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The Constrained Bottleneck Problem in Networks

Author

Listed:
  • O. Berman

    (University of Massachusetts, Boston, Massachusetts)

  • D. Einav

    (Tel-Aviv University, Tel-Aviv, Israel)

  • G. Handler

    (Stanford University, Stanford, California)

Abstract

We consider problems on networks that are captured by two performance measures. One performance measure is any general cost function of a solution; the other is a bottleneck measure that describes the worst (maximum cost) component of the solution. The paper contains algorithms to solve three problems. In one problem, we minimize the bottleneck subject to a constraint on the generalized cost. In the second problem, we minimize the generalized cost subject to a constraint on the bottleneck. In the third problem, we consider the two criteria simultaneously and find all the Pareto optimum solutions. The major result is that the introduction of the bottleneck measure changes the complexity of the original (general cost) problem by a factor which is at most linear in the number of links.

Suggested Citation

  • O. Berman & D. Einav & G. Handler, 1990. "The Constrained Bottleneck Problem in Networks," Operations Research, INFORMS, vol. 38(1), pages 178-181, February.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:1:p:178-181
    DOI: 10.1287/opre.38.1.178
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    Citations

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    Cited by:

    1. Patrick J. Andersen & Charl J. Ras, 2020. "Degree bounded bottleneck spanning trees in three dimensions," Journal of Combinatorial Optimization, Springer, vol. 39(2), pages 457-491, February.
    2. Lara Turner & Abraham Punnen & Yash Aneja & Horst Hamacher, 2011. "On generalized balanced optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 19-27, February.
    3. Y. Wang & H. Yan & C. Sriskandarajah, 1996. "The weighted sum of split and diameter clustering," Journal of Classification, Springer;The Classification Society, vol. 13(2), pages 231-248, September.
    4. Arora, Shalini & Puri, M. C., 1998. "A variant of time minimizing assignment problem," European Journal of Operational Research, Elsevier, vol. 110(2), pages 314-325, October.
    5. de Lima Pinto, Leizer & Bornstein, Cláudio Thomás & Maculan, Nelson, 2009. "The tricriterion shortest path problem with at least two bottleneck objective functions," European Journal of Operational Research, Elsevier, vol. 198(2), pages 387-391, October.

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