A conic quadratic formulation for a class of convex congestion functions in network flow problems

Gurel S.

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, cilt.211, sa.2, ss.252-262, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 211 Sayı: 2
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.ejor.2010.12.018
  • Dergi Adı: EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.252-262
  • Anahtar Kelimeler: Integer programming, Network flows, Second-order cone programming, Capacity expansion, Congestion costs, Convex increasing power functions, ALGORITHMS, ASSIGNMENT, CAPACITY
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this paper we consider a multicommodity network flow problem with flow routing and discrete capacity expansion decisions. The problem involves trading off congestion and capacity assignment (or expansion) costs. In particular, we consider congestion costs involving convex, increasing power functions of flows on the arcs. We first observe that under certain conditions the congestion cost can be formulated as a convex function of the capacity level and the flow. Then, we show that the problem can be efficiently formulated by using conic quadratic inequalities. As most of the research on this problem is devoted to heuristic approaches, this study differs in showing that the problem can be solved to optimum by branch-and-bound solvers implementing the second-order cone programming (SOCP) algorithms. Computational experiments on the test problems from the literature show that the continuous relaxation of the formulation gives a tight lower bound and leads to optimal or near optimal integer solutions within reasonable CPU times. (C) 2011 Elsevier B.V. All rights reserved.