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2-Facility manifold location routing problem

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Abstract

The location routing problem (LRP), known to be the combination of the facility location and vehicle routing problems, is solved in the literature by either assuming planar or spherical surfaces. In this work, the manifold location routing problem (MLRP), that is an LRP on Riemannian manifold surfaces, is explained for the 2-facility (2-MLRP) case with the corresponding heuristic algorithm solution. The 2-MLRP problem is a mixed integer non-linear programming problem that is determined to be NP-hard. Special cases of MLRP include LRP on planar surfaces, when the manifold’s curvature is 0, and LRP on spherical surfaces when the curvature of the manifold is 1.

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Acknowledgments

Dr. Theodore Trafalis was supported by RSF Grant 14-41-00039 and he conducted research at National Research University Higher School of Economics.

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Authors and Affiliations

  1. School of Engineering, Quinnipiac University, Hamden, CT, USA

    Emre Tokgöz

  2. School of Industrial and Systems Engineering, University of Oklahoma, Norman, OK, USA

    Theodore B. Trafalis

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  1. Emre Tokgöz
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  2. Theodore B. Trafalis
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Correspondence to Emre Tokgöz.

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Tokgöz, E., Trafalis, T.B. 2-Facility manifold location routing problem. Optim Lett 11, 389–405 (2017). https://doi.org/10.1007/s11590-015-0984-2

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  • DOI: https://doi.org/10.1007/s11590-015-0984-2

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