An Improved Algorithm for Fixed-Hub Single Allocation Problems

  • Dong-Dong Ge
  • Zi-Zhuo Wang
  • Lai Wei
  • Jia-Wei Zhang

DOI: 10.1007/s40305-016-0143-1

Cite this article as:
Ge, DD., Wang, ZZ., Wei, L. et al. J. Oper. Res. Soc. China (2016). doi:10.1007/s40305-016-0143-1


This paper discusses the fixed-hub single allocation problem (FHSAP). In this problem, a network consists of hub nodes and terminal nodes. Hubs are fixed and fully connected; each terminal node is assigned to a single hub which routes all its traffic. The goal is to minimize the cost of routing the traffic in the network. In this paper, we propose a new linear programming (LP) relaxation for this problem by incorporating a set of validity constraints into the classical formulations by Ernst and Krishnamoorthy (Locat Sci 4:139–154, Ann Op Res 86:141–159). A geometric rounding algorithm is then used to obtain an integral solution from the fractional solution. We show that by incorporating the validity constraints, the strengthened LP often provides much tighter upper bounds than the previous methods with a little more computational effort and the solution obtained often has a much smaller gap with the optimal solution. We also formulate a robust version of the FHSAP and show that it can guard against data uncertainty with little costs.


Hub location Network design Linear programming Worst-case analysis 

Mathematics Subject Classification


Funding information

Funder NameGrant NumberFunding Note
National Natural Science Foundation of China
  • 11471025

Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Information Management and EngineeringShanghai University of Finance and EconomicsShanghaiChina
  2. 2.Department of Industrial and Systems EngineeringUniversity of MinnesotaMinneapolisUSA
  3. 3.Stephen M. Ross School of BusinessUniversity of MichiganAnn ArborUSA
  4. 4.Leonard N. Stern School of BusinessNew York UniversityNew YorkUSA

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