In this paper, we study the approximability of the capacitated network design problem (Cap-NDP) on undirected graphs: GivenG = (V,E) with non-negative costs c and capacities u on its edges, sourcesink pairs (si, ti) with demand ri, the goal is to find the minimum cost subgraph where the minimum (si, ti) cut with u-capacities is at least ri. When u ≡ 1, we get usual SNDP for which Jain gave a 2-...

Benders decomposition has been widely used for solving network design problems. In this paper, we use a branch-and-cut algorithm to improve the separation procedure of Gabrel et al. and Knippel et al. for capacitated network design. We detail experiments on bilayer networks, comparing with Knippel’s previous results.

This paper examines the effect of the poor road transportation network on crop production in one of the rural agrarian local government of Kwara State, Nigeria. A well-structured interview schedule was conducted to elicit information from 120 crop farmers using a two-stage sampling technique. Findings from the study revealed that the poor road transportation network in their area had led to a r...

An effective evaluation of transportation network efficiency could offer guidance for the optimal control of urban traffic. Based on the introduction and related mathematical analysis of three quantitative evaluation methods for transportation network efficiency, this paper compares the information measured by them, including network structure, traffic demand, travel choice behavior and other f...

This document discusses the aspects of network design.First a brief introduction of network design will be given.Then various types of assignment techniques will be discussed including the mathematical formulation and numerical illustration of the important ones.Then the concept of bilevel programming and few examples will be presented.Finally one such example, namely the network capacity expan...

A discomforting reality has materialized on the transportation scene: our existing air and ground infrastructures will not scale to meet our nation’s 21PP century demands and expectations for mobility, commerce, safety, and security. The consequence of inaction is diminished quality of life and economic opportunity in the 21PP century. Clearly, new thinking is required for transportation that c...

We consider a capacity expansion problem arising in the design of telecommunication networks. The problem is to install capacity on links of the network so as to meet customer demand while minimizing total costs incurred. When studying this and related problems it is customary to assume that point to point demands are given. This will not be the case in practice, however, since future demand is...

We present a branch-and-price-and-cut algorithm for solving large-scale instances of the multicommodity capacitated fixed-charge network design problem. The restricted master problem solved at each column generation iteration is obtained directly from the compact arc-based model by considering only a subset of the commodity flow variables. The pricing subproblem corresponds to a Lagrangian rela...

We consider a mixed integer set which generalizes two well-known sets: the single node fixedcharge network set and the single arc design set. Such set arises as a relaxation of feasible sets of general mixed integer problems such as lot-sizing and network design problems. We derive several families of valid inequalities that, in particular, generalize the arc residual capacity inequalities and ...

We study the polyhedra of splittable and unsplittable single arc{set relaxations of multicommodity ow capacitated network design problems. We investigate the optimization problems over these sets and the separation and lifting problems of valid inequalities for them. In particular, we give a linear{time separation algorithm for the residual capacity inequalities 19] and show that the separation...