1. The MODI method (Modified Distribution method) is used in transportation problems to find the optimal solution that minimizes transportation cost. 2. Start with a basic feasible solution such as the Northwest Corner Rule or Least Cost Method. 3. Calculate the opportunity costs using the formula: $$U_i + V_j = C_{ij}$$ where $U_i$ and $V_j$ are potential variables for row $i$ and column $j$, and $C_{ij}$ is the cost matrix element. 4. Assign $U_1 = 0$ to start and solve the system of equations for all occupied cells. 5. Compute the net evaluations (opportunity cost) for the unoccupied cells: $$\Delta_{ij} = C_{ij} - (U_i + V_j).$$ 6. If all $\Delta_{ij} \geq 0$, the current solution is optimal. 7. If some $\Delta_{ij} < 0$, identify the most negative one and perform an allocation adjustment by tracing a closed loop through occupied cells plus this cell. 8. Increase and decrease allocations along the loop to improve the solution. 9. Repeat steps 3 to 8 until optimality is reached. This method efficiently checks if the current transportation plan is optimal and guides how to improve it iteratively.