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sales Forecasting skills presentation pdf

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The document discusses forecasting in operations management, particularly at Tupperware, where sales projections are collaboratively created by various departments and aggregated for decision-making. It outlines the different types of forecasts based on time horizons (short, medium, and long-range), the methodologies used (both quantitative and qualitative), and emphasizes the importance of understanding product life cycles in forecasting accuracy. Additionally, it details various forecasting methods—including moving averages and exponential smoothing—along with their applications and limitations.

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Operations Management Forecasting By Dr. Hisham Hussein Zaher
Forecasting at Tupperware ¨ Each of 50 profit centers around the world is responsible for computerized monthly, quarterly, and 12-month sales projections ¨ These projections are aggregated by region, then globally at Tupperware’s World Headquarters.
Tupperware - Forecast by Consensus ¨ Although inputs come from sales, marketing, finance, and production, final forecasts are the consensus of all participating managers. ¨ The final step is Tupperware’s version of the “jury of executive opinion”.
What is Forecasting? ¨ Process of predicting a future event. ¨ Underlying basis of all business decisions. ¨ Production ¨ Inventory ¨ Personnel ¨ Facilities Sales will be $200 Million!
¨ Short-range forecast: ¨ Up to 1 year; usually < 3 months. ¨ Job scheduling, worker assignments. ¨ Medium-range forecast: ¨ 3 months to 3 years. ¨ Sales & production planning, budgeting. ¨ Long-range forecast: ¨ 3+ years. ¨ New product planning, facility location. Types of Forecasts by Time Horizon
Short-term vs. Longer-term Forecasting ¨ Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes. ¨ Short-term forecasting usually employs different methodologies than longer-term forecasting. ¨ Short-term forecasts tend to be more accurate than longer-term forecasts.
Influence of Product Life Cycle ¨ Stages of introduction & growth require longer forecasts than maturity and decline. ¨ Forecasts useful in projecting: ¨ staffing levels, ¨ inventory levels, and ¨ factory capacity as product passes through stages.
Types of Forecasts ¨ Economic forecasts: ¨ Address business cycle. ¨ e.g., inflation rate, money supply etc. ¨ Technological forecasts: ¨ Predict technological change. ¨ Predict new product sales. ¨ Demand forecasts: ¨ Predict existing product sales.
) Seven Steps in Forecasting ¨ Determine the use of the forecast. ¨ Select the items to be forecast. ¨ Determine the time horizon of the forecast. ¨ Select the forecasting model(s). ¨ Gather the data. ¨ Make the forecast. ¨ Validate and implement results.
Realities of Forecasting ¨ Forecasts are seldom perfect. ¨ Most forecasting methods assume that there is some underlying stability in the system. ¨ Both product family and aggregated product forecasts are more accurate than individual product forecasts.
Forecasting Approaches ¨ Used when situation is ‘stable’ & historical data exist. ¨ Existing products ¨ Current technology ¨ Involves mathematical techniques. ¨ e.g. forecasting sales of LED color televisions. Quantitative Methods ¨ Used when situation is vague & little data exist. ¨ New products ¨ New technology ¨ Involves intuition and experience. ¨ e.g. forecasting sales on Internet. Qualitative Methods
Overview of Qualitative Methods ¨ Jury of executive opinion ¨ Pool opinions of high-level executives, sometimes augment by statistical models. ¨ Sales force composite ¨ estimates from individual salespersons are reviewed for reasonableness, then aggregated. ¨ Delphi method ¨ Panel of experts, queried iteratively. ¨ Consumer Market Survey ¨ Ask the customer.
¨ Involves small group of high-level managers. “Group estimates demand by working together”. ¨ Combines managerial experience with statistical models. ¨ Relatively quick. ¨ ‘Group-think’ disadvantage. Jury of Executive Opinion
Sales Force Composite ¨ Each salesperson projects their sales. ¨ Combined at district & national levels. ¨ Sales rep’s know customers’ wants. ¨ Tends to be overly optimistic. Sales
Delphi Method ¨ Iterative group process. ¨ 3 types of people: ¨ Decision makers. ¨ Staff. ¨ Respondents. ¨ Reduces ‘group- think’. Respondents Staff Decision Makers (Sales?) (What will sales be? survey) (Sales will be 45, 50, 55) (Sales will be 50!)
