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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 $) Example 12.1

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 $) Example 12.1 a = – b = X r = 0.98 r 2 = 0.96 s yx = 15.61

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 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Sales (thousands of units)

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 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Sales (thousands of units)

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 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units)

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 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units)

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 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units) Forecast for Month 6 X = $1750, Y = – (1.75)

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 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units) Forecast for Month 6 X = $1750, Y = , or 183,015 units

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 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units)

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 $) a = – b = X r = 0.98 r 2 = 0.96 s yx = |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Y = – X Sales (thousands of units) If current stock = 62,500 units, Production = 183,015 – 62,500 = 120,015 units

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

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

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 $) Example 12.1

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 $) a = Y – b X b =  XY – n XY  X 2 – n X 2 Example 12.1

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 , , , , ,681 a = Y – b X b =  XY – n XY  X 2 – n X 2 Example 12.1

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 , , , , ,681 Total ,259 Y = 171X = 1.64 Causal Methods Linear Regression Example 12.1

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 = – 5(1.64)(171) – 5(1.64) 2 Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y , , , , ,681 Total ,259 Y = 171X = 1.64 Example 12.1

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 = Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y , , , , ,681 Total ,259 Y = 171X = 1.64 Example 12.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression a = 171 – (1.64) b = Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y , , , , ,681 Total ,259 Y = 171X = 1.64 Example 12.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression a = – b = Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y , , , , ,681 Total ,259 Y = 171X = 1.64 Example 12.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression a = – b = Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y , , , , ,681 Total ,259 Y = 171X = 1.64 Y = – (X) Example 12.1

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression a = b = Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y , , , , ,681 Total ,259 Y = 171X = 1.64 Y = – (X) Figure 12.3 Advertising (thousands of dollars) |||| — 250 — 200 — 150 — 100 — 50 Sales (thousands of units)

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 = b = Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y , , , , ,681 Total ,259 Y = 171X = 1.64 Y = – (X) |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Sales (thousands of units)

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. Causal Methods Linear Regression a = b = Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y , , , , ,681 Total ,259 Y = 171X = 1.64 Y = – (X) Sales (thousands of units) |||| Advertising (thousands of dollars) 300 — 250 — 200 — 150 — 100 — 50 Figure 12.3

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 , , , , ,681 Total ,259 Y = 171X = 1.64 Example 12.1

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 , , , , ,681 Total ,259 Y = 171X = 1.64 n  XY –  X  Y [ n  X 2 – (  X) 2 ][ n  Y 2 – (  Y) 2 ] r = Example 12.1

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 , , , , ,681 Total ,259 Y = 171X = 1.64 r = 0.98 Example 12.1

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 , , , , ,681 Total ,259 Y = 171X = 1.64 r = 0.98 r 2 = 0.96  YX = Example 12.1

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 , , , , ,681 Total ,259 Y = 171X = 1.64 r = 0.98 r 2 = 0.96  YX = Forecast for Month 6: Advertising expenditure = $1750 Y = (1.75) Example 12.1

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 , , , , ,681 Total ,259 Y = 171X = 1.64 r = 0.98 r 2 = 0.96  YX = Forecast for Month 6: Advertising expenditure = $1750 Y = or 183,015 hinges Example 12.1

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

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 |||||| Example 12.2 Patient arrivals

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 — |||||| Actual patient arrivals Patient arrivals

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 |||||| Patient arrivals

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 |||||| Patient WeekArrivals Patient arrivals

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 |||||| Patient WeekArrivals Patient arrivals

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 — |||||| Patient WeekArrivals F 4 = Example 12.2 Patient arrivals

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 |||||| Patient WeekArrivals F 4 = Patient arrivals

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 |||||| Patient WeekArrivals F 4 = Patient arrivals

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 — |||||| Patient WeekArrivals F 5 = Patient arrivals

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 |||||| Patient WeekArrivals F 5 = Patient arrivals

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 — 430 — 410 — 390 — 370 — Week |||||| Actual patient arrivals Patient arrivals

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 |||||| Actual patient arrivals 3-week MA forecast Figure 12.5 Patient arrivals

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 — |||||| Actual patient arrivals 3-week MA forecast 6-week MA forecast Figure 12.6 Patient arrivals

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 — |||||| Actual patient arrivals 3-week MA forecast 6-week MA forecast Weighted Moving Average Assigned weights t 0.70 t t Example 12.3 Patient arrivals

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 |||||| Actual patient arrivals 3-week MA forecast 6-week MA forecast Weighted Moving Average Assigned weights t 0.70 t t F 4 = 0.70(411) (380) (400) Example 12.3 Patient arrivals

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 |||||| Actual patient arrivals 3-week MA forecast 6-week MA forecast Weighted Moving Average Assigned weights t 0.70 t t F 4 = Example 12.3 Patient arrivals

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 |||||| Actual patient arrivals 3-week MA forecast 6-week MA forecast Weighted Moving Average Assigned weights t 0.70 t t F 4 = 404 F 5 = Example 12.3 Patient arrivals

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 |||||| Actual patient arrivals 3-week MA forecast 6-week MA forecast Weighted Moving Average Assigned weights t 0.70 t t F 4 = 404 F 5 = 411 Example 12.3 Patient arrivals

