Solving the Arizona Plumbing Problem with Modified Distribution Method and Vogel's Approximation Method
CD Tutorial 4 The MODI and VAM
Methods of Solving
Transportation Problems
Tutorial Outline
MODI METHOD
How to Use the MODI Method
Solving the Arizona Plumbing Problem with
MODI
VOGEL’S APPROXIMATION METHOD:
ANOTHER WAY TO FIND AN INITIAL
SOLUTION
DISCUSSION QUESTIONS
PROBLEMS
T4-2 CD TUTORIAL 4 THE MODI AND VAM METHODS OF SOLVING TRANSPORTATION PROBLEMS
This tutorial deals with two techniques for solving transportation problems: the MODI method and
Vogel’s Approximation Method (VAM).
MODI METHOD
The MODI (modified distribution) method allows us to compute improvement indices quickly for each unused square without drawing all of the closed paths. Because of this, it can often provide considerable time savings over other methods for solving transportation problems.
MODI provides a new means of finding the unused route with the largest negative improvement index. Once the largest index is identified, we are required to trace only one closed path. This path helps determine the maximum number of units that can be shipped via the best unused route.
How to Use the MODI Method
In applying the MODI method, we begin with an initial solution obtained by using the northwest corner rule or any other rule. But now we must compute a value for each row (call the values R1, R2, R3 if there are three rows) and for each column (K1, K2, K3 ) in the transportation table. In general, we let
The MODI method then requires five steps:
1. To compute the values for each row and column, set
Ri + Kj = Cij but only for those squares that are currently used or occupied. For example, if the square at the intersection of row 2 and column 1 is occupied, we set R2 + K1 = C21.
2. After all equations have been written, set R1 = 0.
3. Solve the system of equations for all R and K values.
4. Compute the improvement index for each unused square by the formula improvement index (Iij) = Cij Ri Kj.
5. Select the largest negative index and proceed to solve the problem
Methods of Solving
Transportation Problems
Tutorial Outline
MODI METHOD
How to Use the MODI Method
Solving the Arizona Plumbing Problem with
MODI
VOGEL’S APPROXIMATION METHOD:
ANOTHER WAY TO FIND AN INITIAL
SOLUTION
DISCUSSION QUESTIONS
PROBLEMS
T4-2 CD TUTORIAL 4 THE MODI AND VAM METHODS OF SOLVING TRANSPORTATION PROBLEMS
This tutorial deals with two techniques for solving transportation problems: the MODI method and
Vogel’s Approximation Method (VAM).
MODI METHOD
The MODI (modified distribution) method allows us to compute improvement indices quickly for each unused square without drawing all of the closed paths. Because of this, it can often provide considerable time savings over other methods for solving transportation problems.
MODI provides a new means of finding the unused route with the largest negative improvement index. Once the largest index is identified, we are required to trace only one closed path. This path helps determine the maximum number of units that can be shipped via the best unused route.
How to Use the MODI Method
In applying the MODI method, we begin with an initial solution obtained by using the northwest corner rule or any other rule. But now we must compute a value for each row (call the values R1, R2, R3 if there are three rows) and for each column (K1, K2, K3 ) in the transportation table. In general, we let
The MODI method then requires five steps:
1. To compute the values for each row and column, set
Ri + Kj = Cij but only for those squares that are currently used or occupied. For example, if the square at the intersection of row 2 and column 1 is occupied, we set R2 + K1 = C21.
2. After all equations have been written, set R1 = 0.
3. Solve the system of equations for all R and K values.
4. Compute the improvement index for each unused square by the formula improvement index (Iij) = Cij Ri Kj.
5. Select the largest negative index and proceed to solve the problem