In this paper, system planning network is formulated with mixed-integer programming. Two meta-heuristic procedures are considered for this problem. The cost function of this problem consists of the capital investment cost in discrete form, the cost of transmission losses and the power generation costs. The DC load flow equations for the network are embedded in the constraints of the mathematica...

This paper presents and solves in polynomial time the minimum convex cost dynamic network flow problem, an infinite horizon integer programming problem which involves network flows evolving over time. The model is a finite network in which each arc has an associated transit time for flow to pass through it. An integral amount of flow is to be sent through arcs of the network in each period over...

The main aim of this paper is to study the maximum flow problem when the underlying associated structure is not well defined and must be modeled as a fuzzy graph. However, to deal with the problem it is necessary to develop several well known concepts from classical theory, in the fuzzy graph context, such as flow, network, and admissible flow. The above maximum flow problem is formulated and s...

The maximum flow problem is one of the important problems of network optimization and covers a wide range of engineering and management applications. Different from the existing works, this paper investigates the maximum flow problem of an uncertain random network under the framework of chance theory. An model of uncertain random α-maximum flow problem is exhibited. And then, it is proved that ...