The problem of maximum flow with minimum attainable cost in a network

Abstract

The routing problems pertain to the search for a shortest route (minimum cost or minimum distance or maximum flow, etc.) connecting two specified stations or nodes described as ‘source’ and ‘sink’. The paper aims at obtaining an optimal route of a more realistic situation as to scheduling maximum flows at a minimum cost from a source to a destination. The distance (cost) and arc capacity between any two stations are given. The objective is to find the maximum flow with the minimum cost from the source to the destination in a network. The problem has many applications in the field of network flow theories. Several special cases of the problem were intensively studied in the literature and proposed various techniques to solve. Here we solved the present problem by the lexicographic search technique, which gives the exact solution to the problem. The solution procedure is illustrated with a suitable example. The algorithm is also tested in C-language and the computational details are also reported.