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On the impact of spatial pattern, aggregation, and model parameters in planar Huff-type competitive location and design problems

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Abstract

A chain wants to set up a single new facility in a planar market where similar facilities of competitors, and possibly of its own chain, are already present. Fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational or logit type model. Both the location and the quality (design) of the new facility are to be found so as to maximize the profit obtained for the chain. Several types of constraints and costs are considered. Applying an interval analysis based global optimization method on several spatial patterns in a quasi-real-world environment, the behaviour of optimal solutions is investigated when changes are made in the basic model parameters. The study yields valuable insight for modellers into the impact of spatial pattern and various model parameters of the model on the resulting location and design decision. Spatial patterns differ in distribution of demand, of own and/or competing facilities, and of facility qualities. Studied model parameters include push force effects, investment restrictions and aggregation of demand.

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Authors and Affiliations

  1. Department of Differential Equations, Budapest University of Technology and Economics, Budapest, Hungary

    Boglárka Tóth

  2. MOSI, Department of Mathematics, Operational Research, Statistics and Informations Systems for Management, Vrije Universiteit Brussel, Brussels, Belgium

    Frank Plastria

  3. Department of Statistics and Operations Research, University of Murcia, Murcia, Spain

    José Fernández & Blas Pelegrín

Authors
  1. Boglárka Tóth
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  2. Frank Plastria
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  3. José Fernández
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  4. Blas Pelegrín
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Corresponding author

Correspondence to Boglárka Tóth.

Additional information

An extended version of this paper including additional studies on model parameters and the exact data used in the computational experiments is available at Optimization Online (see Tóth et al. (2008)). This work has been supported by grants from the Ministry of Science and Innovation of Spain (TIN2008-01117, SEJ2005-06273/ECON and ECO2008-00667/ECON), Junta de Andalucía (P08-TIC-3518), and in part by the European Regional Development Fund (ERDF).

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Tóth, B., Plastria, F., Fernández, J. et al. On the impact of spatial pattern, aggregation, and model parameters in planar Huff-type competitive location and design problems. OR Spectrum 31, 601–627 (2009). https://doi.org/10.1007/s00291-008-0163-2

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