Benders decomposition approach for the robust network design problem with flow bifurcations

Abstract

We consider a network design problem in which flow bifurcations are allowed. The demand data are assumed to be uncertain, and the uncertainties of demands are expressed by an uncertainty set. The goal is to install facilities on the edges at minimum cost. The solution should be able to deliver any of the demand requirements defined in the uncertainty set. We propose an exact solution algorithm based on a decomposition approach in which the problem is decomposed into two distinct problems: (1) designing edge capacities; and (2) checking the feasibility of the designed edge capacities with respect to the uncertain demand requirements. The algorithm is a special case of the Benders decomposition method. We show that the robust version of the Benders subproblem can be formulated as a linear program whose size is polynomially bounded. We also propose a simultaneous cut generation scheme to accelerate convergence of the Benders decomposition algorithm. Computational results on real-life telecommunication problems are reported, and these demonstrate that robust solutions with very small penalties in the objective values can be obtained.

Robust Metric Inequalities for Network Loading Under Demand Uncertainty

“…However, the derivations of the result differ. Hence, the presented proof is an alternative to Lee et al (2013). Further, the LP (9) to compute the rhs of a RLI is comparable to the problem (subsep max ) of Mattia (2013).…”

“…Note that an RLI is similar to a Benders cut given by Lee et al (2013). However, the derivations of the result differ.…”

“…Recently, Koster et al (2013) have studied the RNLP deriving cutset-based valid inequalities whereas Altin et al (2011) used a decomposition property for the RNLP considering the Hose model which allows to avoid the use of metric inequalities. Further, Lee et al (2013) present a Benders decomposition approach for the robust network loading problem.…”

Solving the bifurcated and nonbifurcated robust network loading problem with k‐adaptive routing

“…Many approaches have been presented to solve static routing network design problems, experimenting the effect of different formulations, uncertainty sets or solution methods through robust reformulation, decomposition and/or valid inequalities (as examples, see [1], [2], [23], [24], [21]) As presented, static and dynamic are two extremes routing schemes. In [20], they show that the solution for static routing RN L (splittable or unsplittable, under polyhedral uncertainty set) may be a factor of Ω(log |V |) more than the cost required when using dynamic routing.…”

Single‐commodity stochastic network design under demand and topological uncertainties with insufficient data

“…(35), (37), and (38), u i , i ∈ N + ∪ N = correspond to Eqs. (36) and (39), and w ij , (i, j) ∈ A correspond to Eq. (40).…”