Journal ArticleDOI
Modeling and Solving the Two-Facility Capacitated Network Loading Problem
TLDR
The results show that strong cutting planes can be an effective modeling and algorithmic tool for solving problems of the size that arise in the telecommunications industry.Abstract:
This paper studies a topical and economically significant capacitated network design problem that arises in the telecommunications industry. In this problem, given point-to-point communication demand in a network must be met by installing loading capacitated facilities on the arcs: Loading a facility incurs an arc specific and facility dependent cost. This paper develops modeling and solution approaches for loading facilities to satisfy the given demand at minimum cost. We consider two approaches for solving the underlying mixed integer program: a Lagrangian relaxation strategy, and a cutting plane approach that uses three classes of valid inequalities that we identify for the problem. We show that a linear programming formulation that includes these inequalities always approximates the value of the mixed integer program at least as well as the Lagrangian relaxation bound. Our computational results on a set of prototypical telecommunication data show that including these inequalities considerably improves the gap between the integer programming formulation and its linear programming relaxation: from an average of 25% to an average of 8%. These results show that strong cutting planes can be an effective modeling and algorithmic tool for solving problems of the size that arise in the telecommunications industry.read more
Citations
More filters
Journal ArticleDOI
Service network design in freight transportation
TL;DR: A state-of-the-art review of service network design modelling efforts and mathematical programming developments for network design is presented and a new classification ofservice network design problems and formulations is introduced.
Journal ArticleDOI
A survey on benders decomposition applied to fixed-charge network design problems
TL;DR: Network design problems concern the selection of arcs in a graph in order to satisfy, at minimum cost, some flow requirements, usually expressed in the form of origin-destination pair demands.
Journal ArticleDOI
Cutting planes in integer and mixed integer programming
TL;DR: This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs and the use of valid inequalities for classes of problems with structure, such as network design, is explored.
Proceedings ArticleDOI
Strengthening integrality gaps for capacitated network design and covering problems
TL;DR: The authors show that by adding additional inequalities, the ratio between the optimal integer solution and the optimal solution to the linear program relaxation can be improved significantly, and provide a polynomial-time approximation algorithm to achieve this bound.
Book ChapterDOI
Multicommodity Capacitated Network Design
TL;DR: Network design models have wide applications in telecommunications and transportation planning and the objective is to determine the optimal amounts of flows to be routed and the facilities to be installed.
References
More filters
Book
Integer and Combinatorial Optimization
TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.
Journal ArticleDOI
The Lagrangian Relaxation Method for Solving Integer Programming Problems
TL;DR: This paper is a review of Lagrangian relaxation based on what has been learned in the last decade and has led to dramatically improved algorithms for a number of important problems in the areas of routing, location, scheduling, assignment and set covering.
Journal ArticleDOI
The ellipsoid method and its consequences in combinatorial optimization
TL;DR: The method yields polynomial algorithms for vertex packing in perfect graphs, for the matching and matroid intersection problems, for optimum covering of directed cuts of a digraph, and for the minimum value of a submodular set function.
Journal ArticleDOI
Network Design and Transportation Planning: Models and Algorithms
TL;DR: It is shown that many of the most celebrated combinatorial problems that arise in transportation planning are specializations and variations of a generic design model, Consequently, the network design concepts described in this paper have great potential application in a wide range of problem settings.
Related Papers (5)
Capacitated Network Design—Polyhedral Structure and Computation
Daniel Bienstock,Oktay Günlük +1 more