scholarly journals Solving Robust Variants of Integer Flow Problems with Uncertain Arc Capacities

2021 ◽  
Vol 33 (1) ◽  
pp. 77-89
Author(s):  
Marko Špoljarec ◽  
Robert Manger
Keyword(s):  
Flow Problem ◽  
Network Flows ◽  
Minimum Cost ◽  
Maximum Flow ◽  
Approximate Algorithm ◽  
Minimum Cost Flow ◽  
Flow Problems ◽  
Unit Costs ◽  
Minimum Cost Flow Problem ◽  
Integer Flow

This paper deals with robust optimization and network flows. Several robust variants of integer flow problems are considered. They assume uncertainty of network arc capacities as well as of arc unit costs (where applicable). Uncertainty is expressed by discrete scenarios. Since the considered variants of the maximum flow problem are easy to solve, the paper is mostly concerned with NP-hard variants of the minimum-cost flow problem, thus proposing an approximate algorithm for their solution. The accuracy of the proposed algorithm is verified by experiments.

Networks Flow Applications

2013 ◽  
pp. 246-256
Author(s):  
Alireza Boloori ◽  
Monirehalsadat Mahmoudi
Keyword(s):  
Network Flow ◽  
Large Scale ◽  
Flow Problem ◽  
Minimum Cost ◽  
Maximum Flow ◽  
Shortest Path Problems ◽  
Flow Problems ◽  
Large Scale Integration ◽  
Minimum Cost Flow Problem ◽  
Scale Integration

In this chapter, some applications of network flow problems are addressed based on each type of problem being discussed. For example, in the case of shortest path problems, their concept in facility layout, facility location, robotics, transportation, and very large-scale integration areas are pointed out in the first section. Furthermore, the second section deals with the implementation of the maximum flow problem in image segmentation, transportation, web communities, and wireless networks and telecommunication areas. Moreover, in the third section, the minimum-cost flow problem is discussed in fleeting and routing problems, petroleum, and scheduling areas. Meanwhile, a brief explanation about each application as well as some corresponding literature and research papers are presented in each section. In addition, based on available literature in each of these areas, some research gaps are identified, and future trends as well as chapter’s conclusion are pointed out in the fourth section.

Minimum cost flow problem with conflicts

Networks ◽  
2021 ◽  
Author(s):  
Zeynep Şuvak ◽  
İ. Kuban Altınel ◽  
Necati Aras
Keyword(s):  
Flow Problem ◽  
Minimum Cost ◽  
Minimum Cost Flow ◽  
Minimum Cost Flow Problem ◽  
Cost Flow

Minimum Cost Flow Problem

2008 ◽  
pp. 2095-2108
Author(s):  
Ravindra K. Ahuja ◽  
Thomas L. Magnanti ◽  
James B. Orlin
Keyword(s):  
Flow Problem ◽  
Minimum Cost ◽  
Minimum Cost Flow ◽  
Minimum Cost Flow Problem ◽  
Cost Flow

The Minimum Cost Flow Problem of Uncertain Random Network

2018 ◽  
Vol 35 (03) ◽  
pp. 1850016
Author(s):  
Soheila Abdi ◽  
Fahimeh Baroughi ◽  
Behrooz Alizadeh
Keyword(s):  
Flow Model ◽  
Flow Problem ◽  
Random Network ◽  
Minimum Cost ◽  
Random Variable ◽  
Minimum Cost Flow ◽  
Feasible Set ◽  
Uncertain Random Network ◽  
Minimum Cost Flow Problem ◽  
Cost Flow

The aim of this paper is to present a novel method for solving the minimum cost flow problem on networks with uncertain-random capacities and costs. The objective function of this problem is an uncertain random variable and the constraints of the problem do not make a deterministic feasible set. Under the framework of uncertain random programming, a corresponding [Formula: see text]-minimum cost flow model with a prespecified confidence level [Formula: see text], is formulated and its main properties are analyzed. It is proven that there exists an equivalence relationship between this model and the classical deterministic minimum cost flow model. Then an algorithm is proposed to find the maximum amount of [Formula: see text] such that for it, the feasible set of [Formula: see text]-minimum cost flow model is nonempty. Finally, a numerical example is presented to illustrate the efficiency of our proposed method.

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