Consumer Market Survey ¨ Ask customers about purchasing plans. ¨ What consumers say, and what they actually do are often different. ¨ Sometimes difficult to answer. How many hours will you use the Internet next week? © 1995 Corel Corp.
Overview of Quantitative Approaches ¨ Naïve approach ¨ Moving averages ¨ Exponential smoothing ¨ Trend projection ¨ Linear regression Time-series Models Causal models
Quantitative Forecasting Methods (Non-Naive) Quantitative Forecasting Linear Regression Causal Models Exponential Smoothing Moving Average Time Series Models Trend Projection
¨ Set of evenly spaced numerical data. ¨ Obtained by observing response variable at regular time periods. ¨ Forecast based only on past values. ¨ Assumes that factors influencing past, present, & future will continue. ¨ Example Year: 2005 2006 2007 2008 2009 Sales: 78.7 63.5 89.7 93.2 92.1 What is a Time Series?
Trend Seasonal Cyclical Random Time Series Components
¨ Persistent, overall upward or downward pattern. ¨ Due to population, technology etc... ¨ Several years duration. Mo., Qtr., Yr. Response Trend Component
¨ Repeating up & down movements. ¨ Due to interactions of factors influencing economy. ¨ Usually 2-10 years duration. Mo., Qtr., Yr. Response Cycle B Cyclical Component
¨ Regular pattern of up & down fluctuations. ¨ Due to weather, customs etc. ¨ Occurs within 1 year. Mo., Qtr. Response Summer Seasonal Component
¨ Erratic, unsystematic, ‘residual’ fluctuations. ¨ Due to random variation or unforeseen events. ¨ Union strike ¨ Tornado ¨ Short duration & no repeating. Random Component
Naive Approach ¨ Assumes demand in next period is the same as demand in most recent period. ¨ e.g., If May sales were 48, then June sales will be 48. ¨ Sometimes cost effective & efficient.
¨ MA is a series of arithmetic means ¨ Used if little or no trend ¨ Used often for smoothing ¨ Provides overall impression of data over time ¨ Equation: MA n n =  Demand in Previous Periods Moving Average Method
You’re manager of a museum store that sells historical replicas. You want to forecast sales in (000) for 2010 using a 3-period moving average. 2005 4 2006 6 2007 5 2008 3 2009 7 Moving Average Example
Time Response Yi Moving Total (n = 3) Moving Avg. (n = 3) 2005 4 2006 6 2007 5 NA NA NA NA NA NA 2008 3 2009 7 2010 NA 4 + 6 + 5 = 15 Moving Average Solution
Time Response Yi Moving Total (n = 3) Moving Avg. (n = 3) 2005 4 NA NA 2006 6 NA NA 2007 5 NA NA 2008 3 4 + 6 + 5 = 15 15/3 = 5.0 2009 7 2010 NA 6 + 5 + 3 = 14 Moving Average Solution
Time Response Yi Moving Total (n = 3) Moving Avg. (n = 3) 2005 4 NA NA 2006 6 NA NA 2007 5 NA NA 2008 3 4 + 6 + 5 = 15 15/3 = 5.0 2009 7 6 + 5 + 3 = 14 14/3 = 4.7 2010 NA 5 + 3 + 7 = 15 15/3 = 5.0 Moving Average Solution
Year Sales 0 2 4 6 8 05 06 07 08 09 10 Actual Forecast Moving Average Graph
¨ Used when trend is present. ¨ Older data usually less important. ¨ Weights based on intuition. ¨ Equation: WMA =  (Weight for period n) (Demand in period n) Weights Weighted Moving Average Method
¨ Increasing n makes forecast less sensitive to changes. ¨ Do not forecast trend well. ¨ Require much historical data. Disadvantages of Moving Average Method
¨ Form of weighted moving average. ¨ Weights decline exponentially. ¨ Most recent data weighted most. ¨ Requires smoothing constant (a). ¨ Ranges from 0 to 1. ¨ Subjectively chosen. ¨ Involves little record keeping of past data. Exponential Smoothing Method
