To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Chapter 8 Forecasting To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved.

Forecasting Predicting future events Predicting future events Usually demand behavior over a time frame Usually demand behavior over a time frame Qualitative methods Qualitative methods Based on subjective methods Based on subjective methods Quantitative methods Quantitative methods Based on mathematical formulas Based on mathematical formulas

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Strategic Role of Forecasting Focus on supply chain management Focus on supply chain management Short term role of product demand Short term role of product demand Long term role of new products, processes, and technologies Long term role of new products, processes, and technologies Focus on Total Quality Management Focus on Total Quality Management Satisfy customer demand Satisfy customer demand Uninterrupted product flow with no defective items Uninterrupted product flow with no defective items Necessary for strategic planning Necessary for strategic planning

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Time Frame Time Frame Short-range, medium- range, long-range Short-range, medium- range, long-range Demand Behavior Demand Behavior Trends, cycles, seasonal patterns, random Trends, cycles, seasonal patterns, random Components of Forecasting Demand

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Time Frame Short-range to medium-range Short-range to medium-range Daily, weekly monthly forecasts of sales data Daily, weekly monthly forecasts of sales data Up to 2 years into the future Up to 2 years into the future Long-range Long-range Strategic planning of goals, products, markets Strategic planning of goals, products, markets Planning beyond 2 years into the future Planning beyond 2 years into the future

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Demand Behavior Trend Trend gradual, long-term up or down movement gradual, long-term up or down movement Cycle Cycle up & down movement repeating over long time frame up & down movement repeating over long time frame Seasonal pattern Seasonal pattern periodic oscillation in demand which repeats periodic oscillation in demand which repeats Random movements follow no pattern Random movements follow no pattern

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Forms of Forecast Movement

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Forms of Forecast Movement Time (a) Trend Time (d) Trend with seasonal pattern Time (c) Seasonal pattern Time (b) Cycle Demand Demand Demand Demand Random movement Figure 8.1

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Forecasting Methods Time series Time series Regression or causal modeling Regression or causal modeling Qualitative methods Qualitative methods Management judgment, expertise, opinion Management judgment, expertise, opinion Use management, marketing, purchasing, engineering Use management, marketing, purchasing, engineering Delphi method Delphi method Solicit forecasts from experts Solicit forecasts from experts

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Forecasting Process

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Forecasting Process 6. Check forecast accuracy with one or more measures 4. Select a forecast model that seems appropriate for data 5. Develop/compute forecast for period of historical data 8a. Forecast over planning horizon 9. Adjust forecast based on additional qualitative information and insight 10. Monitor results and measure forecast accuracy 8b. Select new forecast model or adjust parameters of existing model 7. Is accuracy of forecast acceptable? 1. Identify the purpose of forecast 3. Plot data and identify patterns 2. Collect historical data Figure 8.2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Time Series Methods Statistical methods using historical data Statistical methods using historical data Moving average Moving average Exponential smoothing Exponential smoothing Linear trend line Linear trend line Assume patterns will repeat Assume patterns will repeat Naive forecasts Naive forecasts Forecast = data from last period Forecast = data from last period Demand?

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Moving Average Average several periods of data Average several periods of data Dampen, smooth out changes Dampen, smooth out changes Use when demand is stable with no trend or seasonal pattern Use when demand is stable with no trend or seasonal pattern

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Moving Average MA n = n i = 1  DiDiDiDi n where n =number of periods in the moving average D i =demand in period i Average several periods of data Average several periods of data Dampen, smooth out changes Dampen, smooth out changes Use when demand is stable with no trend or seasonal pattern Use when demand is stable with no trend or seasonal pattern

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Simple Moving Average

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Simple Moving Average Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 ORDERS MONTHPER MONTH Example 8.1

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 ORDERS MONTHPER MONTH Example 8.1 MA 3 = 3 i = 1  DiDiDiDi 3 = = 110 orders for Nov Simple Moving Average

