Abstract
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.
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Notes
In fact, his formulation is for a more general problem, the uncapacitated single allocation p-hub median problem (USApHMP). In this paper, we only confine our discussion to the FHSAP, and thus adapt his formulation (and later formulations) to the FHSAP.
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The authors would like to thank anonymous referees for their helpful comments.
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The first author was supported by the National Natural Science Foundation of China (No. 11471205).
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Ge, DD., Wang, ZZ., Wei, L. et al. An Improved Algorithm for Fixed-Hub Single Allocation Problems. J. Oper. Res. Soc. China 5, 319–332 (2017). https://doi.org/10.1007/s40305-016-0143-1
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DOI: https://doi.org/10.1007/s40305-016-0143-1