0. The Context for MPC

3. Forecasting

Homework problems: 2,4,5,6,7,11,12,14.

3.1. Providing Appropriate Forecast InformationThe forecasting process involves much more than just the estimation of future demand. The forecast also needs to take into consideration the intended use of the forecast, the methodology for aggregating and disaggregating the forecast, and assumptions about future conditions.Selection of an appropriate forecast method is determined by different levels of aggregation, cost of data acquisition and processing, length of forecast (timeframe), top management involvement, forecast frequency, etc.

Figure 3.1

3.1. Forecast InformationThe forecast information and technique must match the intended application:For strategic decisions such as capacity or market expansion highly aggregated estimates of general trends are necessary.Sales and operations planning (SOP) activities require more detailed forecasts in terms of product families and time periods.Master production scheduling (MPS) and control demand highly detailed forecasts, which only need to cover a short period of time.

3.1.1 Forecasting for Strategic Business PlanningForecast is presented in general terms (sales dollars, tons, hours)Aggregation level may be related to broad indicators (gross national product (GNP), income)Causal models and regression/correlation analysis are typical toolsManagerial insight is critical and top management involvement is intenseForecast is generally prepared annually and covers a period of years

3.1.2 Forecasting for Sales and Operations PlanningForecast is presented in aggregate measures (dollars, units)Aggregation level is related to product families (common family measurement)Forecast is typically generated by summing forecasts for individual products.Managerial involvement is moderate, and limited to adjustment of aggregate valuesForecast is generally prepared several times each year and covers a period of several months to a year.

3.1.3 Forecasting for MPS and ControlForecast is presented in terms of individual products (units, not dollars)Forecast is typically generated by mathematical procedures, often using softwareProjection techniques are commonAssumption is that the past is a valid predictor of the futureManagerial involvement is minimal.Forecast is updated almost constantly and covers a period of days or weeks.

3.2. Regression Analysis & DecompositionRegression identifies a relationship between two or more correlated variables.Linear regression is a special case where the relationship is defined by a straight line, used for both time series and causal forecasting.Data should be plotted to see if they appear linear before using linear regression.Y = a + bXY is value of dependent variable, a is the y-intercept of the line, b is the slope, and X is the value of the independent variable.

3.2 Least Squares MethodObjectivefind the line that minimizes the sum of the squares of the vertical distance between each data point and the lineY calculated dependent variable value

yi actual dependent variable point

a y intercept

b slope of the line

x time periodY = a + bx

See Fig. 3.2

Least Squares Regression Line (Fig.3.2)

Regression errors are the vertical distance from the point to the line

Least Squares Equation (3.3)

Or

Least Squares Example (Fig. 3.3)Quarter (x)Sales (y)xyx2y2Y16006001360,000801.321,5503,10042,402,5001,160.931,5004,50092,250,0001,520.541,5006,000162,250,0001,880.152,40012,000255,760,0002,239.763,10018,600369,610,0002,599.472,60018,200496,760,0002,959.082,90023,200648,410,0003,318.693,80034,2008114,440,0003,678.2104,50045,00010020,250,0004,037.8114,00044,00012116,000,0004,397.4124,90058,80014424,010,0004,757.1Sum7833,350268,200650112,502,500

Least Squares Example (Fig. 3.2)

Least Squares ExampleQuarterCalculationForecast13Y13=441.6+359.6(13)5,119.414Y14=441.6+359.6(14)5,476.015Y15=441.6+359.6(15)5,835.616Y16=441.6+359.6(16)6,195.2

Standard Error of Estimate (Syx) how well the line fits the data

=363.9

Regression Using Excel

Time Series Decomposition

SeasonalitySeasonality may or may not be relative to the general demand trendAdditive seasonal variation is constant regardless of changes in average demandMultiplicative seasonal variation maintains a consistent relationship to the average demand (this is the more common case)

SeasonalityAdditive seasonal variation is constant regardless of changes in average demand

Forecast=Trend + Seasonal

Multiplicative seasonal variation maintains a consistent relationship to the average demand (this is the more common case)

Forecast= Trend x Seasonal factors

Seasonal Factor/IndexTo account for seasonality within the forecast, the seasonal factor/index is calculated.The amount of correction needed in a time series to adjust for the season of the yearSeasonPast SalesAverage Sales for Each SeasonSeasonal FactorSpring2001000/4=250Actual/Average=200/250=0.8Summer3501000/4=250350/250=1.4Fall3001000/4=250300/250=1.2Winter1501000/4=250150/250=0.6Total1000

Seasonal Factor/IndexIf we expect (forecast) next years sales to be 1,100 units, the seasonal forecast is calculated using the seasonal factors:SeasonExpectedSalesAverage Sales for Each SeasonSeasonal FactorForecastSpring1100/4=275X0.8=220Summer1100/4=275X1.4=385Fall1100/4=275X1.2=330Winter1100/4=275X0.6=165Total1,100

SeasonalityTrend and Seasonal FactorQuarterAmountI 2008300II 2008200III 2008220IV 2008530I 2009520II 2009420III 2009400IV - 2009700

Trend = 170 +55tEstimate of trend, use linear regression software to obtain more precise results

SeasonalityTrend and Seasonal FactorSeasonal factors are calculated for each season, then averaged for similar seasonsSeasonal Factor = Actual/Trend

