| In this paper, The Allocation Method of Element Discriminant Value (AMEDV) has been studied. Linear Programming has a vast applicant filed. However different kinds of iterative algorithms have been shown imperfect in theoretical analysis and computational practice these years. Therefore, it has great significance to reduce computational complexity and pursuit elegant method as possible as we can.We have found that many application of Linear Programming, such as Assignment Problem., Traveling Salesman Problem, Flow Shop Sequencing Problem, Hamilton Problem and so on, fall into the category of transportation problem, that is, of shipping at minimum total cost a homogeneous good from a set of M warehouses to a set of N markets. Based on thoughts quite different from existed methods, we have considered some special properties of the working method on the tableau and built up novel discriminant theories and a direct method.In order to complete the discriminant theories, a new concept namely Zx, has been presented and a new algorithm has been designed. By this algorithm, the optimal solution can been obtained in Transportation Problem N Assignment Problem, Traveling Salesman Problenu Flow Shop Sequencing Problems Hamilton problem. In addition, numerical examples have been given to demonstrate the actual applicant procedure.Besides, of the several algorithms those have been proposed in the literature for solving the transportation problem, previous computational results indicated that the primal algorithm (MODI method) is more efficient, so we have compared the AMEDV versus the MODI method. Because very little experimentation was carried out on algorithmic techniques used in the codes of AMEDV, We have also performed a number of runs that test the overall solution time as the number of significant digits in each of the parameters is varied. Finally, a brief algorithm analysis has been made by a benefit-cost investigation for each subroutine that constitutes the AMEDV. |
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