Networks and flows

The study of networks and flows is an area of linear programming. This thesis begins with an intuitive approach which later develops into a rigorous treatment of the ideas of networks, flows, cuts and maximum value of a flow. The concepts of feasibility and duality are introduced in Chapter Two. A particular kind of flow, a demand function, is found to be feasible under certain conditions in the network. A cost function is also introduced and two methods are given by which it can be minimized for a given network. Ultimately the concepts introduced in the first two chapters are used to solve transshipment and transportation problems. The transshipment problem consists of a fixed time period, products stored in warehouses and retail outlets which demand certain amounts of products. A shipping schedule is found which will send the maximum number of products from the warehouses to the retail outlets. The transportation problem is not only concerned with shipping products to retail outlets during a fixed time period, but is also concerned with minimizing the cost. A method which uses duality is given and an optimal solution is found for a given network.