What is the MODI Method?

The MODI Method (Modified Distribution Method), also frequently referred to as the U-V Method, is a formal procedure used in Operations Research to test the optimality of an Initial Basic Feasible Solution (IBFS) in a transportation problem. While methods like the Northwest Corner or Vogels Approximation Method (VAM) provide an initial starting point, the MODI method determines if that solution is the absolute cheapest possible option or if further cost reductions are possible.

How to Use the MODI Method Calculator

To use this tool effectively, follow these three simple steps:

1. Set Grid Size: Define the number of supply sources (rows) and demand destinations (columns).
2. Input Costs and Allocations: Enter the unit transportation costs in the top boxes and your current allocations (from VAM or Least Cost) in the blue-bordered boxes.
3. Analyze Results: The calculator computes the U and V values and provides the net evaluation (opportunity cost) for every unoccupied cell.

Understanding the Optimality Rule

The MODI method follows a specific mathematical logic. For every occupied cell (where an allocation exists), we solve the equation C_ij = u_i + v_j. Once all u and v values are determined, we calculate the opportunity cost Δ_ij = C_ij - (u_i + v_j) for all empty cells. If all Δ values are greater than or equal to zero, your current transportation plan is optimal. If any value is negative, the cost can be further reduced.

Frequently Asked Questions

Is MODI better than the Stepping Stone Method?
While both provide the same result, MODI is generally considered more efficient for larger matrices because it avoids the need to draw multiple closed loops for every empty cell.

What is Degeneracy?
In the MODI method, degeneracy occurs when the number of allocated cells is less than (Rows + Columns - 1). For the method to work, this condition must be met.