¨ Ft = a·At - 1 + a·(1-a)·At - 2 + a·(1- a)2·At - 3 + a·(1- a)3·At - 4 + ... + (1- a)t-1·A0 ¨ Ft = Forecast value ¨ At = Actual value  a = Smoothing constant ¨ Ft = Ft-1 + a·(At-1 - Ft-1) ¨ Use for computing forecast. Exponential Smoothing Equations
You’re organizing a Kwanza meeting. You want to forecast attendance for 2010 using exponential smoothing (a = .10). The 2005 forecast was 175. 2005 180 2006 168 2007 159 2008 175 2009 190 Exponential Smoothing Example
Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 2007 159 2008 175 2009 190 2010 NA 175.00 + Exponential Smoothing Solution
Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10( 2007 159 2008 175 2009 190 2010 NA Exponential Smoothing Solution
Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 2007 159 2008 175 2009 190 2010 NA Exponential Smoothing Solution
Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) 2007 159 2008 175 2009 190 2010 NA Exponential Smoothing Solution
Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) = 175.50 2007 159 2008 175 2009 190 2010 NA Exponential Smoothing Solution
Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) = 175.50 2007 159 175.50 + .10(168 - 175.50) = 174.75 2008 175 2009 190 2010 NA Exponential Smoothing Solution
Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) = 175.50 2007 159 175.50 + .10(168 - 175.50) = 174.75 2008 175 2009 190 2010 NA 174.75 + .10(159 - 174.75) = 173.18 Exponential Smoothing Solution
Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) = 175.50 2007 159 175.50 + .10(168 - 175.50) = 174.75 2008 175 174.75 + .10(159 - 174.75) = 173.18 2009 190 173.18 + .10(175 - 173.18) = 173.36 2010 NA Exponential Smoothing Solution
Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) = 175.50 2007 159 175.50 + .10(168 - 175.50) = 174.75 2008 175 174.75 + .10(159 - 174.75) = 173.18 2009 190 173.18 + .10(175 - 173.18) = 173.36 2010 NA 173.36 + .10(190 - 173.36) = 175.02 Exponential Smoothing Solution
Year Sales 140 150 160 170 180 190 05 06 07 08 09 10 Actual Forecast Exponential Smoothing Graph
Choosing a Seek to minimize the Mean Absolute Deviation (MAD) If: Forecast error = demand - forecast Then: n errors forecast  = MAD
¨ Used for forecasting linear trend line. ¨ Assumes relationship between response variable, Y, and time, X, is a linear function. ¨ Estimated by least squares method. ¨ Minimizes sum of squared errors. $i Y a bXi = + Linear Trend Projection
$ Y a bX i i = + $ Y a bX i i = + b > 0 b < 0 a a Y Time, X Linear Trend Projection Model
Time Sales 0 1 2 3 4 04 05 06 07 08 Sales vs. Time Scatter Diagram
Least Squares Equations Equation: i i bx a Ŷ + = Slope:     =  =     = x n x y x n y x b i n i i i n i Y-Intercept: x b y a  =
Xi Yi Xi 2 Yi 2 XiYi X1 Y1 X1 2 Y1 2 X1Y1 X2 Y2 X2 2 Y2 2 X2Y2 : : : : : Xn Yn Xn 2 Yn 2 XnYn SXi SYi SXi 2 SYi 2 SXiYi Computation Table
You’re a marketing analyst for Hasbro Toys. You gather the following data: YearSales (Units) 2004 1 2005 1 2006 2 2007 2 2008 4 What is the trend equation? Linear Trend Projection Example
Y X i i = + a b ¨ Shows linear relationship between dependent & explanatory variables. ¨ Example: Sales & advertising (not time) Dependent (response) variable Independent (explanatory) variable Slope Y-intercept ^ Linear Regression Model
