This slide introduces the topic of forecasting at Tupperware. The next several slides elaborate. One might ask students several questions: - “What does a useful forecast consist of at Tupperware? - What problems might a company such as Tupperware experience in developing a useful forecast. As you move through the following two slides, you could point out the application of multiple forecasting techniques to help solve some of the problems identified.
Ask students: “Why does the number of ‘active’ dealers change so often?” and “ If the number of ‘active’ dealers changes so often, should not this problem be addressed before attempting to forecast sales?” This question raises the issue of the impact of the distribution chain on one’s ability to forecast.
You might take the notion of “problems” one step further and ask students why Tupperware uses a “jury of executive opinion” as part of its forecasting process.
At this point, it may be useful to point out the “time horizons” considered by different industries. For example, some colleges and universities look 30 to fifty years ahead, industries engaged in long distance transportation (steam ship, railroad) or provision of basic power (electrical and gas utilities, etc.) also look far ahead (20 to 100 years). Ask them to give examples of industries having much shorter long-range horizons.
At this point it may be helpful to discuss the actual variables one might wish to forecast in the various time periods.
This slide introduces the impact of product life cycle on forecasting The following slide, reproduced from chapter 2, summarizes the changing issues over the product’s lifetime for those faculty who wish to treat the issue in greater depth.
One can use an example based upon one’s college or university. Students can be asked why each of these forecast types is important to the college. Once they begin to appreciate the importance, one can then begin to discuss the problems. For example, is predicting “demand” merely as simple as predicting the number of students who will graduate from high school next year (i.e., a simple counting exercise)?
A point to be made here is that one requires a forecasting “plan,” not merely the selection of a particular forecasting methodology.
This slide illustrates a typical demand curve. You might ask students why it is important to know more than simply the actual demand over time. Why, for example, would one wish to be able to break out a “seasonality” factor?
This slide illustrates one of the simplest forecasting techniques - the moving average. It may be useful to point out the lag introduced by exponential smoothing - and ask how one can actually make use of the forecast.
This slide provides a framework for discussing some of the inherent difficulties in developing reliable forecasts. You may wish to include in this discussion the difficulties posed by attempting forecast in a continuously, and rapidly changing environment where product life-times are measured less often in years and more often in months than ever before. One might wish to emphasize the inherent difficulties in developing reliable forecasts.
This slide distinguishes between Quantitative and Qualitative forecasting. If you accept the argument that the future is one of perpetual, and perhaps significant change, you may wish to ask students to consider whether quantitative forecasting will ever be sufficient in the future - or will we always need to employ qualitative forecasting also. (Consider Tupperware’s ‘jury of executive opinion.’)
This slide outlines several qualitative methods of forecasting. Ask students to give examples of occasions when each might be appropriate. The next several slides elaborate on these qualitative methods.
Ask your students to consider other potential disadvantages. (Politics?)
You might ask your students to consider what problems might occur when trying to use this method to predict sales of a potential new product.
You might ask your students to consider whether there are special examples where this technique is required. ( Questions of technology transfer or assessment, for example; or other questions where information from many different disciplines is required.)
You might discuss some of the difficulties with this technique. Certainly there is the issue that what consumers say is often not what they do. There are other problems such as that consumers sometime wish to please the surveyor; and for unusual, future, products, consumers may have a very imperfect frame of reference within which to consider the question.
A point you may wish to make here is that only in the case of linear regression are we assuming that we know “why” something happened. General time-series models are based exclusively on “what” happened in the past; not at all on “why.” Does operating in a time of drastic change imply limitations on our ability to use time series models?
This and subsequent slide frame a discussion on time series - and introduce the various components.
This slide introduces two general forms of time series model. You might provide examples of when one or the other is most appropriate.
This slide introduces the naïve approach. Subsequent slides introduce other methodologies.
At this point, you might discuss the impact of the number of periods included in the calculation. The more periods you include, the closer you come to the overall average; the fewer, the closer you come to the value in the previous period. What is the tradeoff?
This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast.
This slide introduces the “weighted moving average” method. It is probably most important to discuss choice of the weights.
This slide illustrates one of the simplest forecasting techniques - the moving average. It may be useful to point out the lag introduced by exponential smoothing - and ask how one can actually make use of the forecast.
These points should have been brought out in the example, but can be summarized here.
This slide introduces the exponential smoothing method of time series forecasting. The following slide contains the equations, and an example follows.
You may wish to discuss several points: - this is just a moving average wherein every point in included in the forecast, but the weights of the points continuously decrease as they extend further back in time. - the equation actually used to calculate the forecast is convenient for programming on the computer since it requires as data only the actual and forecast values from the previous time point. - we need a formal process and criteria for choosing the “best” smoothing constant.
This slide begins an exponential smoothing example.
This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps.
This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps.
This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps.
This slide illustrates the decrease in magnitude of the smoothing constant. In the Power Point presentation, the several previous slides show the steps leading to this slide.
