The neutrosophic primal simplex algorithm moves from a neutrosophic basic feasible solution. If there is no such a solution, we cannot apply the neutrosophic primal simplex method for solving the neutrosophic linear programming problem. This work contributes other new neutrosophic linear programming models and it proposes a ranking function for both maximization neutrosophic linear programs and minimization neutrosophic linear programs. On the other hand, this chapter uses the same ranking function when there is a comparison between the fuzzy approach and neutrosophic approach which solve the same example so this comparison is fair. Finally, this chapter proposes a neutrosophic two-phase method involving neutrosophic artificial variables, to obtain an initial neutrosophic basic feasible solution to a slightly modified the set of constraints. Then the neutrosophic primal simplex method is used to eliminate the neutrosophic artificial variables and to solve the original problem.