A

basic feasible solution (BFS) is a basic solution that satisfies the constraints of the LP.

In a recent paper, Ru, Shen and Xue [1] considered the problem of finding an initial

basic feasible solution (bfs) of the LP problem of the form

4] is a transportation type linear programming problem with upper bound restrictions on some variables, therefore its global maximum exists at a basic feasible solution of its constraints.

As none of the constraints in the original system is redundant, a basic feasible solution to the original system shall contain (m+n) basic variables.

1) resembles a (m+n)x(m+n) standard transportation problem for which an initial basic feasible solution with {2(m+n)-1} basic variables may be obtained as follows:

ij]'s and write down the basic feasible solution by the North-West Corner Rule or any other method for standard transportation.

The existing solution now acts as the initial basic feasible solution for the artificial problem we have just created, and we begin the iterations, keeping in mind the upper bounds on the feasible variables.

To formulate the problem such that an initial basic feasible solution is readily available, and, thus avoid the computational effort involved in Phase 1 of the simplex method.

The third objective of finding an initial basic feasible solution can be easily achieved and the method for doing so is described in the Solution of the Optimization Problem Section.

We will formulate an initial basic feasible solution such that at least a portion of the polyhedron is brought into the positive domain for the search to start.

The initial basic feasible solution is formed at the current value of controls by setting [DELTA]u = 0.

Most specialized primal algorithms represent the

basic feasible solution in a tree structure that is stored as four lists having a total of 4(n+m-1) elements (Cromley and Hanink 1999).