This slide indicates one method of selecting .
This slide introduces exponential smoothing with trend adjustment. The equations and additional material follow.
This slide introduces the topic of least squares. One might try to make the point, using this slide, that the goal of least squares is to minimize the average deviation without regard to the mathematical sign of the deviation. The average of the deviations could be minimized by making their sum equal to zero - but we could still be left with large positive and negative deviations. Minimizing the sum of the square of the deviations produces a more “balanced” set of deviations.
This slide illustrates a regression line along with the actual demand. You might wish to highlight the actual deviations.
This slide introduces the equation produced in linear trend progression.
This slide illustrates the general result of the linear trend model for various values of the coefficient, b.
It is probably useful to go through this slide in detail, indicating the differences between the individual values of the variable, and its average.
This slide illustrates how one might do, by hand, the calculations required to solve for the linear trend coefficients. If you are expecting students to solve even the simplest linear trend or regression problems using a computer program, you may wish to skip this slide.
This slide provides a quick view of the development of a multiplicative seasonal model.
This slide introduces the linear regression model. This can be approached as simply a generalization of the linear trend model where the variable is something other than time and the values do not necessarily occur a t equal intervals.
Again, this is basically a repeat of the slide for the linear trend problem.
This too.
This slide probably merits discussion - additional to that for the linear trend model. You might make the point here that the dependent and independent variable are not necessarily of the same nature - they need not both be dollars, for example. You might also wish to note that setting x = 0 may not have a useful physical interpretation.
Here you may wish to at least begin the discussion of the distinction between explainable and unexplainable, and random and non-random error variation. There are also slides which come later in the presentation that will refer to this topic.
This slide raises several points: - What does it mean to be “linear”? How does one tell if something is linear or not? Or perhaps, how does one tell if something is sufficiently linear that a linear regression model is appropriate? - If the relationship is assumed to hold only within or slightly outside the data range, how do we use this model to make projections into the future (for which we don’t have data)? - What does it mean for data to be random? How can we tell? You might discuss making scatter plots not only of the original data, but also of the resulting deviations. (Obviously there are more rigorous methods of determining if the deviations are random, but a scatter plot is a good start.)
Again, it is probably useful to point out which elements in the equations represent the actual data values and which the averages of these values.
This slide can frame the start of a discussion of correlation.. You should probably expect to add to this a discussion of cause and effect, emphasizing in particular that correlation does not imply a cause and effect relationship. Ask student to suggest examples of significant correlation of unrelated phenomenon.
Here again an explanation of each variable is probably useful.
While this slide introduces the implications of negative and positive correlation, it is probably also a good point to re-emphasis the difference between correlation and cause and effect.
This slide presents additional examples of the meaning of the correlation coefficient.
This slide introduces overall guideline for selecting a forecasting model. You may also wish to re-emphasize the role of scatter plots, and discuss the role of “understanding what is going on” (especially in limiting one’s choice of model).
This slide illustrates both possible patterns in forecast error, and the merit of making a scatter plot of forecast error.
This slide illustrates the equations for two measures of forecast error. Students might be asked if there is an occasion when one method might be preferred over the other.
This slide begins an example of choosing a model.
This slide presents the result of the calculations of MSE and MAD for the Linear and Exponential Smoothing models. Students should be asked to choose the “better” model. Students should also be asked to consider the differences between the values calculated for the error measures for a given model, and between the two models. Do these differences tell us more than simply that one model is preferable to the other? (For example, is the exponential smoothing model 22 times better than the linear model?)
This slide illustrates the last step in the calculation of a tracking signal for a simple example problem. The PowerPoint slide presentation contains this as the last of a sequence of slides - the others stepping through the actual calculation process.
This slide illustrates a graph of a tracking signal form a “practical” problem.
This slide illustrates actual, forecast, and tracking signal. Students should be asked how they would decide when the tracking signal was out of range.
This slide simply raises a few of the forecasting issues peculiar to services.
