This paper provides an analysis of capacitated network design cut–set polyhedra. We give a complete linear description of the cut–set polyhedron of the single commodity – single facility capacitated network design problem. Then we extend the analysis to single commodity – multifacility and multicommodity – multifacility capacitated network design problems. Valid inequalities described here are ...

This paper presents a comprehensive survey of models and algorithms for multicommodity capacitated network design problems, which are mostly encountered in telecommunications and transportation network planning. These problems are important not only due to the major relevance of their applications, but also because they pose considerable modeling and algorithmic challenges. We present a general...

IEEE 802.16, also known as WiMAX (Worldwide Inter-operability for Microwave Access), is a new wireless access technology for current increasing demand of wireless high-speed broadband service. Efficient and effective deployment of such a network to service an area of users with certain traffic demands is an important network planning problem. This network planning can be formulated in a similar...

The fixed-cost Capacitated Multicommodity Network Design (CMND) problem is a well known NP-hard problem. This paper presents a matheuristic algorithm combining Simulated Annealing (SA) metaheuristic and Simplex method for CMND problem. In the proposed algorithm, a binary array is considered as solution representation and the SA algorithm manages open and closed arcs. Several strategies for open...

We consider the Capacitated Multi-Layer Network Design with Unsplittable demands (CMLND-U) problem. Given a two-layer network and a set of traffic demands, this problem consists in installing minimum cost capacities on the upper layer so that each demand is routed along a unique ”virtual” path (even using a unique capacity on each link) in this layer, and each installed capacity is in turn asso...

Network design applications are prevalent in transportation and logistics. We consider the multicommodity capacitated fixedcharge network design problem (MCND), a generic model that captures three important features of network design applications: the interplay between investment and operational costs, the multicommodity aspect, and the presence of capacity constraints. We focus on mathematical...

An unsplittable flow in a multicommodity network is a flow that routes each commoidty on a single path. In this paper, we introduce the unsplittable flow problem and an open conjecture of Goemans, which states that given a fractional flow it is possible to construct an unsplittable flow that only overflows each edge by at most the maximum demand of a commodity. We provide an intuitive explanati...

We consider the node-capacitated routing problem in an undirected ring network along with its fractional relaxation, the node-capacitated multicommodity flow problem. For the feasibility problem, Farkas’ lemma provides a characterization for general undirected graphs asserting roughly that there exists such a flow if and only if the so-called distance inequality holds for every choice of distan...

We study 0–1 reformulations of the multicommodity capacitated network design problem, which is usually modeled with general integer variables to represent design decisions on the number of facilities to install on each arc of the network. The reformulations are based on the multiple choice model, a generic approach to represent piecewise linear costs using 0–1 variables. This model is improved ...