What is the procedure for solving a maximization transportation problem?

Procedure for Solving a Maximization Transportation Problem

Transportation problems are mathematical models used to optimize the allocation of resources, such as goods or services, among multiple sources and destinations. Maximization transportation problems aim to maximize the total profit or revenue generated from these allocations.

To solve a maximization transportation problem, the following procedure can be followed:

1. Transform into a Minimization Problem:

The first step is to transform the maximization problem into an equivalent minimization problem. This is achieved by subtracting each transportation cost from the maximum cost in the cost matrix. The resulting cost matrix will have all non-negative values.

2. Apply Standard Minimization Methods:

Once the cost matrix has been transformed, standard minimization methods can be used to solve the problem. These methods include:

• Northwest Corner Method: This is a simple method that starts with the northwest corner of the cost matrix and allocates supplies and demands in a northwestward direction until the problem is solved.
• Vogel’s Approximation Method: This method identifies the largest penalty cost (the difference between the maximum cost and the actual cost) in each row and column, and prioritizes cells with the highest penalties.
• MODI Method: The Matrix Minimum Difference (MODI) Method is an iterative method that repeatedly allocates supplies and demands to the cell with the smallest non-allocated cost until the problem is solved.

3. Reverse the Transformation:

After solving the minimization problem, the optimal transportation plan can be obtained by adding the maximum cost back to each cost in the transformed cost matrix. This will give the optimal transportation costs and the corresponding allocations.

Advantages of Transforming to a Minimization Problem:

• Standard minimization methods are well-established and widely used, making them easy to apply.
• The transformed cost matrix has non-negative values, which simplifies the calculation process.
• The optimal solution to the minimization problem is the same as the optimal solution to the original maximization problem.

By following these steps, maximization transportation problems can be solved effectively using standard minimization techniques.