A feasible solution x = [([x.sub.B], [x.sub.N]).sup.t] to (4.1) obtained by setting [x.sub.B] = [B.sup.-1]b, [x.sub.N] = 0 is called a neutrosophic basic feasible solution ([N.sub.BFS]).

To solve any N LP-problem by simplex method, the existence of an initial basic feasible solution is always assumed.

Neutrosophic Initial Basic Feasible Solution for Model I

Proceeding the neutrosophic initial basic feasible solution algorithm and after few iterations we get the complete allotment transportation units as given in Table 5.

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

Problem [P.sub.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.

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.

Starting from a non-basic feasible solution, as obtained above, a

basic feasible solution with a superior objective function value is obtained by following a sequence of pivotal steps which we call a purification procedure.

The LMOPSO computes the

basic feasible solutions using linear programming and finds a random set of feasible solutions (particles) based on linear combinations of

basic feasible solutions so that the produced solutions never become infeasible.