Flow Increment through Network Expansion

Adrian Marius Deaconu,Luciana Majercsik

doi:10.3390/math9182308

Abstract

The network expansion problem is a very important practical optimization problem when there is a need to increment the flow through an existing network of transportation, electricity, water, gas, etc. In this problem, the flow augmentation can be achieved either by increasing the capacities on the existing arcs, or by adding new arcs to the network. Both operations are coming with an expansion cost. In this paper, the problem of finding the minimum network expansion cost so that the modified network can transport a given amount of flow from the source node to the sink node is studied. A strongly polynomial algorithm is deduced to solve the problem.

Highlights

In Minimum Cost Network Expansion Problem (MCNEP), when the maximum flow that can be transported in the given network from source to sink becomes insufficient, the network should be expanded so that a given amount of flow can be transported in the modified network, and the cost of expansion is minimized
This paper considered the minimum cost network expansion problem (MCNEP)
The problem arises in cases where a given network must be modified to allow an increase in the amount of flow going from the source to the sink node

Summary

Introduction

Starting with a given network G, the objective is to obtain a new network G 0 , by increasing the capacities of the arcs from G within some given limits, or by adding new arcs, such that the cost of the modification is minimum, and in G 0 , w units of flow can be transported from source to sink. The cost function for the capacity augmentation/arc insertion operations is a linear function with respect to the modification of the respective capacities Both problems, MCNEP and BFEP, study the possibility of expansion of an existing network. In MCNEP, when the maximum flow that can be transported in the given network from source to sink becomes insufficient, the network should be expanded so that a given amount of flow can be transported in the modified network, and the cost of expansion is minimized.

Network Flow

Flow Increment through Network Expansion

Example

Conclusions