Restricted Constraints in the Problem of Maximum Attainable Flow in Minimum Cost in a Network

In this paper we have considered a version of restricted constraints in the problem of maximum attainable flow (capacity) in minimum cost (distance) in a network (Ahmed, Das,&Purusotham, 2012b). By restricted constraints one means that the link(s) (cities or stations or nodes) are completed (or visited) in such a way that a particular link is to be preceded (completed or visited) by another link (precedence relation need not be immediate).

Here the aim is to obtained an optimal route of a more realistic situation as to scheduling a restricted constraints to a maximum flows at a minimum cost from a source to a destination. The distance (cost) and arc capacity between any two stations are given.