Recommended
More Related Content
Similar to McGraw-HillIrwinCopyright © 2008 by The McGraw-Hill Compa
Similar to McGraw-HillIrwinCopyright © 2008 by The McGraw-Hill Compa (20)
More from VannaSchrader3
More from VannaSchrader3 (20)
Recently uploaded
Recently uploaded (20)
McGraw-HillIrwinCopyright © 2008 by The McGraw-Hill Compa
- 1. McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 7 Introduction to Forecasting 7-* ForecastingPlays an important role in many industries marketing financial planning production controlForecasts are not to be thought of as a final product but as a tool in making a managerial decision 7-* ForecastingForecasts can be obtained qualitatively or quantitativelyQualitative forecasts are usually the result of an expert’s opinion and is referred to as a judgmental techniqueQuantitative forecasts are usually the result of conventional statistical analysis 7-* Forecasting ComponentsTime Frame long term forecasts short term forecastsExistence of patterns
- 2. seasonal trends peak periodsNumber of variables 7-* Patterns in ForecastsTrend A gradual long-term up or down movement of demand Demand Time Upward Trend 7-* Patterns in ForecastsCycle An up and down repetitive movement in demand Demand Time Cyclical Movement 7-* Quantitative TechniquesTwo widely used techniques Time series analysis Linear regression analysisTime series analysis studies the numerical values a variable takes over a period of timeLinear regression analysis expresses the forecast variable as a mathematical function of other variables 7-* Time Series AnalysisLatest Period MethodMoving AveragesExample ProblemWeighted Moving
- 3. AveragesExponential SmoothingExample Problem 7-* Latest Period MethodSimplest method of forecastingUse demand for current period to predict demand in the next periode.g., 100 units this week, forecast 100 units next weekIf demand turned out to be only 90 units then the following weeks forecast will be 90 7-* Moving AveragesUses several values from the recent past to develop a forecastTends to dampen or smooth out the random increases and decreases of a latest period forecastGood for stable demand with no pronounced behavioral patterns 7-* Moving AveragesMoving averages are computed for specific periods Three months Five months The longer the moving average the smoother the forecastMoving average formula 7-* Moving Averages - NASDAQ
- 4. 7-* Weighted MAAllows certain demands to be more or less important than a regular MAPlaces relative weights on each of the period demandsWeighted MA is computed as such 7-* Weighted MAAny desired weights can be assigned, but SWi=1Weighting recent demands higher allows the WMA to respond more quickly to demand changesThe simple MA is a special case of the WMA with all weights equal, Wi=1/nThe entire demand history is carried forward with each new computationHowever, the equation can become burdensome 7-* Exponential SmoothingBased on the idea that a new average can be computed from an old average and the most recent observed demande.g., old average = 20, new demand = 24, then the new average will lie between 20 and 24Formally, 7-* Exponential SmoothingNote: a must lie between 0.0 and 1.0Larger values of a allow the forecast to be more responsive to recent demandSmaller values of a allow the forecast to respond more slowly and weights older data more0.1 < a < 0.3 is usually recommended
- 5. 7-* Exponential SmoothingThe exponential smoothing form Rearranged, this form is as such This form indicates the new forecast is the old forecast plus a proportion of the error between the observed demand and the old forecast 7-* Why Exponential Smoothing?Continue with expansion of last expressionAs t>>0, we see (1-a)t appear and <<1The demand weights decrease exponentiallyAll weights still add up to 1Exponential smoothing is also a special form of the weighted MA, with the weights decreasing exponentially over time 7-* Forecasting with SeasonalityCalculate the average demand per season e.g.: average quarterly demandCalculate a seasonal index for each season of each year: Divide the actual demand of each season by the average demand per season for that yearAverage the indexes by season e.g.: take the average of all Spring indexes, then of all Summer indexes, ... 7-* Forecasting with SeasonalityForecast demand for the next year
- 6. & divide by the number of seasons Use regular forecasting method & divide by four for average quarterly demandMultiply next year’s average seasonal demand by each average seasonal index Result is a forecast of demand for each season of next year 7-* Forecast ErrorError Cumulative Sum of Forecast Error Mean Square Error 7-* Forecast ErrorMean Absolute Error Mean Absolute Percentage Error 7-* CFEReferred to as the bias of the forecastIdeally, the bias of a forecast would be zeroPositive errors would balance with the negative errorsHowever, sometimes forecasts are always low or always high (underestimate/overestimate) 7-* MSE and MADMeasurements of the variance in the
- 7. forecastBoth are widely used in forecastingEase of use and understandingMSE tends to be used more and may be more familiarLink to variance and SD in statistics 7-* MAPENormalizes the error calculations by computing percent errorAllows comparison of forecasts errors for different time series dataMAPE gives forecasters an accurate method of comparing errorsMagnitude of data set is negated MA n = D i n å i = 1 to n , n =# of periods in MA, D i =
- 9. = 1 and i = 1 to n å F t = a D t - 1 + ( 1 - a ) F t - 1 F t = a D t - 1 + (
- 12. å | n for t = 1 to n MAPE = | e t å | D t å for t = 1 to n McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All
- 13. rights reserved. Chapter 3 Probability and Statistics A Foundation for Becoming a More Effective and Efficient Problem Solver 3-* Normal DistributionCommon probability distributione.g., height, weight, age, sum of two dice rolled 1,000 times, etc. 3-* Normal Distribution Sheet: Chart1 Sheet: Sheet1 Sheet: Sheet2 Sheet: Sheet3 Sheet: Sheet4 Sheet: Sheet5 Sheet: Sheet6 Sheet: Sheet7 Sheet: Sheet8 Sheet: Sheet9 Sheet: Sheet10 Sheet: Sheet11 Sheet: Sheet12 Sheet: Sheet13 Sheet: Sheet14 Sheet: Sheet15 Sheet: Sheet16
- 23. 3-* Mean and Standard DeviationMost common statistics usedMean or expected value E(x) = SxiP(xi) Standard deviation s(x) = [S [xi - E(x)]2P(xi)]0.5 s(x) = [S [xi - m]2/n-1]0.5 3-* Z-ScoresStandard Z-scoreMeasures the number of standard deviations away from the meanCalculated as such: Look up Z value in table to find probability Normal Distribution 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 1 2 3 4
- 24. 5 6 7 8 x P(x) Normal Distribution 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 1 2 3 4 5 6 7 8 x P(x) mean = 4, std. dev. = 1 -1 std. dev. +1 std. dev. 68% of values m = x