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Technical Note---A Sequential Location Scheme for the Distance-Constrained Multifacility Location Problem on a Tree

Author

Listed:
  • Igor Averbakh

    (Department of Mathematics, Western Washington University, Bellingham, Washington 98225)

  • Oded Berman

    (The Faculty of Management, University of Toronto, Toronto, Ontario M5S 1V4, Canada)

Abstract

The problem of locating p distinguishable facilities on a tree network with n nodes, subject to interfacility distance constraints, is considered. Each facility must be located within its own feasible region, that is selected in advance based on previous analysis. The main difference from the variants of the problem studied earlier is that more general feasible regions are allowed. A sequential location scheme for solving the problem is formulated, and sufficient conditions for the applicability of the scheme are presented. For the special case where the feasible regions are finite (sets of selected nodes of the tree), it is demonstrated that the sufficient conditions can be checked in O ( pn ) time; if they hold, the sequential location scheme can be implemented in O ( np 2 ) time (for the case of finite feasible regions).

Suggested Citation

  • Igor Averbakh & Oded Berman, 1996. "Technical Note---A Sequential Location Scheme for the Distance-Constrained Multifacility Location Problem on a Tree," Transportation Science, INFORMS, vol. 30(3), pages 261-269, August.
    • Handle: RePEc:inm:ortrsc:v:30:y:1996:i:3:p:261-269
    DOI: 10.1287/trsc.30.3.261
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