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VAM - MODI Transportation Scheduling

VOGEL’S APPROXIMATION METHOD (VAM) 

The Vogel’s Approximation Method (Unit Cost Penalty Method) is an iterative procedurefor computing the basic feasible solution which is either optimal or very close to the optimal

solution of a transportation problem.

Example Problem

Carmels, a manufacturing company, has three plants and three destinations to which it has to

supply all the raw materials.

Compute the transportation costs for supplying the raw materials to all the destinations.

Initial Problem Table

Steps in VAM :

1. Identify the boxes having the minimum and next to minimum transportation cost in each row

and write the difference (penalty) along the side of the table against the corresponding row.

2. Identify the boxes having the minimum and next to minimum transportation cost in each

column and write the difference (penalty) below the table against the corresponding column.

Plant D1 D2 D3 Sources Penalties

A 6 8 10 150 2B 7 11 11 175 4

C 4 5 12 275 1

Demand 200 100 300

Penalties 2 3 1

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3. Identify the maximum penalty. If it is along the side of the table, make maximum allotment to

the box having the minimum transportation cost in that row. If it is below the table, make

maximum allotment to the box having the minimum transportation cost in that column.

4. Repeat the above steps until all the constraints are satisfied. If the penalties corresponding to

two or more rows or columns are equal, you are at liberty to break the tie arbitrarily.

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Initial Basic Solution by VAM

Total Cost = 5125

REPORTER:

Abat, Thea Louise

 3BSA2

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What is MODI Method?

The MODI (modif ied distri bution ) method is a method for computing optimum solution of atransportation problem. It 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 newmeans of finding the unused route with the largest negative improvement index. Once the largestindex 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?

Here are the steps.

1.  a. Vi + W j = Cij, where

Vi = the dual variable associated with the ith source constraint

W j = the dual variable associated with the jth destination constraintCij = the cost of shipping one unit from the ith source to the jth destination.

 b. The value of an unoccupied cell: UC = Cij  –  Vi - W j

2. 

Write the complete set of equations in the style of formula 1(a) for all occupied cells in

the transportation table.

3.  Write the complete set of equations in the style of formula 1(b) for all unoccupied cells in

the transportation table.

4.  Set the first Vi in step 2 equal to zero. It will then be possible to obtain numerical values

for all of the dual variables.

5.  Use the numerical values you obtained in step 4 to solve the equations in step 3.

Let us use the example in VAM Method:

Initial Basic Solution by VAM

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