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Facility Dispersion Problems Under Capacity and Cost Constraints

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  • Daniel J. Rosenkrantz

    (University at Albany—State University of New York)

  • Giri K. Tayi

    (University at Albany—State University of New York)

  • S.S. Ravi

    (University at Albany—State University of New York)

Abstract

The MAX-MIN dispersion problem, which arises in the placement of undesirable facilities, involves selecting a specified number of sites among a set of potential sites so as to maximize the minimum distance between any pair of selected sites. We consider different versions of this dispersion problem where each potential site has an associated storage capacity and a storage cost. A typical problem in this context is to choose a subset of potential sites so that the total capacity of the chosen sites is at least a given value, the total storage cost is within the specified budget and the minimum distance between any pair of chosen sites is maximized. Since these constrained optimization problems are NP-hard in general, we consider whether there are efficient approximation algorithms for them with good performance guarantees. Our results include approximation algorithms for some versions, approximation schemes for some geometric versions and polynomial algorithms for special cases. We also present results that bring out the intrinsic difficulty of obtaining near-optimal solutions to some versions.

Suggested Citation

  • Daniel J. Rosenkrantz & Giri K. Tayi & S.S. Ravi, 2000. "Facility Dispersion Problems Under Capacity and Cost Constraints," Journal of Combinatorial Optimization, Springer, vol. 4(1), pages 7-33, March.
    • Handle: RePEc:spr:jcomop:v:4:y:2000:i:1:d:10.1023_a:1009802105661
    DOI: 10.1023/A:1009802105661
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    Cited by:

    1. Juan F. Gomez & Javier Panadero & Rafael D. Tordecilla & Juliana Castaneda & Angel A. Juan, 2022. "A Multi-Start Biased-Randomized Algorithm for the Capacitated Dispersion Problem," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    2. Jia Wang & Shiyan Hu, 2013. "A linear time approximation scheme for computing geometric maximum k-star," Journal of Global Optimization, Springer, vol. 55(4), pages 849-855, April.
    3. Martí, Rafael & Martínez-Gavara, Anna & Pérez-Peló, Sergio & Sánchez-Oro, Jesús, 2022. "A review on discrete diversity and dispersion maximization from an OR perspective," European Journal of Operational Research, Elsevier, vol. 299(3), pages 795-813.

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