Transportation is a critical aspect of logistics and supply chain management. It involves the optimal distribution of goods from multiple sources to various destinations. The goal is to minimize transportation costs while meeting supply and demand constraints. All optimization algorithms developed so far focus on these challenges and their pros and cons. This article compares and classifies the algorithms according to their principles, merits, and demerits. It explores exact and heuristic algorithms, outlining each approach and its appropriateness for transportation applications. It delves into different concepts involved in the simplex method, which is a key algorithm in linear programming, degenerate and specialized methods of simplex such as the transportation method, and network simplest method for transportation problems. Some of the heuristic algorithms proposed in the paper include classical heuristics such as the North-West Corner Method, Least Cost Method, and Vogel's Approximation Method and a collection of metaheuristics including Genetic Algorithms, Simulated Annealing, Tabu Search, Ant Colony Optimization, and Particle Swarm Optimization. As mentioned, many heuristic approaches produce satisfactory solutions in a reasonable time with no optimality guarantees. They are often the only solution technique for large, intractable, complex systems, models, or problem statement types that exact methods cannot tackle.