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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Forecasting Chapter 13
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Patterns of Demand Quantity Time (a) Horizontal: Data cluster about a horizontal line. Figure 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Patterns of Demand Quantity Time (b) Trend: Data consistently increase or decrease. Figure 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Patterns of Demand Quantity |||||||||||| JFMAMJJASOND Months (c) Seasonal: Data consistently show peaks and valleys. Figure 13.1 Year 1 Year 2
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Patterns of Demand Quantity |||||| 123456 Years (c) Cyclical: Data reveal gradual increases and decreases over extended periods. Figure 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Demand Forecast Applications TABLE 13.1DEMAND FORECAST APPLICATIONS Time Horizon Medium TermLong Term Short Term (3 months–(more than Application(0–3 months) 2 years) 2 years) Total sales Groups or families of products or services Staff planning Production planning Master production scheduling Purchasing Distribution Causal Judgment Forecast quantityIndividual products or services Decision areaInventory management Final assembly scheduling Workforce scheduling Master production scheduling ForecastingTime series techniqueCausal Judgment Total sales Facility location Capacity planning Process management Causal Judgment
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Dependent variable Independent variable XY Figure 13.2 Estimate of Y from regressionequation Regressionequation: Y = a + bX Actualvalue of Y Value of X used to estimate Y Deviation, or error {
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.1 a = – 8.136 b = 109.229 X r = 0.98 r 2 = 0.96 s yx = 15.61
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 13.3 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)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 13.3 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)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 13.3 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)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 13.3 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)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 13.3 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
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 13.3 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)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 13.3 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
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 13.4
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 =b =b =b = XY – n XY X 2 – n X 2 Example 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 Example 13.1 a = Y – b X b =b =b =b = XY – n XY X 2 – n X 2
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. 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 13.1 a = Y – b X b =b =b =b = XY – n XY X 2 – n X 2
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression a = Y – b X b =b =b =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 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.3 Advertising (thousands of dollars) |||| 1.01.52.02.5 300 — 250 — 200 — 150 — 100 — 50 Sales (thousands of units)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression Figure 13.3 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)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.3
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 =r =r =r = Example 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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) Y = - 8.136 + 109.229(1.75) Example 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 Y = 183.015 or 183,015 hinges Example 13.1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Figure 13.5 Week 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — |||||| 051015202530 Patient arrivals Actual patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 13.2 Actual patient arrivals 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — Week |||||| 051015202530 Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 13.2 Actual patient arrivals arrivals 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — Week |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 13.2 Actual patient arrivals arrivals 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — Week |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Actual patient arrivals Week 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 F4 =F4 =F4 =F4 = 411 + 380 + 400 3 Example 13.2 Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 13.2 Actual patient arrivals 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — Week |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 F 4 = 397.0 Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 13.2 Actual patient arrivals 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — Week |||||| 051015202530 Patient WeekArrivals 1400 2380 3411 F 4 = 397.0 Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 13.2 Actual patient arrivals Week 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — |||||| 051015202530 Patient WeekArrivals 2380 3411 4415 F5 =F5 =F5 =F5 = 415 + 411 + 380 3 Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Example 13.2 Actual patient arrivals 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — Week |||||| 051015202530 Patient WeekArrivals 2380 3411 4415 F 5 = 402.0 Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Simple Moving Averages Figure 13.6 Week 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — |||||| 051015202530 Patient arrivals Actual patient arrivals 3-week MA forecast 6-week MA forecast
