Which of the following methods is used to verify the optimality of the current solution of the transportation problem-

General
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which of the following methods is used to verify the optimality of the current solution of the transportation problem-

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The least cost method is one of the methods used to verify the optimality of the current solution of the transportation problem. This method involves selecting the cell with the lowest cost in the transportation table and allocating the maximum possible units to that cell, based on the available supply and demand.

To apply the least cost method, follow these steps:

  1. Start with the given initial feasible solution for the transportation problem.
  2. Calculate the opportunity costs for each unallocated cell in the table. The opportunity cost represents the cost of not using that cell for transportation.
  3. Identify the cell with the lowest opportunity cost. This is the cell that offers the lowest cost for additional transportation.
  4. Allocate as many units as possible from the available supply to the cell, considering both the cell’s capacities and the remaining demands.
  5. Update the supply and demand values for the respective row and column of the allocated cell.
  6. Repeat steps 2-5 until all units are allocated or until there are no more cells with non-negative opportunity costs.
  7. Once all units are allocated, check if the solution obtained is optimal. The optimality condition in the transportation problem is when all opportunity costs are non-negative (zero or positive).

By applying the least cost method and ensuring that the obtained solution satisfies the optimality condition, it indicates that the current solution is optimal for the transportation problem. However, it’s important to note that there are other methods, such as the Vogel’s approximation method and the stepping stone method, which can also be used to verify optimality and improve the initial solution if necessary.