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Aggregation without Loss of Optimality in Competitive Location Models

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  • Frank Plastria

  • Lieselot Vanhaverbeke

Abstract

In the context of competitive facility location problems demand points often have to be aggregated due to computational intractability. However, usually this spatial aggregation biases the value of the objective function and the optimality of the solution cannot be guaranteed for the original model. We present a preprocessing aggregation method to reduce the number of demand points which prevents this loss of information, and therefore avoids the possible loss of optimality. It is particularly effective in the frequent situation with a large number of demand points and a comparatively low number of potential facility sites, and coverage defined by spatial nearness. It is applicable to any spatial consumer behaviour model of covering type. This aggregation approach is applied in particular to a Competitive Maximal Covering Location Problem and to a recently developed von Stackelberg model. Some empirical results are presented, showing that the approach may be quite effective. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Frank Plastria & Lieselot Vanhaverbeke, 2007. "Aggregation without Loss of Optimality in Competitive Location Models," Networks and Spatial Economics, Springer, vol. 7(1), pages 3-18, March.
    • Handle: RePEc:kap:netspa:v:7:y:2007:i:1:p:3-18
    DOI: 10.1007/s11067-006-9004-5
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    References listed on IDEAS

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    1. Plastria, Frank, 2001. "Static competitive facility location: An overview of optimisation approaches," European Journal of Operational Research, Elsevier, vol. 129(3), pages 461-470, March.
    2. Plastria, Frank, 2002. "Formulating logical implications in combinatorial optimisation," European Journal of Operational Research, Elsevier, vol. 140(2), pages 338-353, July.
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    Cited by:

    1. Nicole Adler & Alfred Hakkert & Jonathan Kornbluth & Tal Raviv & Mali Sher, 2014. "Location-allocation models for traffic police patrol vehicles on an interurban network," Annals of Operations Research, Springer, vol. 221(1), pages 9-31, October.
    2. Pelegrín, Blas & Fernández, Pascual & García Pérez, María Dolores, 2015. "On tie breaking in competitive location under binary customer behavior," Omega, Elsevier, vol. 52(C), pages 156-167.
    3. Stephanie A. Snyder & Robert G. Haight, 2016. "Application of the Maximal Covering Location Problem to Habitat Reserve Site Selection," International Regional Science Review, , vol. 39(1), pages 28-47, January.
    4. Mamta Mishra & Surya Prakash Singh & Manmohan Prasad Gupta, 2024. "Two phase algorithm for bi-objective relief distribution location problem," Annals of Operations Research, Springer, vol. 335(3), pages 1363-1399, April.
    5. Paul Berglund & Changhyun Kwon, 2014. "Solving a Location Problem of a Stackelberg Firm Competing with Cournot-Nash Firms," Networks and Spatial Economics, Springer, vol. 14(1), pages 117-132, March.

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