Flow Optimization in Dynamic Networks on Time Scales

Abstract

Network flow optimization has a wide range of real world applications such as in transportation, in electric, in civil engineering, in industrial engineering and in communication networks and so on. In the minimum cost network flow model, the goal is to find the values of the decisions variables that minimize the total cost of flows over the given network. In this work, a new formulation of flow optimization in dynamic networks using time scales approach has been presented. The continuous network model and the quantum case model are also obtained as special cases. The formulation has been given for both dynamic models and time scales models. Moreover, the new approach provides the exact optimal solution for this type of optimization problems. Furthermore, a new version of some duality theorems for time scales flow optimization in dynamic networks has been introduced.