Tight linear programming relaxations of uncapacitated p-hub median problems

Skorin-Kapov, Darko; Skorin-Kapov, Jadranka; O’Kelly, Morton E.

doi:10.1016/0377-2217(95)00100-x

Cited by 367 publications

(228 citation statements)

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“…The -hub median problem aims to select hub facilities from a set of available candidates, to allocate spoke nodes to hubs and to simultaneously route freight flows. There are two kinds of mathematical models to formulate the hub-and-spoke network problem, including path-based mixed integer linear programming models with four-dimensional variables (e.g., [9][10][11][12]) and origin-based mixed integer linear programming models with three-dimensional variables (e.g., [13][14][15]). Meng and Wang [3], both, apply a mathematical program with equilibrium constraints model for the intermodal hub-and-spoke network design problem with multiple stakeholders and multitype containers.…”

Section: Literature Reviewmentioning

confidence: 99%

Using Improved Entropy‐Cloud Model to Select High‐Speed Railway Express Freight Train Service Sites

Huang

Shen

2017

Mathematical Problems in Engineering

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High-speed railway (HSR) express freight train service sites selection is critical to the development of China's Third Party Logistics market. In this paper, we formulate an improved entropy-cloud model based approach to solve the HSR express sites selection problem for the first time. The basic data of the indicators, for example, existing railway network conditions, traffic environment, express freight market demand, and policy, will be used as the inputs. We apply improved entropy method to obtain each subindicator's weight. The cloud model will be used to select and classify each station under evaluation.

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Section: Literature Reviewmentioning

confidence: 99%

Using Improved Entropy‐Cloud Model to Select High‐Speed Railway Express Freight Train Service Sites

Huang

Shen

2017

Mathematical Problems in Engineering

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“…[37] propose mixed integer formulations for both SA and MA p-hub HLPs that yield tight linear relaxations.…”

Section: Literature Reviewmentioning

confidence: 99%

“…A similar strategy is also applied to SA p-hub HLP. Pirkul and Schilling [35] propose a Lagrangian relaxation approach to the SA p-hub model presented in Skorin-Kapov et al [37]. By adding a new type of cut constraints, their algorithm is very effective in generating optimal solutions.…”

Section: Literature Reviewmentioning

confidence: 99%

“…So, we can just consider flows with j > i in our study. Next, we present R-SAHLP that generalizes and extends the classical SA hub-and-spoke model developed by [37]. To keep our model trackable and to focus on the impacts of hubs' unavailabilities, our reliable models do not consider the loss of traffic due to spoke disruptions.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Constraints (2)- (5) are classical constraints for SA p-hub problem [37]. Constraints (6) and (8) ensure that the regular hubs and the backup hubs of any flow can only be the nodes chosen to be hubs and the regular hubs and the backup hubs must be different.…”

Section: Literature Reviewmentioning

confidence: 99%

See 2 more Smart Citations

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

An¹,

Zhang²,

Zeng³

2015

Transportation Research Part B: Methodological

108

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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.

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The single allocation problem in the interacting three-hub network

Sohn

Park

2000

Networks

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We consider the single allocation problem in the interacting three‐hub network with fixed hub locations. In the single allocation hub network, the hubs are fully interconnected and each nonhub node has to be connected to exactly one of the hubs. The flows between each pair of nodes are sent using the hubs as intermediate switching points. The problem is to find an optimal allocation of nonhub nodes to the hubs which minimizes the total flow cost. We show that the single allocation problem is NP‐hard as soon as the number of hubs is three, although the problem in a two‐hub system has polynomial time algorithms. This paper provides a mixed integer formulation of the problem and considers the polyhedral properties of it. The formulation can also be used for the single allocation problem with fixed costs for opening links, the three‐terminal cut problem, and the three‐processor distribution problem. Computational experiences are reported for data given in the literature and randomly generated problems. © 2000 John Wiley & Sons, Inc.

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Tight linear programming relaxations of uncapacitated p-hub median problems

Cited by 367 publications

References 8 publications

Using Improved Entropy‐Cloud Model to Select High‐Speed Railway Express Freight Train Service Sites

Using Improved Entropy‐Cloud Model to Select High‐Speed Railway Express Freight Train Service Sites

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

The single allocation problem in the interacting three-hub network

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