patients T 0 = 3 patients  = 0.20  = 0.20 A t =  D t + (1 –  )(A t-1 + T t-1 ) T t =  (A t – A t-1 ) + (1 –  )T t-1 Example 12.5

82. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week A 1 = 30.2 T 1 = 2.8 Medanalysis, Inc. Demand for blood analysis A 0 = 28 patients T 0 = 3 patients  = 0.20  = 0.20 A t =  D t + (1 –  )(A t-1 + T t-1 ) T t =  (A t – A t-1 ) + (1 –  )T t-1 Forecast 2 = 30.2 + 2.8 = 33 Example 12.5

83. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Medanalysis, Inc. Demand for blood analysis A 2 = 30.2 D 2 = 44 T 1 = 2.8  = 0.20  = 0.20 A t =  D t + (1 –  )(A t-1 + T t-1 ) T t =  (A t – A t-1 ) + (1 -  )T t-1 A 2 = 0.2(44) + 0.80(30.2 + 2.8) T 2 = 0.2(35.2 - 30.2) + 0.80(2.8) Example 12.5

84. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Medanalysis, Inc. Demand for blood analysis A 2 = 30.2 D 2 = 44 T 1 = 2.8  = 0.20  = 0.20 A t =  D t + (1 –  )(A t-1 + T t-1 ) T t =  (A t – A t-1 ) + (1 -  )T t-1 A 2 = 35.2 T 2 = 3.2 Forecast = 35.2 + 3.2 = 38.4 Example 12.5

85. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Figure 12.7 Actual blood test requests

86. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Figure 12.7 Trend-adjusted forecast Actual blood test requests

87. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing Figure 12.7 ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Trend-adjusted forecast Actual blood test requests Number of time periods15.00 Demand smoothing coefficient (  )0.20 Initial demand value28.00 Trend-smoothing coefficient (  )0.20 Estimate of trend3.00

88. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing Figure 12.7 ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Trend-adjusted forecast Actual blood test requests SmoothedTrendForecast WeekArrivalsAverageAverageForecastError 02828.003.000.000.00 12730.202.8431.00–4.00 24435.233.2733.0410.96 33738.203.2138.51–1.51 43540.142.9641.42–6.42 55345.083.3543.109.89 63846.352.9348.43–10.43 75750.833.2449.297.71 86155.463.5254.086.92 93954.992.7258.98–19.98 105557.172.6157.71–2.71 115458.632.3859.78–5.78 125259.212.0261.01–9.01 136060.991.9761.23–1.23 146062.371.8562.96–2.96 157566.382.2864.2210.77

89. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing Figure 12.7 ||||||||||||||| 0123456789101112131415 80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Trend-adjusted forecast Actual blood test requests SmoothedTrendForecast WeekArrivalsAverageAverageForecastError 02828.003.000.000.00 12730.202.8431.00–4.00 24435.233.2733.0410.96 33738.203.2138.51–1.51 43540.142.9641.42–6.42 55345.083.3543.109.89 63846.352.9348.43–10.43 75750.833.2449.297.71 86155.463.5254.086.92 93954.992.7258.98–19.98 105557.172.6157.71–2.71 115458.632.3859.78–5.78 125259.212.0261.01–9.01 136060.991.9761.23–1.23 146062.371.8562.96–2.96 157566.382.2864.2210.77 SUMMARY Average demand49.80 Mean square error76.13 Mean absolute deviation7.35 Forecast for week 1668.66 Forecast for week 1770.95 Forecast for week 1873.24

90. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Time-Series Methods Seasonal Influences

91. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. QuarterYear 1Year 2Year 3Year 4 14570100100 2335370585725 35205908301160 4100170285215 Total1000120018002200 Average250300450550 Time-Series Methods Seasonal Influences Example 12.6

92. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.6

93. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. QuarterYear 1Year 2Year 3Year 4 14570100100 2335370585725 35205908301160 4100170285215 Total1000120018002200 Average250300450550 Seasonal Index = = 0.18 45 250 Time-Series Methods Seasonal Influences Example 12.6

94. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.6

95. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Time-Series Methods Seasonal Influences Example 12.6

96. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 3 4 Time-Series Methods Seasonal Influences Example 12.6

97. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.6

98. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.6

99. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.6

100. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.6

101. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Seasonal Patterns

102. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Seasonal Patterns Period |||||||||||||||| 0245810121416 Demand Figure 12.7

103. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Seasonal Patterns Figure 12.8 Period Demand (a) Multiplicative pattern |||||||||||||||| 0245810121416

104. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Seasonal Patterns Figure 12.8 Period |||||||||||||||| 0245810121416 Demand (b) Additive pattern

105. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error

106. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Measures of Forecast Error E t = D t – F t Choosing a Method Forecast Error Example 12.7

107. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error Measures of Forecast Error E t = D t – F t  |E t | n Et2nEt2n CFE =  E t  = MSE = MAD = MAPE =  [ |E t | (100) ] / D t n  (E t – E ) 2 n – 1 Example 12.7

108. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, 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 Example 12.7

109. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error 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% Measures of Error Example 12.7

110. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error 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% CFE = – 15 Measures of Error Example 12.7

111. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error 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% CFE = – 15 Measures of Error E = = – 1.875 –15 8 Example 12.7

112. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error 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 E = = – 1.875 – 15 8 Example 12.7

113. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error 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 E = = – 1.875 – 15 8  = 27.4 Example 12.7

114. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error 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 E = = – 1.875 – 15 8  = 27.4 Example 12.7

115. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error 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 E = = – 1.875 – 15 8  = 27.4 Example 12.7

116. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error 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 E = = – 1.875 – 15 8  = 27.4 Example 12.7

117. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Tracking Signals

118. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Tracking Signals Table 12.2 Percentage of the Area of the Normal Probability Distribution within the Control Limits of the Tracking Signal Control Limit SpreadEquivalentPercentage of Area (number of MAD)Number of  2 within Control Limits ± 1.0 ± 1.5 ± 2.0 ± 2.5 ± 3.0 ± 3.5 ± 4.0

119. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Tracking Signals Table 12.2 Percentage of the Area of the Normal Probability Distribution within the Control Limits of the Tracking Signal Control Limit SpreadEquivalentPercentage of Area (number of MAD)Number of  2 within Control Limits ± 1.0± 0.80 ± 1.5± 1.20 ± 2.0± 1.60 ± 2.5± 2.00 ± 3.0± 2.40 ± 3.5± 2.80 ± 4.0± 3.20

120. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Tracking Signals Table 12.2 Percentage of the Area of the Normal Probability Distribution within the Control Limits of the Tracking Signal Control Limit SpreadEquivalentPercentage of Area (number of MAD)Number of  2 within Control Limits ± 1.0± 0.8057.62 ± 1.5± 1.2076.98 ± 2.0± 1.6089.04 ± 2.5± 2.0095.44 ± 3.0± 2.4098.36 ± 3.5± 2.8099.48 ± 4.0± 3.2099.86

121. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Tracking Signals

122. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Tracking Signals Tracking signal = CFE MAD +2.0 — +1.5 — +1.0 — +0.5 — 0 — –0.5 — –1.0 — –1.5 — ||||| 0510152025 Observation number Tracking signal Control limit Figure 12.9

123. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Tracking Signals Tracking signal = CFE MAD +2.0 — +1.5 — +1.0 — +0.5 — 0 — –0.5 — –1.0 — –1.5 — ||||| 0510152025 Observation number Tracking signal Control limit Out of control Figure 12.9

124. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error

125. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error Figure 12.10

126. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error Figure 12.10

127. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error Figure 12.10

128. To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Air-Quality — Discussion Questions 250 – 225 – 200 – 175 – 150 – 125 – 100 – 75 – 50 – 25 – 0 |||||||||||||| 2225283136912151821142730 Year 2 Year 1 JulyAugust Date Visibility rating