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The Modified Distribution Method or MODI is a systematic practice of checking the optimality of the initial feasible solutions. This method is more time efficient as compared to Stepping Stone Method. It provides new ways of finding the unused route with the largest negative improvement index. Just as with the stepping stone approach, we are required to trace only one path, once the largest index is identified. In this way, it helps to determine the maximum number of unit that can be shipped by the best unused route. Some of the special cases of Modified Distribution
Method given by The Modified Distribution Assignment Help are
• Balanced Problem
• Unbalanced Problem
• Profit Maximization
• Degeneracy- occurs in two cases as given in The Modified Distribution Assignment Help
Degeneracy occurs in initial basic solution.
Degeneracy occurs in during the test of optimality.
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Steps in Modified Distribution Method
The step wise explanation given by The Modified Distribution Assignment Help are
• Firstly, an initial basic feasible solution is determined using any of the three given methods-Matrix Minimum method, Vogel Approximation Method, North West Corner Rule. All the three methods are explained briefly in The Modified Distribution Assignment Help.
• The values of dual variable, ui and vj is determined using ui+vj=Cij.
• The opportunity cost is computed using Cij-(ui+vj)
• The sign of each opportunity cost is checked. If the sign of opportunity cost of all the unoccupied cost is either positive or zero, then the given solution is the optimal solution. On the other hand, if the sign of opportunity cost of one or more unoccupied cells is negative, then the given solution is not an optimal solution and further savings in transportation cost is possible.
• The unoccupied cell with the smallest negative opportunity cost is selected as the cell to be included in the next solution.
• A closed path or loop for unoccupied cells selected in the previous step is drawn. It is to be noted that the right angle turn in this path is permitted only at the original unoccupied cells and at the occupied cells.
• An alternate plus and minus signs are assigned at the unoccupied cells on the corner points of the closed path with a plus sign at the cell which is to be evaluated.
• The maximum number of units that should be shipped to this unoccupied cell is determined. The number of units that can be shipped to the entering cell is indicated by the smallest value with a negative position on the closed path. Then, this quantity is added to all the cells on the corner points of the closed path marked with the plus sign and subtracted from those cells marked with minus signs. In this way an unoccupied cell transforms and becomes an occupied cell.
• The whole procedure is repeated until an optimal solution is obtained.
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