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 |||||| Exponential Smoothing  = 0.10 F t +1 = F t +  (D t – F t ) Example 12.4 Patient arrivals

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 |||||| Exponential Smoothing  = 0.10 F 4 = 0.10(411) (390) F 3 = ( )/2 D 3 = 411 F t +1 = F t +  (D t – F t ) Example 12.4 Patient arrivals

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

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 — |||||| F 4 = D 4 = 415 Exponential Smoothing  = 0.10 F 4 = F 5 = F t +1 = F t +  (D t – F t ) Patient arrivals

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 — |||||| Example 12.4 Patient arrivals

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 |||||| Example 12.4 Exponential smoothing  = 0.10

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

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

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 ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Example 12.5 Actual blood test requests

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 ||||||||||||||| — 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

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 ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week A 1 = 0.2(27) (28 + 3) T 1 = 0.2( ) (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

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 ||||||||||||||| — 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 = = 33 Example 12.5

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 ||||||||||||||| — 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) ( ) T 2 = 0.2( ) (2.8) Example 12.5

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 ||||||||||||||| — 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 = = 38.4 Example 12.5

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 ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Figure 12.7 Actual blood test requests

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 ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Figure 12.7 Trend-adjusted forecast Actual blood test requests

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 ||||||||||||||| — 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

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 ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Trend-adjusted forecast Actual blood test requests SmoothedTrendForecast WeekArrivalsAverageAverageForecastError – – – – – – – – – –

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 ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Patient arrivals Week Trend-adjusted forecast Actual blood test requests SmoothedTrendForecast WeekArrivalsAverageAverageForecastError – – – – – – – – – – SUMMARY Average demand49.80 Mean square error76.13 Mean absolute deviation7.35 Forecast for week Forecast for week Forecast for week

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

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. QuarterYear 1Year 2Year 3Year Total Average Time-Series Methods Seasonal Influences Example 12.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. QuarterYear 1Year 2Year 3Year Total Average Seasonal Index = Actual Demand Average Demand Time-Series Methods Seasonal Influences Example 12.6

To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Sixth Edition © 2002 Prentice Hall, Inc. All rights reserved. QuarterYear 1Year 2Year 3Year Total Average Seasonal Index = = Time-Series Methods Seasonal Influences Example 12.6

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 = Total Average Seasonal Index = = Time-Series Methods Seasonal Influences Example 12.6

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 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = 0.39 Time-Series Methods Seasonal Influences Example 12.6

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 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = 0.39 QuarterAverage Seasonal Index 1( )/4 = Time-Series Methods Seasonal Influences Example 12.6

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 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = 0.39 QuarterAverage Seasonal Index 1( )/4 = ( )/4 = ( )/4 = ( )/4 = 0.50 Time-Series Methods Seasonal Influences Example 12.6

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 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = 0.39 QuarterAverage Seasonal IndexForecast 1( )/4 = ( )/4 = ( )/4 = ( )/4 = 0.50 Projected Annual Demand = 2600 Average Quarterly Demand = 2600/4 = 650 Time-Series Methods Seasonal Influences Example 12.6

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 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = 0.39 QuarterAverage Seasonal IndexForecast 1( )/4 = (0.20) =130 2( )/4 = ( )/4 = ( )/4 = 0.50 Projected Annual Demand = 2600 Average Quarterly Demand = 2600/4 = 650 Time-Series Methods Seasonal Influences Example 12.6

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 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = 0.39 QuarterAverage Seasonal IndexForecast 1( )/4 = (0.20) =130 2( )/4 = (1.30) =845 3( )/4 = (2.00) =1300 4( )/4 = (0.50) =325 Time-Series Methods Seasonal Influences Example 12.6

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

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

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 ||||||||||||||||

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 (b) Additive pattern

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

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

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

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) % – – – Total– % Choosing a Method Forecast Error Example 12.7

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) – % – – – Total– % Measures of Error Example 12.7

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) – % – – – Total– % CFE = – 15 Measures of Error Example 12.7

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) – % – – – Total– % CFE = – 15 Measures of Error E = = – –15 8 Example 12.7

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) – % – – – Total– % MSE = = CFE = – 15 Measures of Error E = = – – 15 8 Example 12.7

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) – % – – – Total– % MSE = = CFE = – 15 Measures of Error E = = – – 15 8  = 27.4 Example 12.7

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) – % – – – Total– % MSE = = CFE = – 15 Measures of Error MAD = = E = = – – 15 8  = 27.4 Example 12.7

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) – % – – – Total– % MSE = = CFE = – 15 Measures of Error MAD = = MAPE = = 10.2% 81.3% 8 E = = – – 15 8  = 27.4 Example 12.7

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) – % – – – Total– % MSE = = CFE = – 15 Measures of Error MAD = = MAPE = = 10.2% 81.3% 8 E = = – – 15 8  = 27.4 Example 12.7

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

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

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

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±

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

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 — ||||| Observation number Tracking signal Control limit Figure 12.9

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 — ||||| Observation number Tracking signal Control limit Out of control Figure 12.9

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

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

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

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

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 |||||||||||||| Year 2 Year 1 JulyAugust Date Visibility rating