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appointment policy approximately assume assumptions average lifetime basic calculate Chapter cohort column Consider constraints Continuation of Example Continuation of Problem costs cross-sectional data cross-sectional model current stock define distribution dropouts dual linear program enrollment enter equations equilibrium es(t expected value faculty feasible flow conservation flow model flow process forecasting fractional flow freshmen given gives graduates Grinold inflow input flows legacy length of service linear program longitudinal model lower bound manpower classification manpower flow manpower planning manpower system Markov Markov chain matrices P(u Naval Postgraduate School Navy nonnegative obtain one-class one-chain model Operations Research optimal solution optimal value organization personnel pik(u planning models possible present promotion Q matrix random variable reader requirements retirement semester si(t skill rating solved Sophomore stationary policy stochastic matrix stock levels stocks and flows Suppose survivor fractions Table tion U.S. Navy vacancies vector zero