An Application of Freight systems

• Author: Schiopu C.
• Pages: 499-506

Bulletin of the Transilvania University of Braşov

Series V: Economic Sciences • Vol. 8 (57) No. 2 - 2015

An Application of Freight systems

Camelia ŞCHIOPU1

Abstract: There are important applications of the maximal dynamic flow problem and its

variations in the areas of freight systems, material handling systems and building

evacuation. The early freight system application of maximal dynamic network flow models

arose in the railroad industry in the scheduling of freight cars. In this paper we present an

application of his model.

Key-words: dynamic network flows, maximum flow, freight systems

1. Introduction

The theory of flow is one of the most important parts of Combinatorial

Optimization. The static network flow models arises in a number of combinatorial

applications that on the surface might not appear to be optimal flow problems at all.

The problem also arises directly in problems as far reaching as machine scheduling,

the assignment of computer modules to computer processor, tanker scheduling etc.

(Ahuja, Magnanti and Orlin, 1993). However, in some applications, the time is an

essential ingredient (Aronson 1989), (Cai, Sha and Wong, 2007), (Ford and

Fulkerson, 1962), (Hamacher and Tjandra, 2001), (Tjandra, 2003). In this case we

need to use the dynamic network flow model (Wilkinson, 1971).

In Section 2 of this paper we present some notions and results for maximum

flow problem in general dynamic networks. Section 3 deals with a freight system

application for the problem presented in Section 2.

2. Maximum flows in dynamic networks

Dynamic network models arise in many problem settings, including production

distribution systems, economic planning, energy systems, traffic systems, and

building evacuation systems.

1 Transilvania University of Braşov, camelia.s@unitbv.ro