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The planar hub location problem: a probabilistic clustering approach

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Abstract

Given the demand between each origin-destination pair on a network, the planar hub location problem is to locate the multiple hubs anywhere on the plane and to assign the traffic to them so as to minimize the total travelling cost. The trips between any two points can be nonstop (no hubs used) or started by visiting any of the hubs. The travel cost between hubs is discounted with a factor. It is assumed that each point can be served by multiple hubs.

We propose a probabilistic clustering method for the planar hub-location problem which is analogous to the method of Iyigun and Ben-Israel (in Operations Research Letters 38, 207–214, 2010; Computational Optmization and Applications, 2013) for the solution of the multi-facility location problem. The proposed method is an iterative probabilistic approach assuming that all trips can be taken with probabilities that depend on the travel costs based on the hub locations. Each hub location is the convex combination of all data points and other hubs. The probabilities are updated at each iteration together with the hub locations. Computations stop when the hub locations stop moving.

Fermat-Weber problem and multi-facility location problem are the special cases of the proposed approach.

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Authors and Affiliations

  1. Department of Industrial Engineering, Middle East Technical University, Ankara, Turkey

    Cem Iyigun

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  1. Cem Iyigun
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Correspondence to Cem Iyigun.

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Iyigun, C. The planar hub location problem: a probabilistic clustering approach. Ann Oper Res 211, 193–207 (2013). https://doi.org/10.1007/s10479-013-1394-4

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