抄録
In this paper, a variant of the basis factorization methods is developed for solving a multi-stage linear programming, in which the output of one stage is an input to the next stage. The method is devised to use the special staircase structure of the original basis. In this method, a set ofelementary column operations transforms the original basis into a staircase matrix which significantly reduces computational efforts for matrix inversion.
It is shown that the original basis can be obtained by a pivot among the several columns. Based on this fact, a new algorithm is proposed where the relative cost factor of the original non-basis is easily obtained by memorizing the column vectors corresponding to the variables which are included in the original basis but not in the working ones.
The algorithm has been coded by FORTRAN and applied to an in-plant energy control system. The results prove that the method is practical and superior to a conventional simplex method (MPS-II) in terms of computational time and storage.