Y X Y a i + ^ i i b X i = + Error Error Observed value Y a b X = + Regression line Linear Regression Model
Linear Regression Equations Equation: i i bx a Ŷ + = Slope:     =  =     = x n x y x n y x b i n i i i n i Y-Intercept: x b y a  =
Xi Yi Xi 2 Yi 2 XiYi X1 Y1 X1 2 Y1 2 X1Y1 X2 Y2 X2 2 Y2 2 X2Y2 : : : : : Xn Yn Xn 2 Yn 2 XnYn SXi SYi SXi 2 SYi 2 SXiYi Computation Table
¨ Slope (b) ¨ Estimated Y changes by b for each 1 unit increase in X. ¨ If b = 2, then sales (Y) is expected to increase by 2 for each 1 unit increase in advertising (X). ¨ Y-intercept (a) ¨ Average value of Y when X = 0. ¨ If a = 4, then average sales (Y) is expected to be 4 when advertising (X) is 0. Interpretation of Coefficients
¨ Answers: ‘how strong is the linear relationship between the variables?.’ ¨ Coefficient of correlation Sample correlation coefficient denoted r. ¨ Values range from -1 to +1. ¨ Measures degree of association. Correlation
Sample Coefficient of Correlation                                    =        2 2 2 2 y y n x x n y x y x n r
-1.0 +1.0 0 Perfect Positive Correlation Increasing degree of negative correlation -.5 +.5 Perfect Negative Correlation No Correlation Increasing degree of positive correlation Coefficient of Correlation Values
r = 1 r = -1 r = .89 r = 0 Y X Yi = a + b Xi ^ Y X Y X Y X Yi = a + b Xi ^ Yi = a + b Xi ^ Yi = a + b Xi ^ Coefficient of Correlation and Regression Model
¨ You want to achieve: ¨ No pattern or direction in forecast error ¨ Error = (Yi - Yi) = (Actual - Forecast) ¨ Seen in plots of errors over time ¨ Smallest forecast error ¨ Mean square error (MSE) ¨ Mean absolute deviation (MAD) ^ Guidelines for Selecting Forecasting Model
Time (Years) Error 0 Desired Pattern Time (Years) Error 0 Trend Not Fully Accounted for Pattern of Forecast Error
¨ Mean Square Error (MSE) ¨ Mean Absolute Deviation (MAD) Forecast Error Equations n errors forecast n ) ŷ y ( MSE n i i i   =  =  =  n | errors forecast | n | ŷ y | MAD n i i i   =  =  =
You’re a marketing analyst for Hasbro Toys. You’ve forecast sales with a linear model & exponential smoothing. Which model do you use? Actual Linear Model Exponential Smoothing Year Sales Forecast Forecast (.9) 2004 1 0.6 1.0 2005 1 1.3 1.0 2006 2 2.0 1.9 2007 2 2.7 2.0 2008 4 3.4 3.8 Selecting Forecasting Model Example
Year ^ Yi Yi ^ 2004 1 0.6 0.4 0.16 0.4 2005 1 1.3 -0.3 0.09 0.3 2006 2 2.0 0.0 0.00 0.0 2007 2 2.7 -0.7 0.49 0.7 2008 4 3.4 0.6 0.36 0.6 Total 0.0 1.10 2.0 Error Error2 |Error| Linear Model Evaluatin
Year ^ Yi Yi ^ 2004 1 0.6 0.4 0.16 0.4 2005 1 1.3 -0.3 0.09 0.3 2006 2 2.0 0.0 0.00 0.0 2007 2 2.7 -0.7 0.49 0.7 2008 4 3.4 0.6 0.36 0.6 Total 0.0 1.10 2.0 MSE = Error2 / n = 1.10 / 5 = .220 MAD =  |Error| / n = 2.0 / 5 = .400 Error Error2 |Error| Linear Model Evaluation
Year Yi Yi 2004 1 1.0 0.0 0.00 0.0 2005 1 1.0 0.0 0.00 0.0 2006 2 1.9 0.1 0.01 0.1 2007 2 2.0 0.0 0.00 0.0 2008 4 3.8 0.2 0.04 0.2 Total 0.3 0.05 0.3 ^ MSE = Error2 / n = 0.05 / 5 = 0.01 MAD = |Error| / n = 0.3 / 5 = 0.06 Error Error2 |Error| Exponential Smoothing Model Evaluation

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sales Forecasting skills presentation pdf

  • 2. Forecasting at Tupperware ¨ Each of 50 profit centers around the world is responsible for computerized monthly, quarterly, and 12-month sales projections ¨ These projections are aggregated by region, then globally at Tupperware’s World Headquarters.
