PROJECT ON: QUANTITATIVE TECHNIQUES OF FORECASTING DEMAND
DEMAND FORECASTING • Demand forecasting is a scientific and analytical estimation of demand for a product (service) for a particular period of time. • It is the process of determining how much of what products is needed when and where. • “An estimate of sales in dollars or physical units for a specified future period under a proposed marketing plan.” – American Marketing Association • It is used for planning and decision making in operations research. Categorization of Demand ForecastingBy nature of goods • Capital Goods: Derived demand o Demand for capital goods depends upon demand of consumer goods which they can produce. • Consumer Goods: Direct demand o durable consumer goods: new demand or replacement demand o Non-durable consumer goods: FMCG
By Time Period • Short Term (0 to 3 months): for inventory management and scheduling. • Medium Term (3 months to 2 years): for production planning, purchasing, and distribution. • Long Term (2 years and more): may extend up to 10 to 20 years. o For capacity planning, facility location, and strategic planning, long term capital requirement, and investment decisions. HOW TO CHOOSE A DEMAND FORECASTING TECHNIQUEConsider the following factors affecting demand: o Imminent objectives of forecast, whether it is for a new product, or to gauge impact of a new advertisement, etc. o Cost involved, cost of forecasting should not be more than its benefits, and here opportunity cost of resources will also be important.
o Time perspective, whether the forecast is meant for the short run or the long run o Complexity of the technique, vis-à-vis availability of expertise; this would determine whether the firm would look for experts “in house” or outsource it o Nature and quality of available data, i.e. does the time series show a clear trend or is it highly unstable. Quantitative Methods of Demand Forecasting Trend Projection This statistical tool is used to predict future values of avariable on the basis of time series data. • Time series data are composed of: o Secular trend (T): change occurring consistently over a long time and is relatively smooth in its path. o Seasonal trend (S): seasonal variations of the data within a year
o Cyclical trend (C): cyclical movement in the demand for a product that may have a tendency to recur in a few years o Random events (R): have no trend of occurrence hence they create random variation in the series. Additive Form: Y = T + S + C + R………..(1) Multiplicative Form: Y = T.S.C.R………….(2) Log Y= log T + log S + log C + log R………….(3)Methods of Trend Projection• Graphical method o Past values of the variable on vertical axis and time on horizontal axis and line are plotted. o Movement of the series is assessed and future values of the variable are forecasted. o simple but provides a general indication and fails to predict future value of demand
Least squares method• Based on the minimization of squared deviations between the best fitting line and the original observations given.• Estimates coefficients of a linear function.• Y=a+bX where a =intercept• and b =slope• The normal equations:• ΣY=na + bΣX• ΣXY= aΣX+ bΣX2• Once the coefficients of the trend equation are estimated, we can easily project the trend for future periods.• Solving the normal equations: (Y Y )( X X)A= (X X )2 Y bX
QUANTITATIVE METHODSOF TREND PROJECTIONARIMA method: also known as Box Jenkins method • It is considered to be the most sophisticated technique of forecasting as it combines moving average and auto regressive techniques. o Stage One: trend in the series is removed with help of „differencing‟, i.e. the difference between values at adjacent period of time. o Stage Two: Various possible combinations are created on basis of: i. order of involvement ofauto regressive terms;ii. the order of moving average termsiii. the number of differences of the original series.Combinations are selected which provide an adequate fit tothe series. o Stage Three: Parameter estimation is done using Least Squares.
o Stage Four: „Goodness of fit‟ is tested and if it is not a good fit then the whole process is repeated from Stage Two. o Stage Five: Once a „good fit‟ is attained, its coefficients can be used to forecast future demand. Quantitative Methods • Simple (or Bivariate) Regression Analysis: o deals with a single independent variable that determines the value of a dependent variable. o Demand Function: D = a+bP, where b is negative. o If we assume there is a linear relation between D and P, there may also be some random variation in this relation.Sum of Squared Errors (SSE): a measure of the predictiveaccuracySmaller the value of SSE, the more accurate is theregression equation. • Nonlinear Regression Analysis o Log linear function log D =A + B log P + e
where A and B are the parameters to be estimated and erepresents errors or disturbances.Linear form of log linear function D* = a + b P* + e WhereD*= log D and P*=log P o Multiple Regression Analysis: D = a1+a2.P+a3.A+e (Where A = advertising expenditure incurred). D^ = a^1 + a^2P + a^3A, (where a1, a2 and a3 are the parameters and e is the random error term (or disturbance), having zero mean).Similar to simple regression analysis, multiple regressionanalysis would aim at estimation of the parameters a1, a2and a3. o Choose such values of the coefficients that would minimize the sum of squares of the deviations. Problems Associated with Regression Analysis • Multicollinearity: when two or more explanatory variables in the regression model are found to be
highly correlated the estimated coefficients may not be accurately determined.• Heteroscedasticity: Classical regression models assume that the variance of error terms is constant for all values of the independent variables in the model; i.e. variables are homoscedastic.• Specification errors: Omission of one or more of the independent variables, or when the functional form itself is wrongly constructed or estimates a demand function in linear form, though the function should have been nonlinear.• Identification problem: where the equations have common variables, like a demand supply model.