November 04, 2011

Roberto benit de souça

AGENDA

QUESTION 1……………………………………………………………………………………………………………..3

QUESTION 2……………………………………………………………………………………………………………..5

QUESTION 2.1………………………………………………………………………………………...……5 QUESTION 2.2………………………………………………………………………………………...……7 QUESTION 2.3………………………………………………………………………………………...……7

QUESTION 3……………………………………………………………………………………………………………..9

ANEXO 1…..……………………………………………………………………………………………………………..14

QUESTION 1

Consider monthly demand for the SONY LAPTOP as shown in Table 1. Forecast the monthly demand for year 6 using the static method, moving average, simple exponential smoothing, Holt's model and winter’s model for forecasting. In each case, evaluate the bias, TS, MAD, MAPE and MSE. Comment on the quality of the each forecast and which forecasting methods do you prefer? Why?

Moving Average

When we talk about the simple moving average method, is appropriate when there is neither trend nor seasonality in the demand pattern. The problem with the method is that N periods of historical data must be stored for each sku and that equals weight is given to N most recent pieces of historical data with no weight to data prior to that.

So talking about our case we have 12 period months, so to the forecast we have divided the previous demand of 12 months between 12 numbers of periods. As we see in the excel the last year, that is 2011, have the same values in each month because we haven’t got yet the demand that correspond with the period for year 6.

Simple exponential smoothing

This is probably the most widely used forecasting model for short term forecasting. The model is useful when the demand pattern equals the level and unpredictable noise, that is there should be no seasonality or trend in the demand pattern.

Having a look on what we have done for this model in the assignment, we have the smoothing constant =0,6. The first forecast value of January 2006 we got it from doing the mean of the last K observations. So to do the forecast we use the following equation:

Forecast smothing= * Dp-1+(1-)*Fp-1;

Where:

Dp-1= Before period demand

Fp-1= Before period forecast smoothing

We couldn’t get the forecast for year 6.

Holts model

This model is appropriate when the demand is assumed to have a level and trend in the systematic component of demand nut no seasonality. So to update the procedure we have to find out how to estimate the level and the trend. So holts suggest a procedure that is natural extensions of simple exponential smoothing.

* at=αHWxt+1-αHWat-1+bt-1 and

* bt=βHWxtat-at-1+1-βHWbt-1

Where αHW and βHW are smoothing constants, and at-at-1 is an estimate of the actual trend in period t. For getting the” old trend” and the “old level” we did a regression where parameter y= whole demand and the parameter x= whole period (1-60) thus excel give us a table. In this table we found both value; level= y (12001,41243) and trend= x (280,0083356).

Winters model

This model is used if a level trend and seasonality is present.

In the work that we have done the three constants are α = 0.0004 ; β =0.932 and γ =0. For this model we have to follow some step for getting forecast: - At first we found the deseanosalized value.

- we found the value of “old trend” and “old level” by the same way that in the holt´s model although, in this model we have used the Deseanosalized demand instead of demand. - And alter we found deseasonal demand all period, seasonal factor and seasonal factor all period.

Errors

In the measures of forecast error we have 3 measures variability:

1) The mean square errors, MSE

2) The mean absolute deviation, MAD

3) The mean absolute percentage error, MAPE

The MSE measures the difference between the estimate and the true value of the quality being estimated. Measures the average square of the error. The error is the amount by which the estimate...