MATLAB Source Code for Transportation Problem with Algorithm Implementations

The transportation problem represents a classic linear programming challenge in operations research, focusing on minimizing transportation costs when shipping goods from multiple supply points to multiple demand points. In MATLAB, this problem can be solved either using built-in optimization toolbox functions or by implementing custom algorithms.

The core solution approach involves constructing a mathematical model where supply capacities, demand requirements, and transportation costs serve as key parameters. Using linear programming methodology, MATLAB's `linprog` function can efficiently determine the optimal transportation plan that satisfies all constraints. The basic implementation requires defining the objective function coefficients (transportation costs), equality/inequality constraints for supply-demand balance, and variable bounds.

For more complex scenarios involving capacity constraints or dynamic demand fluctuations, extended models can incorporate additional constraints while heuristic algorithms like the Northwest Corner Method or Vogel's Approximation Method can provide initial feasible solutions. MATLAB's flexibility in matrix operations and numerical computation makes it ideal for implementing these enhancements, where users can customize algorithms using functions like `fmincon` for nonlinear constraints or implement iterative improvement procedures through loop structures and conditional statements.