Mathematical Methods
MATHEMATICAL METHODS
1. Finding An Initial Basic Feasible Solution: An initial basic feasible solution to a transportation problem can be found by any one of the three following methods: I. North West Corner Rule II. The Least Cost Method III. Vogel’s Approximation Method
1. North West Corner Rule The North West corner rule is a method for computing a basic feasible solution of a transportation problem, where the basic variables are selected from the North-West Corner (i.e. top left corner). The standard North West corner rule instructions are paraphrased below:
Steps:
Step 1. Select the north west (upper left hand) corner cell of the transportation table and allocate as many units as possible equal to the minimum between available supply and demand. Step 2. Adjust the supply and demand numbers in the respective rows and columns. Step 3. If the demand for the first cell is satisfied, then move horizontally to the next cell in the second row. Step 4. If the supply for the first row is exhausted, then move down to the first cell in the second row. Step 5. If for any cell, supply equals demand, then the next allocation can be made in either in the next row or column. Step 6. Continue the process until all supply and demand values are exhausted.
2. The Least-Cost Method The least-Cost Method is a method for computing a basic feasible solution of a transportation problem, where the basic variables are chosen according to the unit cost of transportation. This method is very useful because it reduces the computation and the time required to determine the optimal solution. The following steps summarize the approach.
Steps:
Step 1. Indentify the box having minimum unit transportation cost. Step 2. If the minimum cost is not unique, then you are liberty o choose any cell. Step 3. Choose the value of the corresponding cell as much as possible subject to the capacity and requirement
1. Finding An Initial Basic Feasible Solution: An initial basic feasible solution to a transportation problem can be found by any one of the three following methods: I. North West Corner Rule II. The Least Cost Method III. Vogel’s Approximation Method
1. North West Corner Rule The North West corner rule is a method for computing a basic feasible solution of a transportation problem, where the basic variables are selected from the North-West Corner (i.e. top left corner). The standard North West corner rule instructions are paraphrased below:
Steps:
Step 1. Select the north west (upper left hand) corner cell of the transportation table and allocate as many units as possible equal to the minimum between available supply and demand. Step 2. Adjust the supply and demand numbers in the respective rows and columns. Step 3. If the demand for the first cell is satisfied, then move horizontally to the next cell in the second row. Step 4. If the supply for the first row is exhausted, then move down to the first cell in the second row. Step 5. If for any cell, supply equals demand, then the next allocation can be made in either in the next row or column. Step 6. Continue the process until all supply and demand values are exhausted.
2. The Least-Cost Method The least-Cost Method is a method for computing a basic feasible solution of a transportation problem, where the basic variables are chosen according to the unit cost of transportation. This method is very useful because it reduces the computation and the time required to determine the optimal solution. The following steps summarize the approach.
Steps:
Step 1. Indentify the box having minimum unit transportation cost. Step 2. If the minimum cost is not unique, then you are liberty o choose any cell. Step 3. Choose the value of the corresponding cell as much as possible subject to the capacity and requirement