In this article, we present Approximation Schemes for Capacitated Vehicle Routing Problem (CVRP) on several classes of graphs. CVRP, introduced by Dantzig and Ramser in 1959 [ 14 ], are given a graph G=(V,E) with metric edges costs, depot r ∈ V , vehicle bounded capacity Q . The goal is to find minimum cost collection tours the that returns depot, each visiting at most nodes, such they cover al...

We present a branch-and-cut algorithm to solve capacitated network design problems. Given a capacitated network and point-to-point traac demands, the objective is to install more capacity on the edges of the network and route traac simultaneously, so that the overall cost is minimized. We study a mixed-integer programming formulation of the problem and identify some new facet deening inequaliti...

We analyze the probabilistic variation of the multicommodity discrete network design problem named the probabilistic network design problem in which the commodities are generated probabilistically and the objective is to calculate the expected value of all possible network design instances. We extend the a priori strategy which has been successfully applied to the probabilistic variations of th...

Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network, in which vertices express their preferences over their incident edges. A network flow is stable if there is no group of vertices that all could benefit from rero...

The network design problem is a well known optimization problem with applications in telecommunication, infrastructure designs and military operations. This paper devises the first formulation and solution methodology for the multi-commodity k-splittable two-edge disjoint survivable network design problem with capacitated edges and relays. This problem realistically portrays telecommunications ...

We present an algorithmic scheme, which we call the Structured Dantzig-Wolfe decomposition method, that can be used for solving large-scale structured Linear Programs (LPs). The required structure of the LPs is the same as in the original DantzigWolfe approach, that is, a polyhedron over which optimization is “easy” plus a set of “complicating” constraints. Under the hypothesis that an alternat...

This abstract describes a branch, cut, and price (BCP) algorithm for the solution of a class of network design problems with routing and packing constraints that can all be seen as special cases of a general model we will call the Capacitated Node Routing Problem (CNRP). We present several alternative integer programming formulation of the CNRP that can be shown to generalize a number of other ...

Facility location-network design (FLND) problem, which determines the location of facilities and also communication links between the demand and facility nodes, is arisen from the combination of the facility location and network design problems. This paper deals with fuzzy capacitated facility location-network design model which aims to select the facilities and candidate links in a way that yi...