Transcript
1. Forecasting
2. Outline <ul><li>GLOBAL COMPANY PROFILE: TUPPERWARE CORPORATION </li></ul><ul><li>WHAT IS FORECASTING? </li></ul><ul><ul><li>Forecasting Time Horizons </li></ul></ul><ul><ul><li>The Influence of Product Life Cycle </li></ul></ul><ul><li>TYPES OF FORECASTS </li></ul><ul><li>THE STRATEGIC IMPORTANCE OF FORECASTING </li></ul><ul><ul><li>Human Resources </li></ul></ul><ul><ul><li>Capacity </li></ul></ul><ul><ul><li>Supply-Chain Management </li></ul></ul><ul><li>SEVEN STEPS IN THE FORECASTING SYSTEM </li></ul>
3. Outline - Continued <ul><li>FORECASTING APPROACHES </li></ul><ul><ul><li>Overview of Qualitative Methods </li></ul></ul><ul><ul><li>Overview of Quantitative Methods </li></ul></ul><ul><li>TIME-SERIES FORECASTING </li></ul><ul><ul><li>Decomposition of Time Series </li></ul></ul><ul><ul><li>Naïve Approach </li></ul></ul><ul><ul><li>Moving Averages </li></ul></ul><ul><ul><li>Exponential Smoothing </li></ul></ul><ul><ul><li>Exponential Smoothing with Trend Adjustment </li></ul></ul><ul><ul><li>Trend Projections </li></ul></ul><ul><ul><li>Seasonal Variations in Data </li></ul></ul><ul><ul><li>Cyclic Variations in Data </li></ul></ul>
4. Outline - Continued <ul><li>ASSOCIATIVE FORECASTING METHODS: REGRESSION AND CORRELATION ANALYSIS </li></ul><ul><ul><li>Using Regression Analysis to Forecast </li></ul></ul><ul><ul><li>Standard Error of the Estimate </li></ul></ul><ul><ul><li>Correlation Coefficients for Regression Lines </li></ul></ul><ul><ul><li>Multiple-Regression Analysis </li></ul></ul><ul><li>MONITORING AND CONTROLLING FORECASTS </li></ul><ul><ul><li>Adaptive Smoothing </li></ul></ul><ul><ul><li>Focus Forecasting </li></ul></ul><ul><li>FORECASTING IN THE SERVICE SECTOR </li></ul>
5. Learning Objectives When you complete this chapter, you should be able to : Identify or Define : Forecasting Types of forecasts Time horizons Approaches to forecasts
6. Learning Objectives - continued <ul><li>When you complete this chapter, you should be able to : </li></ul><ul><li>Describe or Explain : </li></ul><ul><ul><li>Moving averages </li></ul></ul><ul><ul><li>Exponential smoothing </li></ul></ul><ul><ul><li>Trend projections </li></ul></ul><ul><ul><li>Regression and correlation analysis </li></ul></ul><ul><ul><li>Measures of forecast accuracy </li></ul></ul>
7. Forecasting at Tupperware <ul><li>Each of 50 profit centers around the world is responsible for computerized monthly, quarterly, and 12-month sales projections </li></ul><ul><li>These projections are aggregated by region, then globally, at Tupperware’s World Headquarters </li></ul><ul><li>Tupperware uses all techniques discussed in text </li></ul>
8. Three Key Factors for Tupperware <ul><li>The number of registered “consultants” or sales representatives </li></ul><ul><li>The percentage of currently “active” dealers (this number changes each week and month) </li></ul><ul><li>Sales per active dealer, on a weekly basis </li></ul>
9. Tupperware - Forecast by Consensus <ul><li>Although inputs come from sales, marketing, finance, and production, final forecasts are the consensus of all participating managers. </li></ul><ul><li>The final step is Tupperware’s version of the “jury of executive opinion” </li></ul>
10. What is Forecasting? Process of predicting a future event Underlying basis of all business decisions Production Inventory Personnel Facilities Sales will be $200 Million!
11. <ul><li>Short-range forecast </li></ul><ul><ul><li>Up to 1 year; usually less than 3 months </li></ul></ul><ul><ul><li>Job scheduling, worker assignments </li></ul></ul><ul><li>Medium-range forecast </li></ul><ul><ul><li>3 months to 3 years </li></ul></ul><ul><ul><li>Sales & production planning, budgeting </li></ul></ul><ul><li>Long-range forecast </li></ul><ul><ul><li>3 + years </li></ul></ul><ul><ul><li>New product planning, facility location </li></ul></ul>Types of Forecasts by Time Horizon
12. Short-term vs. Longer-term Forecasting <ul><li>Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes. </li></ul><ul><li>Short-term forecasting usually employs different methodologies than longer-term forecasting </li></ul><ul><li>Short-term forecasts tend to be more accurate than longer-term forecasts. </li></ul>
13. Influence of Product Life Cycle <ul><li>Stages of introduction and growth require longer forecasts than maturity and decline </li></ul><ul><li>Forecasts useful in projecting </li></ul><ul><ul><li>staffing levels, </li></ul></ul><ul><ul><li>inventory levels, and </li></ul></ul><ul><ul><li>factory capacity </li></ul></ul><ul><li>as product passes through life cycle stages </li></ul>Introduction, Growth, Maturity, Decline
