Computing Optimal Weights by Linear Programming Model

7 Computing Optimal Weights by Linear Programming Model 

To determine the best weights for the weighted moving average method, a linear programming (LP) model can be used. The objective of fhe LP model is to find fhe opfimal weighfs fhaf minimize the forecast error. Let denote the forecast error in period t. Then, e, is given by 

Note that g( can be positive or negative. Define the total forecast error as 

In fact, Z/n is called the mean absolute deviation (MAD) in forecasting and is used as a key measure of forecast error in validating the forecasting method (refer to Section 2.9). For the LP model, the unrestricted variable g( will be replaced by the difference of two non-negative variables as follows  

Since at most one of the non-negative variables, et or ef, can be positive in the LP optimal solution, we can write ed as 

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