Reload cost trees and network design

  • Authors:

  • Ioannis Gamvros;Luis Gouveia;S. Raghavan

  • Affiliations:

  • IBM Software Group, ILOG Optimization, 4400 North First Street, San Jose, California 95134;Departamento de Estatística e Investigação Operacional, Faculdade de Ciências da Universidade de Lisboa, Centro de Investigação Operacional Bloco C6, Piso ...;Robert H. Smith School of Business & Institute for Systems Research, University of Maryland, College Park, Maryland 20742

  • Venue:
  • Networks
  • Year:
  • 2012

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Abstract

In this article, we consider the notion of “reload costs” in network design. Reload costs occur naturally in many different settings including telecommunication networks using diverse technologies. However, reload costs have not been studied extensively in the literature. Given that reload costs occur naturally in many settings, we are motivated by the desire to develop “good” models for network design problems involving reload costs. In this article, and as a first step in this direction, we propose and discuss the reload cost spanning tree problem (RCSTP). We show that the RCSTP is NP-complete. We discuss several ways of modeling network design problems with reload costs. These involve models that expand the original graph significantly—to a directed line graph and a colored graph—to model reload costs. We show that the different modeling approaches lead to models with the same linear programming bound. We then discuss several variations of reload cost spanning tree and network design problems, and discuss both their complexity and models for these variations. To assess the effectiveness of the proposed models to solve RCSTP instances, we present results taken from instances with up to 50 nodes, 300 edges, and nine technologies for several variations of the problem. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011 © 2012 Wiley Periodicals, Inc.