14. Strategy and Issues During a Product’s Life Introduction Growth Maturity Decline Standardization Less rapid product changes - more minor changes Optimum capacity Increasing stability of process Long production runs Product improvement and cost cutting Little product differentiation Cost minimization Over capacity in the industry Prune line to eliminate items not returning good margin Reduce capacity Forecasting critical Product and process reliability Competitive product improvements and options Increase capacity Shift toward product focused Enhance distribution Product design and development critical Frequent product and process design changes Short production runs High production costs Limited models Attention to quality Best period to increase market share R&D product engineering critical Practical to change price or quality image Strengthen niche Cost control critical Poor time to change image, price, or quality Competitive costs become critical Defend market position OM Strategy/Issues Company Strategy/Issues HDTV CD-ROM Color copiers Drive-thru restaurants Fax machines Station wagons Sales 3 1/2” Floppy disks Internet
15. Types of Forecasts <ul><li>Economic forecasts </li></ul><ul><ul><li>Address business cycle, e.g., inflation rate, money supply etc. </li></ul></ul><ul><li>Technological forecasts </li></ul><ul><ul><li>Predict rate of technological progress </li></ul></ul><ul><ul><li>Predict acceptance of new product </li></ul></ul><ul><li>Demand forecasts </li></ul><ul><ul><li>Predict sales of existing product </li></ul></ul>
16. Seven Steps in Forecasting <ul><li>Determine the use of the forecast </li></ul><ul><li>Select the items to be forecasted </li></ul><ul><li>Determine the time horizon of the forecast </li></ul><ul><li>Select the forecasting model(s) </li></ul><ul><li>Gather the data </li></ul><ul><li>Make the forecast </li></ul><ul><li>Validate and implement results </li></ul>
17. Product Demand Charted over 4 Years with Trend and Seasonality Year 1 Year 2 Year 3 Year 4 Seasonal peaks Trend component Actual demand line Average demand over four years Demand for product or service Random variation
18. Actual Demand, Moving Average, Weighted Moving Average Actual sales Moving average Weighted moving average
19. Realities of Forecasting <ul><li>Forecasts are seldom perfect </li></ul><ul><li>Most forecasting methods assume that there is some underlying stability in the system </li></ul><ul><li>Both product family and aggregated product forecasts are more accurate than individual product forecasts </li></ul>
20. Forecasting Approaches <ul><li>Used when situation is ‘stable’ & historical data exist </li></ul><ul><li>Existing products </li></ul><ul><li>Current technology </li></ul><ul><li>Involves mathematical techniques </li></ul><ul><li>e.g., forecasting sales of color televisions </li></ul>Quantitative Methods <ul><li>Used when situation is vague & little data exist </li></ul><ul><li>New products </li></ul><ul><li>New technology </li></ul><ul><li>Involves intuition, experience </li></ul><ul><li>e.g., forecasting sales on Internet </li></ul>Qualitative Methods
21. Overview of Qualitative Methods <ul><li>Jury of executive opinion </li></ul><ul><ul><li>Pool opinions of high-level executives, sometimes augment by statistical models </li></ul></ul><ul><li>Delphi method </li></ul><ul><ul><li>Panel of experts, queried iteratively </li></ul></ul><ul><li>Sales force composite </li></ul><ul><ul><li>Estimates from individual salespersons are reviewed for reasonableness, then aggregated </li></ul></ul><ul><li>Consumer Market Survey </li></ul><ul><ul><li>Ask the customer </li></ul></ul>
24. Delphi Method <ul><li>Iterative group process </li></ul><ul><li>3 types of people </li></ul><ul><ul><li>Decision makers </li></ul></ul><ul><ul><li>Staff </li></ul></ul><ul><ul><li>Respondents </li></ul></ul><ul><li>Reduces ‘group-think’ </li></ul>Respondents Staff Decision Makers (Sales?) ( What will sales be? survey) (Sales will be 45, 50, 55) (Sales will be 50!)
27. Quantitative Forecasting Methods (Non-Naive) Quantitative Forecasting Linear Regression Associative Models Exponential Smoothing Moving Average Time Series Models Trend Projection
28. <ul><li>Set of evenly spaced numerical data </li></ul><ul><ul><li>Obtained by observing response variable at regular time periods </li></ul></ul><ul><li>Forecast based only on past values </li></ul><ul><ul><li>Assumes that factors influencing past and present will continue influence in future </li></ul></ul><ul><li>Example </li></ul><ul><ul><li>Year: 1998 1999 2000 2001 2002 </li></ul></ul><ul><ul><li>Sales: 78.7 63.5 89.7 93.2 92.1 </li></ul></ul>What is a Time Series?