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing 450 450 — 430 430 — 410 410 — 390 390 — 370 370 —Week |||||| 051015202530 Exponential Smoothing = 0.10 F t +1 = F t + (D t – F t ) Example 13.3 Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing 450 450 — 430 430 — 410 410 — 390 390 — 370 370 —Week |||||| 051015202530 Exponential Smoothing = 0.10 F 4 = 0.10(411) + 0.90(390) F 3 = (400 + 380)/2 F 3 = (400 + 380)/2 D 3 = 411 F t +1 = F t + (D t – F t ) Example 13.3 Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing Example 13.3 450 450 — 430 430 — 410 410 — 390 390 — 370 370 —Week |||||| 051015202530 F 4 = 392.1 Exponential Smoothing = 0.10 F 3 = (400 + 380)/2 F 3 = (400 + 380)/2 D 3 = 411 F t +1 = F t + (D t – F t ) Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing Example 13.3 Week 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — |||||| 051015202530 F 4 = 392.1 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
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing Example 13.3 Week 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — |||||| 051015202530 Patient arrivals
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — Patient arrivals Week |||||| 051015202530 Example 13.3 Exponential smoothing = 0.10
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Exponential Smoothing Example 13.3 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — Patient arrivals Week |||||| 051015202530 3-week MA forecast 6-week MA forecast Exponential smoothing = 0.10
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 30 — Patient arrivals Week Example 13.4 Actual blood test requests
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 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 13.4
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 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 13.4
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 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 13.4
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 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 13.4
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 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 13.4
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing Figure 13.7 ||||||||||||||| 0123456789101112131415 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 30 — Patient arrivals Week Actual blood test requests Trend-adjusted forecast
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing Figure 13.7 ||||||||||||||| 0123456789101112131415 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 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
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing ||||||||||||||| 0123456789101112131415 80 80 — 70 70 — 60 60 — 50 50 — 40 40 — 30 30 — Patient arrivals Week Trend-adjusted forecast Actual blood test requests 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 TABLE 13.2FORECASTS FOR MEDANALYSIS SmoothedTrendForecast WeekArrivalsAverageAverageForecastError
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Trend-Adjusted Exponential Smoothing Figure 13.7 ||||||||||||||| 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
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. QuarterYear 1Year 2Year 3Year 4 14570100100 2335370585725 35205908301160 4100170285215 Total1000120018002200 Total1000120018002200 Time-Series Methods Seasonal Influences Example 13.5
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Seasonal Influences Figure 13.8(a)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Time-Series Methods Seasonal Influences Figure 13.8(b)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Seasonal Patterns Figure 13.9 Period Demand |||||||||||||||| 0245810121416 (a) Multiplicative pattern
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Seasonal Patterns Figure 13.9 Period |||||||||||||||| 0245810121416 Demand (b) Additive pattern
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error Measures of Forecast Error E t = D t – F t |E t | n Et2Et2nnEt2Et2nnn CFE = E t = MSE = MAD = MAPE = [ |E t | (100) ] / D t n (E t – E ) 2 n – 1
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.6
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.6
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.6
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.6
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.6
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.6
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.6
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.6
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 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 13.6
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Choosing a Method Tracking Signals TABLE 13.3PERCENTAGE 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 57.62 76.98 89.04 95.44 98.36 99.48 99.86 ± 0.80 ± 1.20 ± 1.60 ± 2.00 ± 2.40 ± 2.80 ± 3.20 ± 1.0 ± 1.5 ± 2.0 ± 2.5 ± 3.0 ± 3.5 ± 4.0
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Choosing a Method Tracking Signals Tracking signal = CFEMAD +2.0 +2.0 — +1.5 +1.5 — +1.0 +1.0 — +0.5 +0.5 — 0 0 — –0.5 –0.5 — –1.0 –1.0 — –1.5 –1.5 — ||||| 0510152025 Observation number Observation number Tracking signal Control limit Figure 13.10 Out of control
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error Figure 13.11(a)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error Figure 13.11(b)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error Figure 13.11(b)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Choosing a Method Forecast Error Figure 13.11(b)
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To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved. Air-Quality – Discussion Question 250 250 – 225 225 – 200 200 – 175 175 – 150 150 – 125 125 – 100 100 – 75 75 – 50 50 – 25 25 –0 |||||||||||||| 2225283136912151821142730 Year 2 Year 1 JulyAugust Date Visibility rating Figure 13.12
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