The single allocation problem in the interacting three-hub network

Abstract

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.

Network hub location problems: The state of the art

“…They presented a mixed integer formulation for a model with fixed hub locations where fixed costs for opening links are also considered. Another study by the same authors (Sohn and Park, 2000) focuses on the single allocation problem on a three-hub network with fixed hub locations. They provided a mixed integer formulation and studied its polyhedral properties.…”

Robust optimization approach to capacitated single and multiple allocation hub location problems

“…In this model there is no direct link among non-hub nodes and flow just distributed in the network through the hubs' linking. This is the case, for example in Abdinnour-Helm (1998), Chen (2007, Correia et al (2010b), Costa et al (2007), de Camargo and Miranda (2012, Ebery (2001), Krishnamoorthy (1996, 1999), Ilić et al (2010), Iwasa et al (2009), Kratica et al (2007, Labbé and Yaman (2004), Labbé et al (2005), Pirkul and Schilling (1998), Puerto et al (2011), Puerto et al (2013, Randall (2008), Silva andCunha (2009), Skorin-Kapov andSkorin-Kapov (1994), and Sohn and Park (2000). In the multiple allocation model, several nodes will be selected as a hub and other nodes, namely non-hub nodes (spoke), can connect to more than one hub.…”

The p-hub Model with Hub-catchment Areas, Existing Hubs, and Simulation: A Case Study of Serbian Intermodal Terminals

“…Ernst and Krishnamoorthy (1998) presented MILP formulations for the multiple allocation p-hub median problem. Sohn and Park (2000) proposed a mixed integer programming formulation for the single allocation problem in the three-hub system, and Hamacher et al (2000) examined the feasibility polyhedron of the uncapacitated hub location problem with multiple allocation. Most recently, Alumur and Kara (2008) included some recent trends of hub-location models, and provided a synthesis of the literature in this area, citing more than 100 papers related to hub location problems.…”