29. Time Series Components Trend Seasonal Cyclical Random
32. Common Seasonal Patterns Period of Pattern “ Season” Length Number of “Seasons” in Pattern Week Day 7 Month Week 4 – 4 ½ Month Day 28 – 31 Year Quarter 4 Year Month 12 Year Week 52
33. <ul><li>Repeating up & down movements </li></ul><ul><li>Due to interactions of factors influencing economy </li></ul><ul><li>Usually 2-10 years duration </li></ul>Cyclical Component Mo., Qtr., Yr. Response Cycle
35. <ul><li>Any observed value in a time series is the product (or sum) of time series components </li></ul><ul><li>Multiplicative model </li></ul><ul><ul><li>Y i = T i · S i · C i · R i (if quarterly or mo. data) </li></ul></ul><ul><li>Additive model </li></ul><ul><ul><li>Y i = T i + S i + C i + R i (if quarterly or mo. data) </li></ul></ul>General Time Series Models
37. <ul><li>MA is a series of arithmetic means </li></ul><ul><li>Used if little or no trend </li></ul><ul><li>Used often for smoothing </li></ul><ul><ul><li>Provides overall impression of data over time </li></ul></ul><ul><li>Equation </li></ul>Moving Average Method MA n n Demand in Previous Periods
42. Moving Average Graph 95 96 97 98 99 00 Year Sales 2 4 6 8 Actual Forecast
43. <ul><li>Used when trend is present </li></ul><ul><ul><li>Older data usually less important </li></ul></ul><ul><li>Weights based on intuition </li></ul><ul><ul><li>Often lay between 0 & 1, & sum to 1.0 </li></ul></ul><ul><li>Equation </li></ul>Weighted Moving Average Method WMA = Σ (Weight for period n ) (Demand in period n ) Σ Weights
44. Actual Demand, Moving Average, Weighted Moving Average Actual sales Moving average Weighted moving average
46. <ul><li>Form of weighted moving average </li></ul><ul><ul><li>Weights decline exponentially </li></ul></ul><ul><ul><li>Most recent data weighted most </li></ul></ul><ul><li>Requires smoothing constant ( ) </li></ul><ul><ul><li>Ranges from 0 to 1 </li></ul></ul><ul><ul><li>Subjectively chosen </li></ul></ul><ul><li>Involves little record keeping of past data </li></ul>Exponential Smoothing Method
47. <ul><li>F t = A t - 1 + (1- ) A t - 2 + (1- ) 2 ·A t - 3 + (1- ) 3 A t - 4 + ... + (1- ) t- 1 ·A 0 </li></ul><ul><ul><li>F t = Forecast value </li></ul></ul><ul><ul><li>A t = Actual value </li></ul></ul><ul><ul><li> = Smoothing constant </li></ul></ul><ul><li>F t = F t -1 + ( A t -1 - F t -1 ) </li></ul><ul><ul><li>Use for computing forecast </li></ul></ul>Exponential Smoothing Equations
48. <ul><li>During the past 8 quarters, the Port of Baltimore has unloaded large quantities of grain. ( = .10 ). The first quarter forecast was 175. . Quarter Actual </li></ul><ul><li>1 180 2 168 3 159 4 175 5 190 </li></ul><ul><li>6 205 </li></ul><ul><li>7 180 </li></ul><ul><li>8 182 </li></ul><ul><li>9 ? </li></ul>Exponential Smoothing Example Find the forecast for the 9 th quarter.
49. Exponential Smoothing Solution F t = F t -1 + 0.1( A t -1 - F t -1 ) Quarter Actual Forecast, F t ( α = .10 ) 1 180 175.00 (Given) 2 168 3 159 4 175 5 190 6 205 175.00 +
50. Exponential Smoothing Solution Quarter Actual Forecast, F t ( α = .10 ) 1 180 175.00 (Given) 2 168 175.00 + .10 ( 3 159 4 175 5 190 6 205 F t = F t -1 + 0.1( A t -1 - F t -1 )
51. Exponential Smoothing Solution Quarter Actual Forecast, F t ( α = .10 ) 1 180 175.00 (Given) 2 168 175.00 + .10 (180 - 3 159 4 175 5 190 6 205 F t = F t -1 + 0.1( A t -1 - F t -1 )
52. Exponential Smoothing Solution Quarter Actual Forecast, F t ( α = .10 ) 1 180 175.00 (Given) 2 168 175.00 + .10 (180 - 175.00 ) 3 159 4 175 5 190 6 205 F t = F t -1 + 0.1( A t -1 - F t -1 )
53. Exponential Smoothing Solution Quarter Actual Forecast, F t ( α = .10 ) 1 180 175.00 (Given) 2 168 175.00 + .10 (180 - 175.00 ) = 175.50 3 159 4 175 5 190 6 205 F t = F t -1 + 0.1( A t -1 - F t -1 )
54. Exponential Smoothing Solution F t = F t -1 + 0.1( A t -1 - F t -1 ) Quarter Actual Forecast, F t ( α = .10 ) 1 180 175.00 (Given) 2 168 175.00 + .10(180 - 175.00) = 175.50 3 159 175.50 + .10 (168 - 175.50 ) = 174.75 4 175 5 190 6 205
55. Exponential Smoothing Solution F t = F t -1 + 0.1( A t -1 - F t -1 ) Quarter Actual Forecast, F t ( α = .10 ) 1995 180 175.00 (Given) 1996 168 175.00 + .10(180 - 175.00) = 175.50 1997 159 175.50 + .10(168 - 175.50) = 174.75 1998 175 1999 190 2000 205 174.75 + .10 (159 - 174.75 ) = 173.18
56. Exponential Smoothing Solution F t = F t -1 + 0.1( A t -1 - F t -1 ) Quarter Actual Forecast, F t ( α = .10 ) 1 180 175.00 (Given) 2 168 175.00 + .10(180 - 175.00) = 175.50 3 159 175.50 + .10(168 - 175.50) = 174.75 4 175 174.75 + .10(159 - 174.75) = 173.18 5 190 173.18 + .10 (175 - 173.18 ) = 173.36 6 205
