How should Vogel’s method be modified to solve amaximization problem?
How should Vogel’s method be modified to solve a
maximization problem?
Vogel's method is a technique used to find an initial feasible solution for the transportation problem.
It is primarily used for minimizing the cost of transportation, but it can also be modified for maximizing the profit or revenue of transportation.
To modify Vogel's method for a maximization problem, we need to change the way we calculate the penalty values for each row and column.
In a minimization problem, the penalty value is calculated as the difference between the two smallest costs in each row or column. However, in a maximization problem, we need to calculate the difference between the two largest profits or revenues in each row or column.
Once we have calculated the penalty values for each row and column, we can follow the same steps as in Vogel's method to find the initial feasible solution.
We select the row or column with the highest penalty value and allocate as much as possible to the cell with the lowest cost. We repeat this process until all supplies and demands are met.
After finding the initial feasible solution, we can use any optimization method to improve the solution and find the optimal solution that maximizes the profit or revenue. One common method is the modified distribution method, which iteratively improves the solution until no further improvement is possible.
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