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

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression 300 — 250 — 200 — 150 — 100 — 50 a = b = Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y , , , , ,681 Total ,259 Y = 171X = 1.64 Y = (X) Sales (000s) |||| Advertising (000s)

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

To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Causal Methods Linear Regression Sales, YAdvertising, X Month(000 units)(000 $)XYX 2 Y , , , , ,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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. QuarterYear 1Year 2Year 3Year 4 145/250 = Total Average Seasonal Index = = Time Series Methods Seasonal Influences

To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Quarter Year 1 Year 2 Year 3 Year 4 145/250 = /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

To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Quarter Year 1 Year 2 Year 3 Year 4 145/250 = /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

To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Quarter Year 1 Year 2 Year 3 Year 4 145/250 = /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

To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Quarter Year 1 Year 2 Year 3 Year 4 145/250 = /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

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

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

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

To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) % Total % Choosing a Method Forecast Error

To accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Fourth Edition  1996 Addison-Wesley Publishing Company, Inc. All rights reserved. Absolute Error AbsolutePercent Month,Demand,Forecast,Error,Squared,Error,Error, tD t F t E t E t 2 |E t |(|E t |/D t )(100) % Total % MSE = = CFE = - 15 Measures of Error MAD = = MAPE = = 10.2% 81.3% 8 Choosing a Method Forecast Error