Restricted vertex generation applied as a CRASHing procedure for linear programming

The dual of Fourier-Motzkin elimination is described and illustrated by a numerical example. It is pointed out that the method can generate an enormous number of columns rendering it impractical. If carried to completion all extreme solutions of the original model are generated. By restricting the generation of columns, only some of the extreme solutions will be produced. The best such feasible basis generated in this way can be used as a starting basis for the simplex algorithm. Therefore this restricted method can be regarded as a CRASHing procedure. Ways in which the method might be adapted for improved computational efficiency are suggested.