Kuljetusongelma

Kuljetusongelma, also known as the transportation problem, is a special class of linear programming problems. It deals with the distribution of goods from a set of sources (origins) to a set of destinations, with the goal of minimizing the total cost of transportation. Each source has a certain supply, and each destination has a certain demand. The cost of transporting one unit of goods from any given source to any given destination is known.

The objective is to determine the optimal quantity of goods to ship from each source to each destination such that the total transportation cost is minimized, while satisfying all demands and not exceeding any supplies. The problem can be formulated as a mathematical model where decision variables represent the quantities shipped between each origin-destination pair. Constraints ensure that the total amount shipped from each source does not exceed its supply, and the total amount received at each destination meets its demand.

Common methods for solving the transportation problem include the North-West Corner Rule, Least Cost Method, and Vogel's Approximation Method for finding an initial basic feasible solution, followed by techniques like the Stepping Stone Method or the MODI (Modified Distribution) method for finding the optimal solution. These methods systematically adjust the shipping plan until no further cost reduction is possible. The transportation problem is a fundamental concept in operations research and has wide applications in logistics, supply chain management, and resource allocation.