Abstract: In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.
Abstract: A DEA model can generally evaluate the performance
using multiple inputs and outputs for the same period. However, it is
hard to avoid the production lead time phenomenon some times, such
as long-term project or marketing activity. A couple of models have
been suggested to capture this time lag issue in the context of DEA.
This paper develops a dual-MPO model to deal with time lag effect in
evaluating efficiency. A numerical example is also given to show that
the proposed model can be used to get efficiency and reference set of
inefficient DMUs and to obtain projected target value of input
attributes for inefficient DMUs to be efficient.