SeasonalityTrend and Seasonal FactorForecasts for 2010 are calculated by extending the linear regression and then adjusting by the appropriate seasonal factorFITSForecast Including Trend and Seasonal Factors

Decomposition Using Least Squares RegressionDecompose the time series into its componentsFind seasonal componentDeseasonalize the demandFind trend componentForecast future values for each componentProject trend component into futureMultiply trend component by seasonal component

Decomposition Using Least Squares RegressionPeriodQuarterActual DemandAverage of Same Quarter of Each YearSeasonal Factor1I600(600+2400+3800)/3=2266.72II1,5503III1,5004IV1,5005I2,4006II3,1007III2,6008IV2,9009I3,80010II4,50011III4,00012IV4,900Total33,350

Calculate average of same period values

Decomposition Using Least Squares RegressionPeriodQuarterActual DemandAverage of Same Quarter of Each YearSeasonal Factor1I600(600+2400+3800)/3=2266.7 2266.7/(33350/12)=0.822II1,550(1550+3100+4500)/3=30503III1,500(1500+2600+4000)/3=27004IV1,500(1500+2900+4900)/3=31005I2,4006II3,1007III2,6008IV2,9009I3,80010II4,50011III4,00012IV4,900Total33,350

Calculate seasonal factor for each period

Decomposition Using Least Squares RegressionPeriodDeseasonalized Demand1735.721412.431544.041344.852942.662824.772676.282599.994659.2104100.4114117.3124392.9

SUMMARY OUTPUTRegression StatisticsMultiple R0.929653282R Square0.864255225Adjusted R Square0.850680748Standard Error512.8180268Observations12ANOVAdfSSMSFSignificance FRegression116743469.6416743469.6463.667660591.20464E-05Residual102629823.286262982.3286Total1119373292.92CoefficientsStandard Errort StatP-valueIntercept555.0045455315.61767761.7584710390.109173704Period 342.180069942.883997757.9792017511.20464E-05

Y= 555.0 + 342.2xUse linear regression to fit trend line to deseasonalized data

Create Forecast by Projecting Trend and ReseasonalizingPeriodQuarterY from RegressionSeasonal FactorForecast13I555+342.2*13=5003.5X0.82=4102.8714II555+342.2*14=5345.7X1.10=5880.2715III555+342.2*15=5687.9X0.97=5517.2616IV555+342.2*16=6030.1X1.12=6753.71

Project Linear TrendProject SeasonalityY= 555.0 + 342.2x

3.3. Short-term Forecasting TechniqueSome basic concepts:dependent/independent demandaggregate/disaggregate demandlong-term/short-term forecast (regression and correlation vs. smoothing out the random fluctuations)The underlying assumption of time series models is that the future values of the time series can be predicted based upon previous time series values (i.e., past conditions that produced the historical data wont change !)The need for some forecasting techniques (Fig. 3.11)Whats wrong with drawing a line (i.e., use the regular averaging process)?

3.3. Short-term Forecasting TechniquesMoving Average:Q: what n to use? large or small (longer or shorter)?Q: Drawback of (simple) moving average?

Weighted Moving Average:Example. Use weighted moving average with weights of 0.1, 0.2, and 0.3 to forecast demand for period 33.Sol:

3.3. Short-term Forecasting TechniquesExponential Smoothing Forecasting (ESF):ESFt = ESFt-1 + (actual demand t ESFt-1) .. (3.6)

=(actual demand t ) + (1- ) ESFt-1 .. (3.7)

where:= the proportion of the forecast error, under or over estimate, that will be incorporated into (next) forecast (i.e., smoothing constant).

ESFt-1 = Exp. smoothing forecast made at the end of period t-1 = Exp. smoothing forecast for period t

3.3. Short-term Forecasting TechniquesExponential Smoothing Forecasting (ESF):Q: Why is it called exponential smoothing? Proof

Q: What happens when =0 or =1?Q: what value to use? Small or large and the effects.

3.3. Short-term Forecasting Techniques

Bias = (actual demand i forecast demand i) /n

Bias (mean error) measures consistently high or low forecast

MAD = |actual demand i forecast demand i| /nMSE=MAD (mean absolute deviation) measures the magnitude of forecast error

What is a good (ideal) forecast? Which (Bias or MAD) is more critical?When the forecast errors are normally distributed, the standard deviation of forecast errors = 1.25 MAD

3.3. Some Insights

Focus forecasting: uses the one forecasting model that would have performed the best in the recent past to make the next forecast.Simple models usually outperform more complex methods, especially for short-term forecasting.There is no one model that would consistently outperform all the others.It might be a good idea to average the forecasts from several models used in each period (combination technique).

3.4. Using the ForecastsAggregating Forecasts:

Long-term or product-line forecasts are more accurate than short-term or detailed forecasts. Theorem: Suppose that X and Y are independent random variables with normal distribution N(1 , 12 ) and N(2 , 22 ), respectively. Let Z=X + Y, then Z is a normal distribution N(1+ 2 ,12 +22 ).Application: Figure 3.17

3.4. Using the ForecastsPyramid Forecasting:

To coordinate, integrate, and assure (force) consistency between forecasts prepared in different parts/levels of the organization and company goals or constraints. Figs. 18~20.

Incorporating External Information:

Change the forecast directly, if we know the activities that will influence demand for sure. e.g., promotions, product changes, competitors action, etc.Change the forecast model, if we are not sure of the impact of the activities. e.g., use larger to be more responsive to demand change.