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Jan120– Feb90 – Mar100 – Apr May June July Aug Sept Oct Nov –110.0 ORDERSTHREE-MONTH MONTHPER MONTHMOVING AVERAGE Example 8.1 Simple Moving Average

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Jan120– Feb90 – Mar100 – Apr May June July Aug Sept Oct Nov –110.0 ORDERSTHREE-MONTH MONTHPER MONTHMOVING AVERAGE Example 8.1 MA 5 = 5 i = 1  DiDiDiDi 5 = = 91 orders for Nov Simple Moving Average

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Example 8.1 Simple Moving Average Jan120– – Feb90 – – Mar100 – – Apr – May – June July Aug Sept Oct Nov – ORDERSTHREE-MONTHFIVE-MONTH MONTHPER MONTHMOVING AVERAGEMOVING AVERAGE

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved – – – – – – 0 0 – ||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNov Orders Month Figure 8.2 Smoothing Effects

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Smoothing Effects – – – – – – 0 0 – ||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNov Orders Month Actual Figure 8.2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Smoothing Effects – – – – – – 0 0 – ||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNov 3-month Actual Orders Month Figure 8.2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Smoothing Effects – – – – – – 0 0 – ||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNov 5-month 3-month Actual Orders Month Figure 8.2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Weighted Moving Average Adjusts moving average method to more closely reflect data fluctuations Adjusts moving average method to more closely reflect data fluctuations

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Weighted Moving Average WMA n = i = 1  Wi DiWi DiWi DiWi Di where W i = the weight for period i, between 0 and 100 percent  W i = 1.00 Adjusts moving average method to more closely reflect data fluctuations Adjusts moving average method to more closely reflect data fluctuations

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Weighted Moving Average Example

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Weighted Moving Average Example MONTH WEIGHT DATA August 17%130 September 33%110 October 50%90 Example 8.2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Weighted Moving Average Example MONTH WEIGHT DATA August 17%130 September 33%110 October 50%90 November forecast WMA 3 = 3 i = 1  Wi DiWi DiWi DiWi Di = (0.50)(90) + (0.33)(110) + (0.17)(130) = orders Example 8.2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Averaging method Averaging method Weights most recent data more strongly Weights most recent data more strongly Reacts more to recent changes Reacts more to recent changes Widely used, accurate method Widely used, accurate method Exponential Smoothing

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. F t +1 =  D t + (1 -  )F t where F t +1 =forecast for next period D t =actual demand for present period F t =previously determined forecast for present period  =weighting factor, smoothing constant Averaging method Averaging method Weights most recent data more strongly Weights most recent data more strongly Reacts more to recent changes Reacts more to recent changes Widely used, accurate method Widely used, accurate method Exponential Smoothing

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Effect of Smoothing Constant 0.0  1.0 If  = 0.20, then F t +1 = 0.20  D t F t If  = 0, then F t +1 = 0  D t + 1 F t 0 = F t Forecast does not reflect recent data If  = 1, then F t +1 = 1  D t + 0 F t =  D t Forecast based only on most recent data

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Exponential Smoothing

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 Example 8.3 Exponential Smoothing

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 Example 8.3 F 2 =  D 1 + (1 -  )F 1 = (0.30)(37) + (0.70)(37) = 37 F 3 =  D 2 + (1 -  )F 2 = (0.30)(40) + (0.70)(37) = 37.9 F 13 =  D 12 + (1 -  )F 12 = (0.30)(54) + (0.70)(50.84) = Exponential Smoothing

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. FORECAST, F t + 1 PERIODMONTHDEMAND(  = 0.3) 1Jan37– 2Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan–51.79 Example 8.3 Exponential Smoothing

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. FORECAST, F t + 1 PERIODMONTHDEMAND(  = 0.3)(  = 0.5) 1Jan37–– 2Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan– Example 8.3 Exponential Smoothing

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved – – – – – – – 0 0 – ||||||||||||| Orders Month Figure 8.3 Exponential Smoothing Forecasts