  • 3. Tupperware - Forecast by Consensus ¨ Although inputs come from sales, marketing, finance, and production, final forecasts are the consensus of all participating managers. ¨ The final step is Tupperware’s version of the “jury of executive opinion”.
  • 4. What is Forecasting? ¨ Process of predicting a future event. ¨ Underlying basis of all business decisions. ¨ Production ¨ Inventory ¨ Personnel ¨ Facilities Sales will be $200 Million!
  • 5. ¨ Short-range forecast: ¨ Up to 1 year; usually < 3 months. ¨ Job scheduling, worker assignments. ¨ Medium-range forecast: ¨ 3 months to 3 years. ¨ Sales & production planning, budgeting. ¨ Long-range forecast: ¨ 3+ years. ¨ New product planning, facility location. Types of Forecasts by Time Horizon
  • 6. Short-term vs. Longer-term Forecasting ¨ Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes. ¨ Short-term forecasting usually employs different methodologies than longer-term forecasting. ¨ Short-term forecasts tend to be more accurate than longer-term forecasts.
  • 7. Influence of Product Life Cycle ¨ Stages of introduction & growth require longer forecasts than maturity and decline. ¨ Forecasts useful in projecting: ¨ staffing levels, ¨ inventory levels, and ¨ factory capacity as product passes through stages.
  • 8. Types of Forecasts ¨ Economic forecasts: ¨ Address business cycle. ¨ e.g., inflation rate, money supply etc. ¨ Technological forecasts: ¨ Predict technological change. ¨ Predict new product sales. ¨ Demand forecasts: ¨ Predict existing product sales.
  • 9. ) Seven Steps in Forecasting ¨ Determine the use of the forecast. ¨ Select the items to be forecast. ¨ Determine the time horizon of the forecast. ¨ Select the forecasting model(s). ¨ Gather the data. ¨ Make the forecast. ¨ Validate and implement results.
  • 10. Realities of Forecasting ¨ Forecasts are seldom perfect. ¨ Most forecasting methods assume that there is some underlying stability in the system. ¨ Both product family and aggregated product forecasts are more accurate than individual product forecasts.
  • 11. Forecasting Approaches ¨ Used when situation is ‘stable’ & historical data exist. ¨ Existing products ¨ Current technology ¨ Involves mathematical techniques. ¨ e.g. forecasting sales of LED color televisions. Quantitative Methods ¨ Used when situation is vague & little data exist. ¨ New products ¨ New technology ¨ Involves intuition and experience. ¨ e.g. forecasting sales on Internet. Qualitative Methods
  • 12. Overview of Qualitative Methods ¨ Jury of executive opinion ¨ Pool opinions of high-level executives, sometimes augment by statistical models. ¨ Sales force composite ¨ estimates from individual salespersons are reviewed for reasonableness, then aggregated. ¨ Delphi method ¨ Panel of experts, queried iteratively. ¨ Consumer Market Survey ¨ Ask the customer.
  • 13. ¨ Involves small group of high-level managers. “Group estimates demand by working together”. ¨ Combines managerial experience with statistical models. ¨ Relatively quick. ¨ ‘Group-think’ disadvantage. Jury of Executive Opinion
  • 14. Sales Force Composite ¨ Each salesperson projects their sales. ¨ Combined at district & national levels. ¨ Sales rep’s know customers’ wants. ¨ Tends to be overly optimistic. Sales
  • 15. Delphi Method ¨ Iterative group process. ¨ 3 types of people: ¨ Decision makers. ¨ Staff. ¨ Respondents. ¨ Reduces ‘group- think’. Respondents Staff Decision Makers (Sales?) (What will sales be? survey) (Sales will be 45, 50, 55) (Sales will be 50!)
  • 16. Consumer Market Survey ¨ Ask customers about purchasing plans. ¨ What consumers say, and what they actually do are often different. ¨ Sometimes difficult to answer. How many hours will you use the Internet next week? © 1995 Corel Corp.
