Optimization of Logistics Cost through Computer Analysis and Simulation of Transport Problem-solving Algorithms

In a global context characterized by increasingly complex supply chains, growing competitive pressure on distribution costs, and the need to strengthen logistics robustness in both private and public sectors, transport optimization has become a major challenge. This research aims to identify algorithms capable of optimizing the transport of goods from source to destination, focusing on cost, time, accuracy, simplicity, and efficiency. This objective is achieved through modeling, simulation, and computational analysis.  To this end, the study is based on a rigorous mathematical modeling methodology derived from linear programming, combined with an experimental approach relying on intensive numerical simulations. A dataset of 10,000 randomly generated balanced transport matrices with varying dimensions was developed and processed in a standardized Python environment to measure, compare, and interpret the algorithm's performance. The performance is evaluated using several key quantitative indicators, including total transport cost and average execution time, mean relative error, computational robustness, and quality of convergence to the global optimum.  The methods analyzed included the Northwest Corner, Minimum Cost, Balas-Hammer, Russell, Minimum Row, Minimum Column, Hybrid Algorithm, and Stepping -Stone methods. The results revealed significant disparities among these approaches in terms of both accuracy and computational efficiency. In particular, the Balas- Hammer, Russell, and Hybrid methods demonstrated a strong ability to generate high-quality initial solutions, significantly closer to the global optimum than those produced by traditional methods such as the Northwest Corner or Minimum Cost methods. This advantage considerably reduces the number of iterations required during subsequent optimization phases.  The Stepping -Stone algorithm, although more computationally intensive, remains the most reliable method for ensuring the optimality of the final solutions. The study also demonstrates that the quality of the initial solution is a determining factor in the speed of convergence, algorithmic stability, and the overall trade-off between accuracy and computational cost. By proposing an analytical and decision-making framework for selecting the most appropriate method based on matrix size, time constraints, and logistical objectives, this research provides a scientific contribution to logistic optimization.  The results show that advanced heuristic methods, particularly Balas- Hammer and hybrid approaches, offer an effective compromise between execution speed and the quality of initial solutions, while the Stepping -Stone method remains the most efficient for ensuring overall optimality. This study also highlights the strategic importance of initial solution quality on the convergence and computational performance of optimization algorithms. In practical terms, these results can help logistics companies and decision-makers select the most suitable solution methods based on matrix size, time constraints, and accuracy requirements.