Various Method Of Finding Initial basic Feasible Solution:
North West Corner Method
The North-West Corner Method is a simple heuristic algorithm used to find an initial feasible solution for the transportation problem. It is named after the starting point of the method, which is the north-west corner of the transportation table.
The North-West Corner Method works as follows:
Start at the top-left corner (northwest corner) of the transportation table.
Allocate the maximum possible quantity of the item to the first supply source and demand destination.
Cross out either the supply or demand quantity that has been completely satisfied and move to the next cell in the same row or column where the unsatisfied supply or demand remains.
Repeat step 2 and 3 until all supply or demand is completely satisfied.
The allocation is repeated until either the total supply or demand has been completely satisfied. Once the initial allocation is complete, the method provides a starting point for further optimization using more advanced algorithms such as the modified distribution method or the stepping-stone method.
The North-West Corner Method is simple and easy to understand but it may not always provide an optimal solution, especially for large and complex transportation problems. It can also result in unbalanced allocations if the total supply does not match the total demand, leading to inefficiencies and higher transportation costs.
Least Cost Method
The Least Cost Method is another heuristic algorithm used to find an initial feasible solution for the transportation problem. It is based on selecting the cell with the lowest cost per unit for allocation. The method works as follows:
Start by identifying the cell with the lowest cost per unit in the transportation table.
Allocate as much quantity as possible to this cell without exceeding the supply and demand constraints.
Cross out either the supply or demand quantity that has been completely satisfied and move to the next cell with the lowest cost per unit.
Repeat steps 2 and 3 until all supply or demand is completely satisfied.
The Least Cost Method can also result in unbalanced allocations if the total supply does not match the total demand. However, this method generally provides a better initial feasible solution than the North-West Corner Method, especially for larger and more complex transportation problems. The method is still a heuristic, meaning that it may not always produce an optimal solution.
Once the initial allocation is complete, the method provides a starting point for further optimization using more advanced algorithms such as the modified distribution method or the stepping-stone method.
Vogel’s Approximation Method (VAM)
Vogel’s Approximation Method (VAM) is another heuristic algorithm used to find an initial feasible solution for the transportation problem. It is based on selecting the cell with the lowest or next lowest cost difference between the two least cost routes that can satisfy the supply and demand constraints.
The method works as follows:
Calculate the difference between the two smallest cost elements in each row and column of the transportation table.
Identify the row or column with the largest difference, and allocate as much quantity as possible to the cell with the least cost.
Cross out either the supply or demand quantity that has been completely satisfied and update the difference values.
Repeat steps 2 and 3 until all supply or demand is completely satisfied.
The VAM method tends to produce better initial feasible solutions than the North-West Corner Method or the Least Cost Method, especially for large and complex transportation problems. It is also less likely to result in unbalanced allocations if the total supply does not match the total demand. However, the VAM method is still a heuristic, meaning that it may not always produce an optimal solution.
Once the initial allocation is complete, the method provides a starting point for further optimization using more advanced algorithms such as the modified distribution method or the stepping-stone method.