Drake winters example with supplement

Drake winters example with supplement - ISyE 3103 Supply...

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ISyE 3103 Supply Chain Modeling: Transportation and Logistics Spring 2006 Winters’ Method Forecasting Example A scatterplot of the following actual demand data suggests the existence of seasonal (quar- terly) variation coupled with an overall increasing trend; consequently, this data is a strong candidate for utilizing Winters’ Method (aka Triple Exponential Smoothing). 2003 2004 2005 Quarter 1 146 192 272 Quarter 2 96 127 155 Quarter 3 59 79 98 Quarter 4 133 186 219 In this note we will fit a Winters model to this data set, compute the a posteriori forecast errors for 2003-2005, and provide a demand forecast for 2006. The smoothing constants are α = 0 . 2, β = 0 . 1, and γ = 0 . 05. Recall that the underlying demand process assumed for the Winters model is D t = ( a + bt ) I t + ² t . In order to initialize the model, we need estimates, ˆ a 0 , ˆ b 0 , and ˆ I - 3 , ˆ I - 2 , ˆ I - 1 , ˆ I 0 . The method we will use to obtain these estimates is very approximate. This is in contrast to the method we used to obtain the initial trend estimates in the Holt model—regression on a subset of the data. If we wanted to utilize a similar methodology for the Winters model, it would be unnecessarily complicated. The implication of using this approximation method of obtaining the initial estimates is that we will still denote time period 1 at the beginning of 2003. (In the Holt model we “threw

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