57. Exponential Smoothing Solution F t = F t -1 + 0.1( A t -1 - F t -1 ) Quarter Actual Forecast, F t ( α = .10 ) 1 180 175.00 (Given) 2 168 175.00 + .10(180 - 175.00) = 175.50 3 159 175.50 + .10(168 - 175.50) = 174.75 4 175 174.75 + .10(159 - 174.75) = 173.18 5 190 173.18 + .10(175 - 173.18) = 173.36 6 205 173.36 + .10 (190 - 173.36 ) = 175.02
58. Exponential Smoothing Solution F t = F t -1 + 0.1( A t -1 - F t -1 ) Time Actual Forecast, F t ( α = .10 ) 4 175 174.75 + .10(159 - 174.75) = 173.18 5 190 173.18 + .10(175 - 173.18) = 173.36 6 205 173.36 + .10(190 - 173.36) = 175.02 7 180 8 175.02 + .10 (205 - 175.02 ) = 178.02 9
59. Exponential Smoothing Solution F t = F t -1 + 0.1( A t -1 - F t -1 ) Time Actual Forecast, F t ( α = .10 ) 4 175 174.75 + .10(159 - 174.75) = 173.18 5 190 173.18 + .10(175 - 173.18) = 173.36 6 205 173.36 + .10(190 - 173.36) = 175.02 7 180 8 175.02 + .10(205 - 175.02) = 178.02 9 178.22 + .10 (182 - 178.22) = 178.58 182 178.02 + .10(180 - 178.02) = 178.22 ?
60. Forecast Effects of Smoothing Constant F t = A t - 1 + (1- ) A t - 2 + (1- ) 2 A t - 3 + ... 10% Weights Prior Period 2 periods ago (1 - ) 3 periods ago (1 - ) 2 = = 0.10 = 0.90
61. Forecast Effects of Smoothing Constant F t = A t - 1 + (1- ) A t - 2 + (1- ) 2 A t - 3 + ... 10% 9% Weights Prior Period 2 periods ago (1 - ) 3 periods ago (1 - ) 2 = = 0.10 = 0.90
62. Forecast Effects of Smoothing Constant F t = A t - 1 + (1- ) A t - 2 + (1- ) 2 A t - 3 + ... 10% 9% 8.1% Weights Prior Period 2 periods ago (1 - ) 3 periods ago (1 - ) 2 = = 0.10 = 0.90
63. Forecast Effects of Smoothing Constant F t = A t - 1 + (1- ) A t - 2 + (1- ) 2 A t - 3 + ... 10% 9% 8.1% 90% Weights Prior Period 2 periods ago (1 - ) 3 periods ago (1 - ) 2 = = 0.10 = 0.90
64. Forecast Effects of Smoothing Constant F t = A t - 1 + (1- ) A t - 2 + (1- ) 2 A t - 3 + ... 10% 9% 8.1% 90% 9% Weights Prior Period 2 periods ago (1 - ) 3 periods ago (1 - ) 2 = = 0.10 = 0.90
65. Forecast Effects of Smoothing Constant F t = A t - 1 + (1- ) A t - 2 + (1- ) 2 A t - 3 + ... 10% 9% 8.1% 90% 9% 0.9% Weights Prior Period 2 periods ago (1 - ) 3 periods ago (1 - ) 2 = = 0.10 = 0.90
66. Impact of
67. Choosing Seek to minimize the Mean Absolute Deviation (MAD) If: Forecast error = demand - forecast Then:
68. Exponential Smoothing with Trend Adjustment Forecast including trend (FIT t ) = exponentially smoothed forecast (F t ) + exponentially smoothed trend (T t )
69. Exponential Smoothing with Trend Adjustment - continued F t = Last period’s forecast + (Last period’s actual – Last period’s forecast) F t = F t-1 + (A t-1 – F t-1 ) or T t = (Forecast this period - Forecast last period) + (1- )(Trend estimate last period T t = (F t - F t-1 ) + (1- )T t-1 or
70. <ul><li>F t = exponentially smoothed forecast of the data series in period t </li></ul><ul><li>T t = exponentially smoothed trend in period t </li></ul><ul><li>A t = actual demand in period t </li></ul><ul><li> = smoothing constant for the average </li></ul><ul><li> = smoothing constant for the trend </li></ul>Exponential Smoothing with Trend Adjustment - continued
71. Comparing Actual and Forecasts
72. Regression
73. Least Squares Deviation Deviation Deviation Deviation Deviation Deviation Deviation Time Values of Dependent Variable Actual observation Point on regression line
74. Actual and the Least Squares Line
75. <ul><li>Used for forecasting linear trend line </li></ul><ul><li>Assumes relationship between response variable, Y, and time, X, is a linear function </li></ul><ul><li>Estimated by least squares method </li></ul><ul><ul><li>Minimizes sum of squared errors </li></ul></ul>Linear Trend Projection i Y a bX i
76. Linear Trend Projection Model b > 0 b < 0 a a Y Time, X
77. Scatter Diagram
78. Least Squares Equations Equation: Slope: Y-Intercept:
79. Computation Table X i Y i X i 2 Y i 2 X i Y i X 1 Y 1 X 1 2 Y 1 2 X 1 Y 1 X 2 Y 2 X 2 2 Y 2 2 X 2 Y 2 : : : : : X n Y n X n 2 Y n 2 X n Y n Σ X i Σ Y i Σ X i 2 Σ Y i 2 Σ X i Y i
80. Using a Trend Line <ul><li>Year Demand </li></ul><ul><li>1997 74 </li></ul><ul><li>1998 79 </li></ul><ul><li>1999 80 </li></ul><ul><li>2000 90 </li></ul><ul><li>2001 105 </li></ul><ul><li>2002 142 </li></ul><ul><li>2003 122 </li></ul>The demand for electrical power at N.Y.Edison over the years 1997 – 2003 is given at the left. Find the overall trend.