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved – – – – – – – 0 0 – ||||||||||||| Actual Orders Month Figure 8.3 Exponential Smoothing Forecasts

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved – – – – – – – 0 0 – ||||||||||||| Actual Orders Month  = 0.30 Figure 8.3 Exponential Smoothing Forecasts

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved – – – – – – – 0 0 – |||||||||||||  = 0.50 Actual Orders Month  = 0.30 Figure 8.3 Exponential Smoothing Forecasts

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. AF t +1 = F t +1 + T t +1 where T = an exponentially smoothed trend factor T t +1 =  (F t +1 - F t ) + (1 -  ) T t where T t = the last period trend factor  = a smoothing constant for trend Adjusted Exponential Smoothing

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Adjusted Exponential Smoothing Example

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Adjusted Exponential Smoothing Example PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 Example 8.4

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Adjusted Exponential Smoothing Example PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 T 3 =  (F 3 - F 2 ) + (1 -  ) T 2 = (0.30)( ) + (0.70)(0) = 0.45 AF 3 = F 3 + T 3 = = T 13 =  (F 13 - F 12 ) + (1 -  ) T 12 = (0.30)( ) + (0.70)(1.77) = 1.36 AF 13 = F 13 + T 13 = = Example 8.4

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Adjusted Exponential Smoothing Example FORECASTTRENDADJUSTED PERIODMONTHDEMANDF t +1 T t +1 FORECAST AF t +1 1Jan –– 2Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan– Example 8.4

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Adjusted Exponential Smoothing Forecasts – – – – – – – 0 0 – ||||||||||||| Demand Period Example 8.4

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Adjusted Exponential Smoothing Forecasts – – – – – – – 0 0 – ||||||||||||| Actual Demand Period Forecast (  = 0.50) Example 8.4

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Adjusted Exponential Smoothing Forecasts – – – – – – – 0 0 – ||||||||||||| Adjusted forecast (  = 0.30) Actual Demand Period Forecast (  = 0.50) Example 8.4

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. y = a + bx where a =intercept (at period 0) b =slope of the line x =the time period y =forecast for demand for period x Linear Trend Line

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. y = a + bx where a =intercept (at period 0) b =slope of the line x =the time period y =forecast for demand for period x b = a = y - b x where n =number of periods x == mean of the x values y == mean of the y values  xy - nxy  x 2 - nx 2  x n  y n Linear Trend Line

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. x (PERIOD) y (DEMAND) Example 8.5 Least Squares Example

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. x (PERIOD) y (DEMAND) xyx Example 8.5 Least Squares Example

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Least Squares Example x (PERIOD) y (DEMAND) xyx x = = 6.5 y = = b = = = 1.72 a = y - bx = (1.72)(6.5) = (12)(6.5)(46.42) (6.5) 2  xy - nxy  x 2 - nx Example 8.5

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Least Squares Example x (PERIOD) y (DEMAND) xyx x = = 6.5 y = = b = = = 1.72 a = y - bx = (1.72)(6.5) = (12)(6.5)(46.42) (6.5) 2  xy - nxy  x 2 - nx Example 8.5 Linear trend line y = x

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Least Squares Example x (PERIOD) y (DEMAND) xyx x = = 6.5 y = = b = = = 1.72 a = y - bx = (1.72)(6.5) = (12)(6.5)(46.42) (6.5) 2  xy - nxy  x 2 - nx Example 8.5 Linear trend line y = x Forecast for period 13 y = (13) y = units

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Linear Trend Line – – – – – – – 0 0 – ||||||||||||| Demand Period Example 8.5

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Linear Trend Line – – – – – – – 0 0 – ||||||||||||| Actual Demand Period Example 8.5

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Linear Trend Line – – – – – – – 0 0 – ||||||||||||| Actual Demand Period Linear trend line Example 8.5

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Seasonal Adjustments Repetitive increase/ decrease in demand Repetitive increase/ decrease in demand Use seasonal factor to adjust forecast Use seasonal factor to adjust forecast

