Grey multi-variables GM(1,N/τ,r) model with delay and its application

Based on the complicated and nonlinear grey system of multi-variables, this paper proposes grey multi-variables GM(1,N/^τ,r) model with delay, and discusses parameter space of the model, then analyses the impacts of multiple transformation for parameters of GM(1,N/^τ,r), as well as iteration of this model. Finally we build GM(1,N/^τ,r) on reverse logistics network of scrap steel for forecasting flux of scrap steel at collected point which can be transformed to a optimized problem of the average comparative error about ^τ and ^r, results indicate that the precision of GM(1,N/^τ,r) is superior to GM(1,N). Therefore, GM(1,N/^τ,r) has important academic and practical significance.