Modelling GM(1,1) under the Criterion of the Minimization of Mean Absolute Percentage Error

In this paper, we present two methods to estimate the parameters of the GM (1,1)model under. The criterion of the minimization of mean absolute percentage error (MAPE) (some authors called Average relative error).A linear programming method is used to optimize the whiting value of grey derivative of GM(1,1),four published articles are chosen for practical tests of this method, the results show that this method can obviously improve the simulation accuracy. Another method is that the problem of estimation parameters of GM(1,1) model is transformed into the minimax optimization problem, then use the library function fminimax in MATLAB to solve the minimax optimization problem, the same four published articles are chosen for practical tests of this modelling method, as shown in these results, this method can obtain the local optimal parameters, yield the lower MAPE than the existing method. But it is sensitive for the initial approximation and requires a good initial approximation, the results of compared with different initial approximations show that the parameters which are obtained by the former method is the better initial approximation.