81. Finding a Trend Line Year Time Period Power Demand x 2 xy 1997 1 74 1 74 1998 2 79 4 158 1999 3 80 9 240 2000 4 90 16 360 2001 5 105 25 525 2002 6 142 36 852 2003 7 122 49 854 x=28 y=692 x 2 =140 xy=3,063
82. The Trend Line Equation
83. Actual and Trend Forecast
84. Monthly Sales of Laptop Computers Sales Demand Average Demand Month 2000 2001 2002 2000-2002 Monthly Seasonal Index Jan 80 85 105 90 94 0.957 Feb 70 85 85 80 94 0.851 Mar 80 93 82 85 94 0.904 Apr 90 95 115 100 94 1.064 May 113 125 131 123 94 1.309 Jun 110 115 120 115 94 1.223 Jul 100 102 113 105 94 1.117 Aug 88 102 110 100 94 1.064 Sept 85 90 95 90 94 0.957 Oct 77 78 85 80 94 0.851 Nov 75 72 83 80 94 0.851 Dec 82 78 80 80 94 0.851
85. Demand for IBM Laptops
86. San Diego Hospital – Inpatient Days
87. Multiplicative Seasonal Model <ul><li>Find average historical demand for each “season” by summing the demand for that season in each year, and dividing by the number of years for which you have data. </li></ul><ul><li>Compute the average demand over all seasons by dividing the total average annual demand by the number of seasons. </li></ul><ul><li>Compute a seasonal index by dividing that season’s historical demand (from step 1) by the average demand over all seasons. </li></ul><ul><li>Estimate next year’s total demand </li></ul><ul><li>Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season. This provides the seasonal forecast . </li></ul>
88. <ul><li>Shows linear relationship between dependent & explanatory variables </li></ul><ul><ul><li>Example: Sales & advertising ( not time) </li></ul></ul>Linear Regression Model Y X i i = a b Dependent (response) variable Independent (explanatory) variable Slope Y-intercept ^ +
89. Linear Regression Model Y X Y a i ^ i i b X i = + + Error Error Observed value Y a b X = + Regression line
90. Linear Regression Equations Equation: Slope: Y-Intercept:
91. Computation Table X i Y i X i 2 Y i 2 X i Y i X 1 Y 1 X 1 2 Y 1 2 X 1 Y 1 X 2 Y 2 X 2 2 Y 2 2 X 2 Y 2 : : : : : X n Y n X n 2 Y n 2 X n Y n Σ X i Σ Y i Σ X i 2 Σ Y i 2 Σ X i Y i
92. <ul><li>Slope ( b ) </li></ul><ul><ul><li>Estimated Y changes by b for each 1 unit increase in X </li></ul></ul><ul><ul><ul><li>If b = 2, then sales ( Y ) is expected to increase by 2 for each 1 unit increase in advertising ( X ) </li></ul></ul></ul><ul><li>Y-intercept ( a ) </li></ul><ul><ul><li>Average value of Y when X = 0 </li></ul></ul><ul><ul><ul><li>If a = 4, then average sales ( Y ) is expected to be 4 when advertising ( X ) is 0 </li></ul></ul></ul>Interpretation of Coefficients
93. <ul><li>Variation of actual Y from predicted Y </li></ul><ul><li>Measured by standard error of estimate </li></ul><ul><ul><li>Sample standard deviation of errors </li></ul></ul><ul><ul><li>Denoted S Y,X </li></ul></ul><ul><li>Affects several factors </li></ul><ul><ul><li>Parameter significance </li></ul></ul><ul><ul><li>Prediction accuracy </li></ul></ul>Random Error Variation
94. Least Squares Assumptions <ul><li>Relationship is assumed to be linear. Plot the data first - if curve appears to be present, use curvilinear analysis. </li></ul><ul><li>Relationship is assumed to hold only within or slightly outside data range. Do not attempt to predict time periods far beyond the range of the data base. </li></ul><ul><li>Deviations around least squares line are assumed to be random. </li></ul>
95. Standard Error of the Estimate