  • 17. Overview of Quantitative Approaches ¨ Naïve approach ¨ Moving averages ¨ Exponential smoothing ¨ Trend projection ¨ Linear regression Time-series Models Causal models
  • 19. ¨ Set of evenly spaced numerical data. ¨ Obtained by observing response variable at regular time periods. ¨ Forecast based only on past values. ¨ Assumes that factors influencing past, present, & future will continue. ¨ Example Year: 2005 2006 2007 2008 2009 Sales: 78.7 63.5 89.7 93.2 92.1 What is a Time Series?
  • 21. ¨ Persistent, overall upward or downward pattern. ¨ Due to population, technology etc... ¨ Several years duration. Mo., Qtr., Yr. Response Trend Component
  • 22. ¨ Repeating up & down movements. ¨ Due to interactions of factors influencing economy. ¨ Usually 2-10 years duration. Mo., Qtr., Yr. Response Cycle B Cyclical Component
  • 23. ¨ Regular pattern of up & down fluctuations. ¨ Due to weather, customs etc. ¨ Occurs within 1 year. Mo., Qtr. Response Summer Seasonal Component
  • 24. ¨ Erratic, unsystematic, ‘residual’ fluctuations. ¨ Due to random variation or unforeseen events. ¨ Union strike ¨ Tornado ¨ Short duration & no repeating. Random Component
  • 25. Naive Approach ¨ Assumes demand in next period is the same as demand in most recent period. ¨ e.g., If May sales were 48, then June sales will be 48. ¨ Sometimes cost effective & efficient.
  • 26. ¨ MA is a series of arithmetic means ¨ Used if little or no trend ¨ Used often for smoothing ¨ Provides overall impression of data over time ¨ Equation: MA n n =  Demand in Previous Periods Moving Average Method
  • 27. You’re manager of a museum store that sells historical replicas. You want to forecast sales in (000) for 2010 using a 3-period moving average. 2005 4 2006 6 2007 5 2008 3 2009 7 Moving Average Example
  • 28. Time Response Yi Moving Total (n = 3) Moving Avg. (n = 3) 2005 4 2006 6 2007 5 NA NA NA NA NA NA 2008 3 2009 7 2010 NA 4 + 6 + 5 = 15 Moving Average Solution
  • 29. Time Response Yi Moving Total (n = 3) Moving Avg. (n = 3) 2005 4 NA NA 2006 6 NA NA 2007 5 NA NA 2008 3 4 + 6 + 5 = 15 15/3 = 5.0 2009 7 2010 NA 6 + 5 + 3 = 14 Moving Average Solution
  • 30. Time Response Yi Moving Total (n = 3) Moving Avg. (n = 3) 2005 4 NA NA 2006 6 NA NA 2007 5 NA NA 2008 3 4 + 6 + 5 = 15 15/3 = 5.0 2009 7 6 + 5 + 3 = 14 14/3 = 4.7 2010 NA 5 + 3 + 7 = 15 15/3 = 5.0 Moving Average Solution
  • 31. Year Sales 0 2 4 6 8 05 06 07 08 09 10 Actual Forecast Moving Average Graph
  • 32. ¨ Used when trend is present. ¨ Older data usually less important. ¨ Weights based on intuition. ¨ Equation: WMA =  (Weight for period n) (Demand in period n) Weights Weighted Moving Average Method
  • 33. ¨ Increasing n makes forecast less sensitive to changes. ¨ Do not forecast trend well. ¨ Require much historical data. Disadvantages of Moving Average Method
  • 34. ¨ Form of weighted moving average. ¨ Weights decline exponentially. ¨ Most recent data weighted most. ¨ Requires smoothing constant (a). ¨ Ranges from 0 to 1. ¨ Subjectively chosen. ¨ Involves little record keeping of past data. Exponential Smoothing Method