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Seasonal Adjustments Repetitive increase/ decrease in demand Repetitive increase/ decrease in demand Use seasonal factor to adjust forecast Use seasonal factor to adjust forecast Seasonal factor = S i = DiDiDDDiDiDD

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Seasonal Adjustment

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Seasonal Adjustment Total DEMAND (1000’S PER QUARTER) YEAR1234Total Example 8.6

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Seasonal Adjustment Total DEMAND (1000’S PER QUARTER) YEAR1234Total S 1 = = = 0.28 D1D1DDD1D1DD S 2 = = = 0.20 D2D2DDD2D2DD S 4 = = = 0.37 D4D4DDD4D4DD S 3 = = = 0.15 D3D3DDD3D3DD Example 8.6

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Seasonal Adjustment Total DEMAND (1000’S PER QUARTER) YEAR1234Total S i Example 8.6

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Seasonal Adjustment Total DEMAND (1000’S PER QUARTER) YEAR1234Total S i Example 8.6 y = x = (4) = For 2002

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Seasonal Adjustment SF 1 = (S 1 ) (F 5 )SF 3 = (S 3 ) (F 5 ) = (0.28)(58.17) = 16.28= (0.15)(58.17) = 8.73 SF 2 = (S 2 ) (F 5 )SF 4 = (S 4 ) (F 5 ) = (0.20)(58.17) = 11.63= (0.37)(58.17) = Total DEMAND (1000’S PER QUARTER) YEAR1234Total S i Example 8.6 y = x = (4) = For 2002

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Forecast Accuracy Error = Actual - Forecast Error = Actual - Forecast Find a method which minimizes error Find a method which minimizes error Mean Absolute Deviation (MAD) Mean Absolute Deviation (MAD) Mean Absolute Percent Deviation (MAPD) Mean Absolute Percent Deviation (MAPD) Cumulative Error (E) Cumulative Error (E)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Mean Absolute Deviation (MAD) where t = the period number t = the period number D t = demand in period t D t = demand in period t F t = the forecast for period t F t = the forecast for period t n = the total number of periods n = the total number of periods  = the absolute value  D t - F t  n MAD =

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. MAD Example PERIODDEMAND, D t F t (  =0.3) Example 8.7

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. MAD Example –– PERIODDEMAND, D t F t (  =0.3)(D t - F t ) |D t - F t | Example 8.7

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. MAD Example –– PERIODDEMAND, D t F t (  =0.3)(D t - F t ) |D t - F t |  D t - F t  n MAD= = = Example 8.7

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Other Accuracy Measures Mean absolute percent deviation (MAPD) Mean absolute percent deviation (MAPD) MAPD =  |D t - F t |  D t Cumulative error Cumulative error E =  e t Average error Average error E = etetnnetetnnn

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Comparison of Forecasts Table 8.1 FORECASTMADMAPDE(E) Exponential smoothing (  = 0.30) % Exponential smoothing (  = 0.50) % Adjusted exponential smoothing % (  = 0.50,  = 0.30) Linear trend line %––

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Forecast Control Reasons for out-of-control forecasts Reasons for out-of-control forecasts Change in trend Change in trend Appearance of cycle Appearance of cycle Weather changes Weather changes Promotions Promotions Competition Competition Politics Politics

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Tracking Signal Compute each period Compute each period Compare to control limits Compare to control limits Forecast is in control if within limits Forecast is in control if within limits Use control limits of +/- 2 to +/- 5 MAD Tracking signal = =  (D t - F t ) MADEMAD

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Tracking Signal Values ––– DEMANDFORECAST,ERROR  E = PERIODD t F t D t - F t  (D t - F t )MAD Example 8.8

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Tracking Signal Values ––– DEMANDFORECAST,ERROR  E = PERIODD t F t D t - F t  (D t - F t )MAD TS 3 = = Tracking signal for period 3 Example 8.8

