Operation Research 13: Transportation Problem: northwest corner, least cost cell & VAM method
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Transportation Problem Solution using northwest
Transportation Problem Solution using northwest corner, least cost cell & vogel's approximation method (VAM).
Steps of northwest corner:
Find the north west corner cell (X11) of the transportation tableau.
Allocate as much as possible to the selected cell, and
Adjust the associated amounts of supply and demand by subtracting the allocated amount.
Cross out the row or column with 0 supply or demand.
Least cost cell method
The unit transportation costs play no role in northwest corner method, which simply selects the upper left-hand corner variable and assigns a value to it.
With the minimum cell cost method, the initial allocation is made to the cell with the lowest cost. Thus, the solution become near to optimal solution.
The steps of the minimum cell cost method are as follows:
Select the least cost
Allocate as much as possible to the feasible cell.
Adjust demand and supply
Cancel the row/column with 0 supply or demand
Vogel's Approximation Method
VAM is an improved version of the least-cost method that generally, but not always, produces better starting solutions.
VAM is a technique which is based on the concept of penalty cost or regret.
If a decision maker incorrectly chooses from several alternative course of action, a penalty may be suffered and the decision maker may regret the decision that was made.
In a transportation problem, the course of actions are the alternative routes and a wrong decision is allocating to a cell that does not contain the lowest cost.
Steps of Vogel's Approximation Method
Determine a penalty measure by subtracting the smallest unit cost in the row (column) from the next smallest unit cost in the same row (column). This penalty is actually a measure of lost opportunity one forgoes if the smallest unit cost cell is not chosen.
Identify the row or column with the largest penalty. Allocate as much as possible to the variable with the least unit cost in the selected row or column.
Adjust the supply and demand, and
Cross out the satisfied row or column. If a row and a column are satisfied simultaneously, only one of the two is crossed out, and the remaining row (column) is assigned zero supply (demand).
Steps of northwest corner:
Find the north west corner cell (X11) of the transportation tableau.
Allocate as much as possible to the selected cell, and
Adjust the associated amounts of supply and demand by subtracting the allocated amount.
Cross out the row or column with 0 supply or demand.
Least cost cell method
The unit transportation costs play no role in northwest corner method, which simply selects the upper left-hand corner variable and assigns a value to it.
With the minimum cell cost method, the initial allocation is made to the cell with the lowest cost. Thus, the solution become near to optimal solution.
The steps of the minimum cell cost method are as follows:
Select the least cost
Allocate as much as possible to the feasible cell.
Adjust demand and supply
Cancel the row/column with 0 supply or demand
Vogel's Approximation Method
VAM is an improved version of the least-cost method that generally, but not always, produces better starting solutions.
VAM is a technique which is based on the concept of penalty cost or regret.
If a decision maker incorrectly chooses from several alternative course of action, a penalty may be suffered and the decision maker may regret the decision that was made.
In a transportation problem, the course of actions are the alternative routes and a wrong decision is allocating to a cell that does not contain the lowest cost.
Steps of Vogel's Approximation Method
Determine a penalty measure by subtracting the smallest unit cost in the row (column) from the next smallest unit cost in the same row (column). This penalty is actually a measure of lost opportunity one forgoes if the smallest unit cost cell is not chosen.
Identify the row or column with the largest penalty. Allocate as much as possible to the variable with the least unit cost in the selected row or column.
Adjust the supply and demand, and
Cross out the satisfied row or column. If a row and a column are satisfied simultaneously, only one of the two is crossed out, and the remaining row (column) is assigned zero supply (demand).
3 سال پیش
در تاریخ 1400/10/13 منتشر شده
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