  • 35. ¨ Ft = a·At - 1 + a·(1-a)·At - 2 + a·(1- a)2·At - 3 + a·(1- a)3·At - 4 + ... + (1- a)t-1·A0 ¨ Ft = Forecast value ¨ At = Actual value  a = Smoothing constant ¨ Ft = Ft-1 + a·(At-1 - Ft-1) ¨ Use for computing forecast. Exponential Smoothing Equations
  • 36. You’re organizing a Kwanza meeting. You want to forecast attendance for 2010 using exponential smoothing (a = .10). The 2005 forecast was 175. 2005 180 2006 168 2007 159 2008 175 2009 190 Exponential Smoothing Example
  • 37. Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 2007 159 2008 175 2009 190 2010 NA 175.00 + Exponential Smoothing Solution
  • 38. Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10( 2007 159 2008 175 2009 190 2010 NA Exponential Smoothing Solution
  • 39. Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 2007 159 2008 175 2009 190 2010 NA Exponential Smoothing Solution
  • 40. Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) 2007 159 2008 175 2009 190 2010 NA Exponential Smoothing Solution
  • 41. Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) = 175.50 2007 159 2008 175 2009 190 2010 NA Exponential Smoothing Solution
  • 42. Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) = 175.50 2007 159 175.50 + .10(168 - 175.50) = 174.75 2008 175 2009 190 2010 NA Exponential Smoothing Solution
  • 43. Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) = 175.50 2007 159 175.50 + .10(168 - 175.50) = 174.75 2008 175 2009 190 2010 NA 174.75 + .10(159 - 174.75) = 173.18 Exponential Smoothing Solution
  • 44. Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) = 175.50 2007 159 175.50 + .10(168 - 175.50) = 174.75 2008 175 174.75 + .10(159 - 174.75) = 173.18 2009 190 173.18 + .10(175 - 173.18) = 173.36 2010 NA Exponential Smoothing Solution
  • 45. Ft = Ft-1 + a· (At-1 - Ft-1) Time Actual Forecast, Ft (a = .10) 2005 180 175.00 (Given) 2006 168 175.00 + .10(180 - 175.00) = 175.50 2007 159 175.50 + .10(168 - 175.50) = 174.75 2008 175 174.75 + .10(159 - 174.75) = 173.18 2009 190 173.18 + .10(175 - 173.18) = 173.36 2010 NA 173.36 + .10(190 - 173.36) = 175.02 Exponential Smoothing Solution
  • 46. Year Sales 140 150 160 170 180 190 05 06 07 08 09 10 Actual Forecast Exponential Smoothing Graph
  • 47. Choosing a Seek to minimize the Mean Absolute Deviation (MAD) If: Forecast error = demand - forecast Then: n errors forecast  = MAD
  • 48. ¨ Used for forecasting linear trend line. ¨ Assumes relationship between response variable, Y, and time, X, is a linear function. ¨ Estimated by least squares method. ¨ Minimizes sum of squared errors. $i Y a bXi = + Linear Trend Projection
  • 49. $ Y a bX i i = + $ Y a bX i i = + b > 0 b < 0 a a Y Time, X Linear Trend Projection Model
  • 50. Time Sales 0 1 2 3 4 04 05 06 07 08 Sales vs. Time Scatter Diagram
  • 51. Least Squares Equations Equation: i i bx a Ŷ + = Slope:     =  =     = x n x y x n y x b i n i i i n i Y-Intercept: x b y a  =
  • 52. Xi Yi Xi 2 Yi 2 XiYi X1 Y1 X1 2 Y1 2 X1Y1 X2 Y2 X2 2 Y2 2 X2Y2 : : : : : Xn Yn Xn 2 Yn 2 XnYn SXi SYi SXi 2 SYi 2 SXiYi Computation Table
  • 53. You’re a marketing analyst for Hasbro Toys. You gather the following data: YearSales (Units) 2004 1 2005 1 2006 2 2007 2 2008 4 What is the trend equation? Linear Trend Projection Example
