Efficient algorithms for the uncapacitated single allocation p-hub median problem

Ernst, Andreas T.; Krishnamoorthy, Mohan

doi:10.1016/s0966-8349(96)00011-3

Cited by 500 publications

(372 citation statements)

References 19 publications

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“…Ernst and Krishnamoorthy [15] and Ernst and Krishnamoorthy [16] formulate SA and MA p-hub HLP, respectively, based on the idea of "multicommodity flow". [37] propose mixed integer formulations for both SA and MA p-hub HLPs that yield tight linear relaxations.…”

Section: Literature Reviewmentioning

confidence: 99%

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

An¹,

Zhang²,

Zeng³

2015

Transportation Research Part B: Methodological

104

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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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Section: Literature Reviewmentioning

confidence: 99%

“…As for the customized algorithm development, Ernst and Krishnamoorthy [17] develop shortest-path based Branch-and-Bound algorithms for the formulations in [15] and [16]. In solving the MA p-hub HLP, the Branch-and-Bound process starts with a cluster of root nodes instead of a single node to improve the initial lower bound.…”

Section: Literature Reviewmentioning

confidence: 99%

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

An¹,

Zhang²,

Zeng³

2015

Transportation Research Part B: Methodological

104

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“…Skorin-Kapov et al [11] propose a new mixed integer formulation whose linear relaxation is tighter than the formulation proposed by Campbell. Ernst and Krishnamoorthy [12] state a different linear integer programming formulation which gives the best computational time and requires fewer variables and constraints. However, in terms of required variables and constraints, Ebery [13] provides the best mathematical formulation.…”

Section: P-hub Median Problemsmentioning

confidence: 99%

“…Using the idea that the multiple allocation p-hub median problem provides a lower bound on the optimal solution of the single allocation p-hub median problem, Campbell [18] proposes two heuristics for the single allocation p-hub median problem. Later, Ernst and Krishnamoorthy [12] develop a simulated annealing heuristic. Pirkul and Schilling [19] propose a Langrangian relaxation method which finds lower and upper bounds in reasonable amount of CPU times.…”

Section: P-hub Median Problemsmentioning

confidence: 99%

“…Ernst and Krishnamoorthy [36] present two new formulations modified versions of the previous mixed integer formulations to the p-hub median problem for the capacitated single allocation hub location problem. In addition, Ebery et al [37] present a formulation based on the one proposed by Ernst and Krishnamoorthy for the multiple allocation p-hub median problem for the multiple allocation capacitated hub location problem.…”

Section: Hub Location Problem With Fixed Costsmentioning

confidence: 99%

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The hub location and routing problem

Bayraktar¹

1996

Location Science

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Hubs are special facilities that consolidate and disseminate flows in many-to-many distribution systems. The hub location problem aims to find locations of hubs and allocate non-hub nodes directly to the hubs. However, this problem is necessary to extend when nodes do not have sufficient demand to justify direct connections between the non-hub nodes to the hubs since such direct connections increase the number of vehicles required and decrease the utilization of vehicles. Hence, it is necessary to construct local tours among the nodes allocated to the same hubs to generate economies of scale and to decrease vehicle costs. Nevertheless, forcing each non-hub node to be visited by a local tour is not the best way to design a many-to-many distribution system. Therefore, in this study two options for each non-hub node are given: (i) either it could be visited by a local tour or (ii) it could be directly connected to a hub without an economy of scale. We develop a mixed integer programming formulation and strengthen it with valid inequalities. We also develop three different Benders formulations as exact solution methods. In addition, we develop a hierarchical heuristic with two phases in order to solve large-sized problem instances. We test the performances of our solution methodologies on CAB and TR data sets. Anahtar sözcükler : ADÜ yer seçimi, rotalama, Benders ayrıştırma yöntemi. Keywordsiv

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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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Efficient algorithms for the uncapacitated single allocation p-hub median problem

Cited by 500 publications

References 19 publications

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

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

The hub location and routing problem

The single allocation problem in the interacting three-hub network

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