96. <ul><li>Answers: ‘ how strong is the linear relationship between the variables?’ </li></ul><ul><li>Coefficient of correlation Sample correlation coefficient denoted r </li></ul><ul><ul><li>Values range from -1 to + 1 </li></ul></ul><ul><ul><li>Measures degree of association </li></ul></ul><ul><li>Used mainly for understanding </li></ul>Correlation
97. Sample Coefficient of Correlation
98. Coefficient of Correlation Values -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
99. Coefficient of Correlation and Regression Model r 2 = square of correlation coefficient (r), is the percent of the variation in y that is explained by the regression equation r = 1 r = -1 r = .89 r = 0 Y X Y i = a + b X i ^ Y X Y X Y X Y i = a + b X i ^ Y i = a + b X i ^ Y i = a + b X i ^
100. <ul><li>You want to achieve: </li></ul><ul><ul><li>No pattern or direction in forecast error </li></ul></ul><ul><ul><ul><li>Error = ( Y i - Y i ) = (Actual - Forecast) </li></ul></ul></ul><ul><ul><ul><li>Seen in plots of errors over time </li></ul></ul></ul><ul><ul><li>Smallest forecast error </li></ul></ul><ul><ul><ul><li>Mean square error (MSE) </li></ul></ul></ul><ul><ul><ul><li>Mean absolute deviation (MAD) </li></ul></ul></ul>Guidelines for Selecting Forecasting Model ^
101. Pattern of Forecast Error Time (Years) Error 0 Desired Pattern Time (Years) Error 0 Trend Not Fully Accounted for
103. <ul><li>You’re a marketing analyst for Hasbro Toys. You’ve forecast sales with a linear model & exponential smoothing. Which model do you use? </li></ul><ul><li>Actual Linear Model Exponential </li></ul><ul><li>Smoothing Year Sales Forecast Forecast (.9) </li></ul><ul><li>1998 1 0.6 1.0 1999 1 1.3 1.0 2000 2 2.0 1.9 2001 2 2.7 2.0 2002 4 3.4 3.8 </li></ul>Selecting Forecasting Model Example
104. Linear Model Evaluation MSE = Σ Error 2 / n = 1.10 / 5 = 0.220 MAD = Σ |Error| / n = 2.0 / 5 = 0.400 MAPE = 100 Σ | absolute percent errors|/ n = 1.20 /5 = 0.240 Y i 1 1 2 2 4 ^ Y i ^ 0.6 1.3 2.0 2.7 3.4 Year 1998 1999 2000 2001 2002 Total 0.4 -0.3 0.0 -0.7 0.6 0.0 Error 0.16 0.09 0.00 0.49 0.36 1.10 Error 2 0.4 0.3 0.0 0.7 0.6 2.0 |Error| |Error| Actual 0.40 0.30 0.00 0.35 0.15 1.20
105. Exponential Smoothing Model Evaluation MSE = Σ Error 2 / n = 0.05 / 5 = 0.01 MAD = Σ |Error| / n = 0.3 / 5 = 0.06 MAPE = 100 Σ |Absolute percent errors|/ n = 0.10 /5 = 0.02 Year 1998 1999 2000 2001 2002 Total Y i 1 1 2 2 4 Y i 1.0 0.0 1.0 0.0 1.9 0.1 2.0 0.0 3.8 0.2 0.3 ^ Error 0.00 0.00 0.01 0.00 0.04 0.05 0.3 Error 2 0.0 0.0 0.1 0.0 0.2 |Error| |Error| Actual 0.00 0.00 0.05 0.00 0.05 0.10
107. <ul><li>Measures how well the forecast is predicting actual values </li></ul><ul><li>Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD) </li></ul><ul><ul><li>Good tracking signal has low values </li></ul></ul><ul><li>Should be within upper and lower control limits </li></ul>Tracking Signal
122. Plot of a Tracking Signal Time Lower control limit Upper control limit Signal exceeded limit Tracking signal Acceptable range MAD + 0 -
123. Tracking Signals Tracking Signal Forecast Actual demand
124. Forecasting in the Service Sector <ul><li>Presents unusual challenges </li></ul><ul><ul><li>special need for short term records </li></ul></ul><ul><ul><li>needs differ greatly as function of industry and product </li></ul></ul><ul><ul><li>issues of holidays and calendar </li></ul></ul><ul><ul><li>unusual events </li></ul></ul>
125. Forecast of Sales by Hour for Fast Food Restaurant 11-12 12-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11