Understanding the Transportation Problem The transportation problem involves moving goods from multiple sources (warehouses or suppliers) to various destinations, aiming to minimize costs and maximize profits. It is represented as an m x n matrix where rows denote sources and columns represent destinations; each element indicates the cost of transporting one unit between a source-destination pair. The problem can be classified into balanced (supply equals demand) or unbalanced types, requiring adjustments for solving in case of imbalance.
Solutions and Methods for Optimization Feasible solutions satisfy supply-demand constraints with non-negative allocations, while basic feasible solutions limit these allocations to m + n - 1 values. Non-degenerate cases meet this exact number, whereas degenerate ones fall short. Optimal solutions aim at minimizing transport costs or maximizing profit using methods like Northwest Corner Rule, Least Cost Entry Method, Row/Column Minima Methods, Vogel's Approximation Method (most accurate), followed by Modified Distribution Method for final optimization if conditions are met.