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The stepping stone method is instrumental in deciding if a particular solution obtained is optimal or not. The solution so obtained beforehand could be by the use of Vogel’s approximation method, least cost method or North West corner. The stepping stone method shall provide the pathway to find out the possibility of any existing empty cells in form of the objective function. This method shall provide the idea as to how the charges for transportation in a transportation problem shall be affected when and if a value is given to one of the empty cells. This in turn shall decide the feasibility of an initial solution. Stepping Stone Method Assignment Help shall cover all the steps involved in the procedure of obtaining the optimal solution.
Steps In The Stepping Stone Method
The algorithm has been explained in Stepping Stone Method Assignment Help as follows.
• For the optimal solution: The very beginning of the test shall be to ensure that the total number of cells that are filled must be equal to the value of m+n-1. Where “m” stands for the total number of rows and “n” stands for the total number of columns.
• For forming a closed loop: an empty cell has to be selected. Starting from this cell, a closed path has to be traced, such that the ending point is the very same empty cell. While tracing the closed path, there shall be cells in the turning points. These cells are called the stepping stones of the closed path. It can be studied in Stepping Stone Method Assignment help.
• Evaluating the change in cost: starting from the first empty cell, “+” and “-” signs are assigned alternatively to all the stepping stones. The very first empty cell must be assigned a + sign and then the rest stepping stones can be assigned the signs accordingly. Addition of each unit’s transportation cost shall provide the change in transportation costs. The above stated steps shall be repeated until all the empty cells have been evaluated.
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• To confirm optimality: When and if all the net changes so evaluated are positive values, then the solution is optimal and no further modifications are required. However if any net change is not positive, there can be a better solution and thus the current solution requires a modification. The change can be brought forward by selecting the empty cell with maximum negative cost change. Then the maximum numbers of units that can be assigned to the cell are found out by locating the smallest value having a “-” sign. This value then is added to the empty cell and all other cells having “+” sign in the closed path. Finally this value is subtracted from all the cells in the closed path having “-” sign. For better understanding of concepts, refer to Stepping Stone Method Assignment Help.
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