The reliable hub-and-spoke design problem: Models and algorithms

Abstract

This paper presents a study on reliable single and multiple allocation hub-and-spoke network design problems where disruptions at hubs and the resulting hub unavailability can be mitigated by backup hubs and alternative routes. It builds nonlinear mixed integer programming models and presents linearized formulas. To solve those difficult problems, Lagrangian relaxation and Branch-and-Bound methods are developed to efficiently obtain optimal solutions. Numerical studies of proposed solution methods on practical instances are reported, along with a few insights of system design.Key words: reliable network design; hub-and-spoke; Lagrangian Relaxation; Branch-and- Bound Background and MotivationThe hub-and-spoke system has been widely employed in various industrial applications.It is a fully connected network with material/information flow between any two nodes being processed at a small number of critical nodes (i.e. hubs) and moved through interhub links. Compared with the one built with the point-to-point structure, it has a much smaller number of links. Also, because traffic flows are consolidated by hubs and interhub links, significantly less operating cost can be achieved because of economies of scale.Given such advantages, industry companies including airlines, logistics companies, and telecommunications firms extensively utilize the hub-and-spoke architecture to reduce the construction and operating costs.

An adaptive large neighborhood search heuristic for solving the reliable multiple allocation hub location problem under hub disruptions

“…In this research one backup hub is selected from the available hub of network for disrupted hub and all of allocated flows of defected hub are allocated to backup hub. An et al (2015) propose a set of reliable hub-and-spoke network design models where the selection of backup hubs and alternative routes are taken into consideration to proactively handle hub disruptions. They develop Lagrangian relaxation and Branch-and-Bound methods to solve these nonlinear mixed integer formulation.…”

Finding p-Hub Median Locations: An Empirical Study on Problems and Solution Techniques

“…Let be if ̸ = and 0 otherwise. For the backup assignment, we use the strategy proposed by [26]. They made two major assumptions: first, only single disruptions are considered; second, for the routes with two hubs, the unaffected hub must still be inside the alternative route.…”

“…As a widely used algorithm, Lagrangian relaxation has also been applied to hub location problems [23,26]. In this section, we introduce the procedure of LR for solving hub location problems mostly based on the formulation CSA-P (see (1)- (8)) presented in Section 2.1.…”

“…They decomposed the problem into subproblems with Lagrangian relaxation. Reference [26] proposed new models with the consideration of uncertainties (hub failures and backup hubs) for single and multiple allocation problems. Based on the heuristics proposed by [23], they used Lagrangian relaxation and branch-and-bound method to solve reliable models for these two allocation problems.…”

Scenario-based modeling for multiple allocation hub location problem under disruption risk: multiple cuts Benders decomposition approach

“…Generally, the random disruption can be modeled in two ways: implicit modeling and scenario-based modeling while the second one is more flexible against disruption (Snyder and Daskin 2007). An et al (2015) propose a quadratic implicit model of hub network where at most one hub in a path can be disrupted, and they propose its linearized formulation. To reach a proper network configuration, they propose Lagrangean relaxation and branch and bound solution approaches.…”