Obtaining Optimal Solution by Using Very Good Non-Basic Feasible Solution of the Transportation and Linear Programming Problem

For the transportation problem, Sharma and Sharma [1] have given a very computationally efficient heuristic (runs in O(c*n²) time) to give very good dual solution to transportation problem. Sharma and Prasad [2] have given an efficient heuristic (complexity O(n³) 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 [2]. In this paper we use the solution given by Sharma and Prasad [2] to get a very good Basic Feasible Solution to transportation problem, so that network simplex (worst case complexity (O(n³*(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 [3] (that generally produces a very good non-basic feasible solution in polynomial time (O(n^5.5)). We give a procedure to obtain a good BFS for LP by starting from the solution given by Karmarkar [3]. We note that this procedure (given here) is significantly different from the procedure given in [4].