A conic quadratic formulation for a class of convex congestion functions in network flow problems
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.
Year of publication: |
2011
|
---|---|
Authors: | Gürel, Sinan |
Published in: |
European Journal of Operational Research. - Elsevier, ISSN 0377-2217. - Vol. 211.2011, 2, p. 252-262
|
Publisher: |
Elsevier |
Keywords: | Integer programming Network flows Second-order cone programming Capacity expansion Congestion costs Convex increasing power functions |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
A strong conic quadratic reformulation for machine-job assignment with controllable processing times
Aktürk, M. Selim, (2009)
-
A conic quadratic formulation for a class of convex congestion functions in network flow problems
Gürel, Sinan, (2011)
-
An anticipative scheduling approach with controllable processing times
Gürel, Sinan, (2010)
- More ...