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41 Counterexamples to Property (B) of the Discrete Time Bomber Problem

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  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

Abstract

The discrete time "bomber problem" has been one of the longest standing open problems in operations research. In particular, the validity of one of the natural monotonicity conjectures ― known as property (B) ― has been an unresolved issue since 1968. In this paper we report 41 counterexamples to property (B) of this problem. We have found them by computing the exact solutions for nearly one million pairs of parameter values utilizing the GNU Multiple Precision (GMP) Arithmetic Library. All our counterexamples can readily be verified using a simple Mathematica program included in this paper.

Suggested Citation

  • Takashi Kamihigashi, 2016. "41 Counterexamples to Property (B) of the Discrete Time Bomber Problem," Discussion Paper Series DP2016-23, Research Institute for Economics & Business Administration, Kobe University.
    • Handle: RePEc:kob:dpaper:dp2016-23
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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2016-23.pdf
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    References listed on IDEAS

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    1. Richard Weber, 2013. "ABCs of the bomber problem and its relatives," Annals of Operations Research, Springer, vol. 208(1), pages 187-208, September.
    2. Jay Bartroff & Larry Goldstein & Yosef Rinott & Ester Samuel-Cahn, 2010. "On Optimal Allocation of a Continuous Resource Using an Iterative Approach and Total Positivity," Discussion Paper Series dp530, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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    Cited by:

    1. Krishna Kalyanam & David Casbeer & Meir Pachter, 2020. "A sequential partial information bomber‐defender shooting problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(3), pages 223-235, April.

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