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On some problems in operations research

  • Ester Samuel (a1)

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Consider an airplane which is at a distance t ≧ 0 from its destination (the distance being measured in time-units) and has n anti-aircraft missiles. The enemy sends its aircraft according to a Poisson process with known parameter, which by redefining the time-scale may, without loss of generality, be taken to be one. When meeting an enemy aircraft, the plane can use, simultaneously, some of its missiles, and it is assumed that the hits are independent random events with known probability 1 > 1 – q > 0. If no missile hits the enemy aircraft, the airplane is shot down with known probability 1 ≧ 1 – u > 0. The case u= 0 is of particular interest. (We have excluded the values q = 0, q = 1 and u= 1 since these yield trivial solutions.)

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[1] Klinger, A. and Brown, T.A. (1968) Allocating unreliable units to random demands. Stochastic Optimization and Control. Edited by Karreman, , Publ. No. 20, Math. Research Center, U.S. Army and Univ. Wisconsin. Wiley, New York.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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