On the Hub-And-Spoke Model with Arc Capacity Conatraints (original) (raw)
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Pesquisa Operacional, 2013
The hub-and-spoke network design problem, also known as the hub location problem, aims to find the concentration points in a given network flow so that the sum of the distances of the linkages is minimized. In this work, we compare discrete solutions of this problem, given by the branch-and-cut method applied to the p-hub median model, with continuous solutions, given by the hyperbolic smoothing technique applied to a min-sum-min model. Computational experiments for particular instances of the Brazilian air transportation system, with the number of hubs varying from 2 to 8, are conducted with the support of a discretization heuristic and the Voronoi diagram.
Sādhanā, 2019
For the last twenty five years, hub location problems have become an important research area in the Location Theory. The use of hub and spoke network structure in modern transportation and telecommunication systems has a great effect on this. In hub and spoke systems flows from sources are collected in the hubs, which are generally located centrally and serve as collection and distribution points, and distributed to the destinations again via hubs to use advantages of the economies of scale. In this study, real-life problem of a Turkish public institution is addressed. Different from the studies in the literature, we consider an intermodal transportation network where spoke-to-hub and hub-to-spoke transportation could be either land or air movement while hub-tohub transportation is only air movement. The proposed study differs in some respects from studies in the literature. Firstly, obligation to use of hubs for the flows between origin and destination pairs is relaxed. Secondly, due to the special nature of the problem being addressed not all the nodes are considered to be candidates as hubs, instead some specific nodes are taken into consideration. Lastly, hubs' capacities are made to be affected by the flow not only from hubs but also spokes. The results showed that the proposed model produced a lower total cost compared to the studies in the literature and the current applied method.
The reliable hub-and-spoke design problem: Models and algorithms
Hub-and-spoke structure is widely adopted in industry, especially in transportation and telecommunications applications. Although hub-and-spoke paradigm demonstrates significant advantages in improving network connectivity with less number of routes and saving operating cost, the failure of hubs and reactive disruption management could lead to substantial recovery cost to the operators. Thus, we propose a set of reliable huband-spoke network design models, where the selection of backup hubs and alternative routes are taken into consideration to proactively handle hub disruptions. To solve these nonlinear mixed integer formulations for reliable network design problems, Lagrangian relaxation and Branch-and-Bound methods are developed to efficiently obtain optimal solutions. Numerical experiments are conducted with respect to real data to demonstrate algorithm performance and to show that the resulting hub-and-spoke networks are more resilient to hub unavailability.
Hub Interdiction & Hub Protection problems: Model formulations & Exact Solution methods. (Revised)
2016
In this paper, we present computationally efficient formulations for the hub interdiction problem. The problem is to identify a set of r critical hubs from an existing set of p hubs that when interdicted, results in the greatest disruption cost for the hub-and-spoke network owner. To begin with, the problem is modeled as a bilevel mixed integer linear program. We explore two ways to reduce this bilevel program to single level by replacing the lower level problem with constraints obtained i) using KKT conditions and ii) by exploiting the structure of the problem. Reduction using KKT conditions is straightforward but computationally inefficient in this context. Exploiting the structure of the problem, we propose two alternate forms of closest assignment constraints and study their computational e ffectiveness while solving the problem. We also show the dominance relationship between our proposed closest assignment constraints and the only other version studied in the literature. Our c...
Capacitated Hub Routing Problem in Hub-and-Feeder Network Design: Modeling and Solution Algorithm
2015
In this paper, we address the Bounded Cardinality Hub Location Routing with Route Capacity wherein each hub acts as a transshipment node for one directed route. The number of hubs lies between a minimum and a maximum and the hub-level network is a complete subgraph. The transshipment operations take place at the hub nodes and flow transfer time from a hub-level transporter to a spoke-level vehicle influences spoketo- hub allocations. We propose a mathematical model and a branch-and-cut algorithm based on Benders decomposition to solve the problem. To accelerate convergence, our solution framework embeds an efficient heuristic producing high-quality solutions in short computation times. In addition, we show how symmetry can be exploited to accelerate and improve the performance of our method.
Valid inequalities for the single arc design problem with set-ups
We consider a mixed integer set which generalizes two well-known sets: the single node fixedcharge network set and the single arc design set. Such set arises as a relaxation of feasible sets of general mixed integer problems such as lot-sizing and network design problems.
Lagrangean Relaxation for the Capacitated Hub Location Problem with Single Assignment
This paper considers the Capacitated Hub Location Problem with Single Assignment. We propose a Lagrangean Relaxation to obtain tight upper and lower bounds. The lagrangean function that we formulate exploits the structure of the problem and can be decomposed into smaller subproblems that can be solved efficiently. In addition, we present some simple reduction tests, based on the lagrangean relaxation bounds, that allows us to reduce considerably the size of the formulation and thus, to reduce the computational effort. Computational experiments have been performed with both benchmark instances from literature and with some new lager instances. The obtained results are remarkable. For all tested instances (ranging from 10 to 200 nodes) we obtain or improve the best known solution and the obtained duality gaps, between our upper and lower bounds, never exceed 3.4%.
Capacitated Bounded Cardinality Hub Routing Problem: Model and Solution Algorithm
arXiv (Cornell University), 2017
In this paper, we address the Bounded Cardinality Hub Location Routing with Route Capacity wherein each hub acts as a transshipment node for one directed route. The number of hubs lies between a minimum and a maximum and the hub-level network is a complete subgraph. The transshipment operations take place at the hub nodes and flow transfer time from a hub-level transporter to a spoke-level vehicle influences spoketo-hub allocations. We propose a mathematical model and a branch-and-cut algorithm based on Benders decomposition to solve the problem. To accelerate convergence, our solution framework embeds an efficient heuristic producing high-quality solutions in short computation times. In addition, we show how symmetry can be exploited to accelerate and improve the performance of our method.
Multiple allocation hub-and-spoke network design under hub congestion
Computers & Operations Research, 2009
The multiple allocation hub-and-spoke network design under hub congestion problem is addressed in this paper. A non-linear mixed integer programming formulation is proposed, modeling the congestion as a convex cost function. A generalized Benders decomposition algorithm has been deployed and has successfully solved standard data set instances up to 81 nodes. The proposed algorithm has also outperformed a commercial leading edge non-linear integer programming package. The main contribution of this work is to establish a compromise between the transportation cost savings induced by the economies of scale exploitation and the costs associated with the congestion effects.
A GENERAL MIXED-INTEGER NONLINEAR OPTIMIZATION MODEL FOR HUB NETWORK DESIGN
A general discrete hub network model that accounts for fixed, capacity, and operating/congestion costs on links and at hubs, with both economies and diseconomies of scale, selects hubs and links, determines their capacities, and assigns O-D flows over paths, while minimizing all system costs. Initially formulated as a mixed-integer non-linear program, the model is transformed into a mixed-integer linear program through the linearization of the capacity and congestion cost functions. The methodology is illustrated by an application to a small-scale network with hypothetical data. Extensive sensitivity analyses are carried out to assess the trade-offs between the different link and hub costs.