  • 54. Y X i i = + a b ¨ Shows linear relationship between dependent & explanatory variables. ¨ Example: Sales & advertising (not time) Dependent (response) variable Independent (explanatory) variable Slope Y-intercept ^ Linear Regression Model
  • 55. Y X Y a i + ^ i i b X i = + Error Error Observed value Y a b X = + Regression line Linear Regression Model
  • 56. Linear Regression Equations Equation: i i bx a Ŷ + = Slope:     =  =     = x n x y x n y x b i n i i i n i Y-Intercept: x b y a  =
  • 57. Xi Yi Xi 2 Yi 2 XiYi X1 Y1 X1 2 Y1 2 X1Y1 X2 Y2 X2 2 Y2 2 X2Y2 : : : : : Xn Yn Xn 2 Yn 2 XnYn SXi SYi SXi 2 SYi 2 SXiYi Computation Table
  • 58. ¨ Slope (b) ¨ Estimated Y changes by b for each 1 unit increase in X. ¨ If b = 2, then sales (Y) is expected to increase by 2 for each 1 unit increase in advertising (X). ¨ Y-intercept (a) ¨ Average value of Y when X = 0. ¨ If a = 4, then average sales (Y) is expected to be 4 when advertising (X) is 0. Interpretation of Coefficients
  • 59. ¨ Answers: ‘how strong is the linear relationship between the variables?.’ ¨ Coefficient of correlation Sample correlation coefficient denoted r. ¨ Values range from -1 to +1. ¨ Measures degree of association. Correlation
  • 61. -1.0 +1.0 0 Perfect Positive Correlation Increasing degree of negative correlation -.5 +.5 Perfect Negative Correlation No Correlation Increasing degree of positive correlation Coefficient of Correlation Values
  • 62. r = 1 r = -1 r = .89 r = 0 Y X Yi = a + b Xi ^ Y X Y X Y X Yi = a + b Xi ^ Yi = a + b Xi ^ Yi = a + b Xi ^ Coefficient of Correlation and Regression Model
  • 63. ¨ You want to achieve: ¨ No pattern or direction in forecast error ¨ Error = (Yi - Yi) = (Actual - Forecast) ¨ Seen in plots of errors over time ¨ Smallest forecast error ¨ Mean square error (MSE) ¨ Mean absolute deviation (MAD) ^ Guidelines for Selecting Forecasting Model
  • 64. Time (Years) Error 0 Desired Pattern Time (Years) Error 0 Trend Not Fully Accounted for Pattern of Forecast Error
  • 65. ¨ Mean Square Error (MSE) ¨ Mean Absolute Deviation (MAD) Forecast Error Equations n errors forecast n ) ŷ y ( MSE n i i i   =  =  =  n | errors forecast | n | ŷ y | MAD n i i i   =  =  =
  • 66. You’re a marketing analyst for Hasbro Toys. You’ve forecast sales with a linear model & exponential smoothing. Which model do you use? Actual Linear Model Exponential Smoothing Year Sales Forecast Forecast (.9) 2004 1 0.6 1.0 2005 1 1.3 1.0 2006 2 2.0 1.9 2007 2 2.7 2.0 2008 4 3.4 3.8 Selecting Forecasting Model Example
  • 67. Year ^ Yi Yi ^ 2004 1 0.6 0.4 0.16 0.4 2005 1 1.3 -0.3 0.09 0.3 2006 2 2.0 0.0 0.00 0.0 2007 2 2.7 -0.7 0.49 0.7 2008 4 3.4 0.6 0.36 0.6 Total 0.0 1.10 2.0 Error Error2 |Error| Linear Model Evaluatin
  • 68. Year ^ Yi Yi ^ 2004 1 0.6 0.4 0.16 0.4 2005 1 1.3 -0.3 0.09 0.3 2006 2 2.0 0.0 0.00 0.0 2007 2 2.7 -0.7 0.49 0.7 2008 4 3.4 0.6 0.36 0.6 Total 0.0 1.10 2.0 MSE = Error2 / n = 1.10 / 5 = .220 MAD =  |Error| / n = 2.0 / 5 = .400 Error Error2 |Error| Linear Model Evaluation
  • 69. Year Yi Yi 2004 1 1.0 0.0 0.00 0.0 2005 1 1.0 0.0 0.00 0.0 2006 2 1.9 0.1 0.01 0.1 2007 2 2.0 0.0 0.00 0.0 2008 4 3.8 0.2 0.04 0.2 Total 0.3 0.05 0.3 ^ MSE = Error2 / n = 0.05 / 5 = 0.01 MAD = |Error| / n = 0.3 / 5 = 0.06 Error Error2 |Error| Exponential Smoothing Model Evaluation