## Rand Memoranda, Issue 5302 |

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allocation strategy allotted unit analysis analytic expressions Assume it holds computed define delivered to terminal demand occurs discontinuity of Y(N dual—purpose unit EFFECTIVENESS RATIO f max holds for n hypothesis of induction induction hypothesis inequality integration with step interval inventory remaining Lemma Let Y(n maximize probability MAXIMUM EXPECTED NUMBER meeting all demands monotone decreasing monotone increasing function number of demands number of encounters number of units o(At optimum point of continuity point of discontinuity PQ(t prob 0 demands probability of meeting probability of success probability of successfully purpose units RAND Corporation random variables rigorous mathematical static strategy strategy function success probability successfully meeting sufficiently large sufficiently small terminal demand theorem follows theorem is true true for n types of units unit fails units are allotted units are available units available units delivered UNITS TO TERMINAL unreliable demand values versus zero