Restricted Constraints in a Max-Flow and Min-Cost problem

Abstract

The present paper defines a combination of two most important and old flow problems such as maximum flow and minimum cost flow. In the first one a flow with the maximum value from source node to sink node is sought. The second one seeks a flow with the minimum total transferring costs from source nodes to demand nodes. Here an attempt is made to obtain an optimal route of a more realistic situation as to scheduling some restricted constraint, in which its transferring cost is minimized and its value is maximized. The proposed algorithm is formulated and solved by the lexicographic search approach. It is seen that the time required for the search of the optimal solution is fairly less. Also the algorithm is applied to different order matrices with number of stations = 5, 8, 10, …, 50 and in the dimensions of 6 to exhibit its effectiveness.