New Approach on Transportation Problems in Linear and Non Linear Methods

Abstract

Operations research is a scientific approach to problem solving for executive decision making which requires the formulation of mathematical, economic and statistical models for decision and control problems to deal with situations arising out of risk and uncertainty. The transportation model is a special case of linear programming that deals with shipping a commodity from sources to destinations (factories to warehouse). The objective of transportation model is to determine the shipping schedule that minimizes the total shipping cost while satisfying supply and demand limitations. The model assumes that the shipping cost if proportional to the number of units shipped on a given route. The transportation can be extended to the areas of operation, inventory control, employment scheduling and personnel assignment. The transportation model can be solved as a regular linear programming; its special structure allows the development of a simplex based computational algorithm that makes uses of the primal-dual relationships to simplify the computations. The transportation problems actually are special cases of the minimum cost flow problem and can be used for network representation of the transportation. The transportation problem constitutes an important part of logistics management. In addition, logistics problems without shipment of commodities may be formulated as transportation problems. newline