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Tracking Signal Values –––– DEMANDFORECAST,ERROR  E =TRACKING PERIODD t F t D t - F t  (D t - F t )MADSIGNAL Example 8.8

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Tracking Signal Plot Example  3  – 2  2  – 1  1  – 0  0  – -1  -1  – -2  -2  – -3  -3  – ||||||||||||| Tracking signal (MAD) Period

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Tracking Signal Plot Example  3  – 2  2  – 1  1  – 0  0  – -1  -1  – -2  -2  – -3  -3  – ||||||||||||| Tracking signal (MAD) Period Exponential smoothing (  = 0.30)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Tracking Signal Plot Example  3  – 2  2  – 1  1  – 0  0  – -1  -1  – -2  -2  – -3  -3  – ||||||||||||| Tracking signal (MAD) Period Exponential smoothing (  = 0.30) Linear trend line

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Statistical Control Charts  = = = =  (D t - F t ) 2 n - 1 Using  we can calculate statistical control limits for the forecast error Using  we can calculate statistical control limits for the forecast error Control limits are typically set at  3  Control limits are typically set at  3 

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Statistical Control Charts Errors – – – 0 0 – – – – ||||||||||||| Period Figure 8.4

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Statistical Control Charts Errors – – – 0 0 – – – – ||||||||||||| Period UCL = +3  LCL = -3  Figure 8.4

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Causal Modeling with Linear Regression Study relationship between two or more variables Study relationship between two or more variables Dependent variable y depends on independent variable x y = a + bx Dependent variable y depends on independent variable x y = a + bx

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Linear Regression Formulas a = y - b x b = where a =intercept (at period 0) b =slope of the line x == mean of the x data y == mean of the y data  xy - nxy  x 2 - nx 2  x n  y n

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Linear Regression Example Example 8.9 xy (WINS)(ATTENDANCE) xyx

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Linear Regression Example Example 8.9 xy (WINS)(ATTENDANCE) xyx x = = y = = b = = = 4.06 a = y - bx = (4.06)(6.125) =  xy - nxy 2  x 2 - nx 2 (2,167.7) - (8)(6.125)(43.36) (311) - (8)(6.125) 2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Linear Regression Example Example 8.9 xy (WINS)(ATTENDANCE) xyx x = = y = = b = = = 4.06 a = y - bx = (4.06)(6.125) =  xy - nxy 2  x 2 - nx 2 (2,167.7) - (8)(6.125)(43.36) (311) - (8)(6.125) 2 y = x y = (7) = 46.88, or 46,880 Regression equation Attendance forecast for 7 wins

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Linear Regression Line Example ,000 60,000 – 50,000 50,000 – 40,000 40,000 – 30,000 30,000 – 20,000 20,000 – 10,000 10,000 – ||||||||||| Wins, x Attendance, y

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Linear Regression Line Example 8.9 ||||||||||| ,000 60,000 – 50,000 50,000 – 40,000 40,000 – 30,000 30,000 – 20,000 20,000 – 10,000 10,000 – Linear regression line, y = x Wins, x Attendance, y

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Correlation and Coefficient of Determination Correlation, r Correlation, r Measure of strength of relationship Measure of strength of relationship Varies between and Varies between and Coefficient of determination, r 2 Coefficient of determination, r 2 Percentage of variation in dependent variable resulting from changes in the independent variable Percentage of variation in dependent variable resulting from changes in the independent variable

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Computing Correlation n  xy -  x  y [ n  x 2 - (  x ) 2 ] [ n  y 2 - (  y ) 2 ] r = Coefficient of determination r 2 = (0.947) 2 = r = (8)(2,167.7) - (49)(346.9) [(8)(311) - (49 )2 ] [(8)(15,224.7) - (346.9) 2 ] r = 0.947

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Multiple Regression Study the relationship of demand to two or more independent variables y =  0 +  1 x 1 +  2 x 2 … +  k x k where  0 =the intercept  1, …,  k =parameters for the independent variables x 1, …, x k =independent variables