%0 Journal Article
%T Obtaining Optimal Solution by Using Very Good Non-Basic Feasible Solution of the Transportation and Linear Programming Problem
%A R. R. K. Sharma
%J American Journal of Operations Research
%P 285-288
%@ 2160-8849
%D 2017
%I Scientific Research Publishing
%R 10.4236/ajor.2017.75021
%X For the transportation problem, Sharma and Sharma [<a href=\"#ref1\">1</a>] have given a very computationally efficient heuristic (runs in O(c*n<sup>2</sup>) time) to give very good dual solution to transportation problem. Sharma and Prasad [<a href=\"#ref2\">2</a>] have given an efficient heuristic (complexity O(n<sup>3</sup>) procedure to give a very good primal solution (that is generally non-basic feasible solution) to transportation problem by using the very good dual solution given by Sharma and Sharma [<a href=\"#ref2\">2</a>]. In this paper we use the solution given by Sharma and Prasad [<a href=\"#ref2\">2</a>] to get a very good Basic Feasible Solution to transportation problem, so that network simplex (worst case complexity (O(n<sup>3</sup>*(log(n))) can be used to reach the optimal solution to transportation problem. In the second part of this paper, we give a simple heuristic procedure to get a very good BFS to linear programming problem from the solution given by Karmarkar [<a href=\"#ref3\">3</a>] (that generally produces a very good non-basic feasible solution in polynomial time (O(n<sup>5.5</sup>)). We give a procedure to obtain a good BFS for LP by starting from the solution given by Karmarkar [<a href=\"#ref3\">3</a>]. We note that this procedure (given here) is significantly different from the procedure given in [<a href=\"#ref4\">4</a>].
%K Optimal BSF Solution
%K Transportation Problem
%K Linear Programming Problem
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=78883