Integer programming formulations of discrete hub location problems

The Benders decomposition algorithm: A literature review

Survey: Hub location problems: A review of models, classification, solution techniques, and applications

Last year was the 25th anniversary of two seminal transportation hub location publications, which appeared in 1986 in Transportation Science and Geographical Analysis. Though there are related hub location and network design articles that predate these works, the 1986 publications provided a key impetus for the growth of hub location as a distinct research area. This paper is not intended as a comprehensive review of hub location literature; rather, our goal is to reflect on the origins of hub location research, especially in transportation, and provide some commentary on the present status of the field. We provide insight into early motivations for analyzing hub location problems and describe linkages to problems in location analysis and network design. We also highlight some of the most recent research, discuss some shortcomings of hub location research and suggest promising directions for future effort.

Twenty-Five Years of Hub Location Research

We consider a bilevel model where the leader wants to maximize revenues from a taxation scheme, while the follower rationally reacts to those tax levels. We focus our attention on the special case of a toll-setting problem defined on a multicommodity transportation network. We show that the general problem is NP-complete, while particular instances are polynomially solvable. Numerical examples are given.

A Bilevel Model of Taxation and its Application to Optimal Highway Pricing

http://neumann.hec.ca/chairedistributique/common/SUHL.pdf

Stochastic Uncapacitated Hub Location

This paper describes an exact algorithm capable of solving large-scale instances of the well-known uncapacitated hub location problem with multiple assignments. The algorithm applies Benders decomposition to a strong path-based formulation of the problem. The standard decomposition algorithm is enhanced through the inclusion of several features such as the use of a multicut reformulation, the generation of strong optimality cuts, the integration of reduction tests, and the execution of a heuristic procedure. Extensive computational experiments were performed to evaluate the efficiency and robustness of the algorithm. Computational results obtained on classical benchmark instances (with up to 200 nodes) and on a new and more difficult set of instances (with up to 500 nodes) confirm the efficiency of the algorithm.

/pdf/benders-decomposition-for-large-scale-uncapacitated-hub-tvj2w4qqkv.pdf

Benders Decomposition for Large-Scale Uncapacitated Hub Location

Hub Location Problems (HLPs) lie at the heart of network design planning in transportation and telecommunication systems. They are a challenging class of optimization problems that focus on the location of hub facilities and on the design of hub networks. This chapter overviews the key distinguishing features, assumptions and properties commonly considered in HLPs. We highlight the role location and network design decisions play in the formulation and solution of HLPs. We also provide a concise overview of the main developments and most recent trends in hub location research. We cover various topics such as hub network topologies, flow dependent discounted costs, capacitated models, uncertainty, dynamic and multi-modal models, and competition and collaboration. We also include a summary of the most successful integer programming formulations and efficient algorithms that have been recently developed for the solution of HLPs.

Ivan Contreras

Papers

Stochastic Uncapacitated Hub Location

Benders Decomposition for Large-Scale Uncapacitated Hub Location

Hub Location Problems

The Tree of Hubs Location Problem

General network design: A unified view of combined location and network design problems