A Compact Linearisation of Euclidean Single Allocation Hub Location Problems

Meier, J. Fabian; Clausen, Uwe; Rostami, Borzou; Buchheim, Christoph

doi:10.1016/j.endm.2016.03.006

Cited by 9 publications

(4 citation statements)

References 5 publications

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“…Results obtained by solving the USApHMP for the AP data set using the proposed Benders decomposition algorithm are presented in Table 8. We also included the CPU times of solving the same instances by the row generation algorithm presented in Meier et al (2016).…”

Section: Numerical Results For the Usaphmpmentioning

confidence: 99%

“…The authors compared their TS algorithm with that of Silva and Cunha (2009) and showed that their algorithm was able to find best known solutions for all standard test problems in short computational time. Meier et al (2016) and Meier and Clausen (2017) proposed a row generation (RG) algorithm for solving the single allocation HLPs assuming that the transportation costs between the hubs are proportional to the corresponding Euclidean distances. This assumption enabled them to construct a new linearization method for the quadratic terms of the single allocation HLP models and incorporate it into the RG procedure for solving instances of up to 200 nodes to optimality.…”

Section: Literature Reviewmentioning

confidence: 99%

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Benders Decomposition Algorithms for Two Variants of the Single Allocation Hub Location Problem

Ghaffarinasab

Kara

2018

Netw Spat Econ

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The hub location problem (HLP) is a special type of the facility location problem with numerous applications in the airline industry, postal services, and computer and telecommunications networks. This paper addresses two basic variants of the HLP, namely the uncapacitated single allocation hub location problem (USAHLP) and the uncapacitated single allocation p-hub median problem (USApHMP). Exact solution procedures based on Benders decomposition algorithm are proposed to tackle large sized instances of these problems. The standard Benders decomposition algorithm is enhanced through implementation of several algorithmic refinements such as using a new cut disaggregation scheme, generating strong optimality cuts, and an efficient algorithm to solve the dual subproblems. Furthermore, a modern implementation of the algorithm is used where a single search tree is established for the problem and Benders cuts are successively added within a branch-and-cut framework. Extensive computational experiments are conducted to examine the efficiency of the proposed algorithms. We have been able to solve all the instances of the problems from all three main data sets of the HLP to optimality in reasonable computational times.

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Section: Numerical Results For the Usaphmpmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Benders Decomposition Algorithms for Two Variants of the Single Allocation Hub Location Problem

Ghaffarinasab

Kara

2018

Netw Spat Econ

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“…On the exact methods side, recent successful approaches have been presented. Meier and Clausen constructed linearizations from the Euclidean structure presented in famous instances of HLPs, which lead to compact formulations with few variables. The authors tested their approach on instances with up to 200 nodes.…”

Section: Literature Review On Uncapacitated Single Allocation P‐hub Mmentioning

confidence: 99%

A 2‐stage biased‐randomized iterated local search for the uncapacitated single allocation p‐hub median problem

Fernandez

Ferone

Juan

et al. 2018

Trans Emerging Tel Tech

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The hub location problem has gained attention over the last decades. In telecommunications network, a hub is a place of concurrence in where the work of the network is centralized with the purpose of delivering out the data that arrives from one or more directions to other destinations. There are different versions of the hub location problem depending upon (1) the existence or not of restrictions on the capacity related to the volume of flow a hub is allowed to support, (2) the existence or not of a set‐up cost associated with selecting any node as a hub, etc. In these types of configurations, the hubs serve as connection point between 2 installations, allowing, in this way, to replace a large amount of direct connections between all pair of the nodes, therefore, minimizing the total transportation cost of the network. Thus, this work proposes a 2‐stage metaheuristic based on the combination of biased‐randomized technique with an iterated local search framework for solving the uncapacitated single allocation p‐hub median problem, with computational results that validate the methodology for large‐size instances from the literature.

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“…(), and a new linearization technique by Meier et al. (). For a more complete and also historical introduction to different kinds of hub location problems, the reader is referred to the paper by Campbell and O'Kelly ().…”

Section: Introductionmentioning

confidence: 99%

An improved mixed integer program for single allocation hub location problems with stepwise cost function

Meier

2016

Int Trans Operational Res

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Recently, a new model for the uncapacitated single allocation p-hub median problem was defined, which uses a more realistic cost structure. Instead of measuring the transport costs as a linear function of the volume, integer variables for the number of used vehicles are introduced. This leads to a more precise model if the number of vehicles is low and capacity utilization plays a major role. We will introduce a new mixed integer program formulation of the problem that uses fewer variables but more constraints. This study shows its numerical advantages.

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A Compact Linearisation of Euclidean Single Allocation Hub Location Problems

Cited by 9 publications

References 5 publications

Benders Decomposition Algorithms for Two Variants of the Single Allocation Hub Location Problem

Benders Decomposition Algorithms for Two Variants of the Single Allocation Hub Location Problem

A 2‐stage biased‐randomized iterated local search for the uncapacitated single allocation p‐hub median problem

An improved mixed integer program for single allocation hub location problems with stepwise cost function

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