Study On Transportation Problem With Capacity Limitation

With the development of economic globalization, transportation enterprise has become more and more important in the national economy. Building a reasonable transportation system is very important and significative for developing economic, strengthening military affairs, improving our life, and enlarging the communion of the international culture and technology, etc. The transportation problem in Management Science is just a kind of optimization problem, which has academic value and practicality to the transportation enterprise in our daily life. But the classical transportation problem is just products'transportation between the plants and warehouses, without caring the detailed paths, the transport points'maximum capacity, the overpass ability of the roads, the vehicles'transportation limitation, etc. in the transportation network, which limit the applied value of the transportation problem model in real life. In this article, we studied the transportation problem model with capacity limitation. According different capacity limitation restrictions, we built various mathematic models. Also, the capacity expansion problems of the transport points and the transportation paths in the network have been concerned. The transportation problem models of the capacity limitation and capacity expansion are the theoretic support and reference of the real transportation affairs. We solve the question we advanced mainly by using auxiliary network, and turn this kind of transportation problem into minimum cost flow problem. Basing on this point, the capacity expansion problems in the transportation network are also considered with the similar thought and method in the article. Firstly, the article introduced some background knowledge of the question we studied in chapter 2 and chapter 3, which included the basic model and solution of the transportation problem, transportation problem with transport points, the summarize of the network capacity expansion problem and the capacity expansion problem in the transportation network. Then, basing on the basic knowledge, we studied three different instances of the transportation problem model with capacity limitation in three chapters and give three different arithmetical examples in every chapter's end. In the end of the article, we summarized our work, and point out the limitation and the future study direction.