Optimal Control of a Graded Manpower System

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Abstract
We consider a fractional flow model of a graded manpower system and develop algorithms for calculating optimal control policies in four situations: (i) finite time horizons with no constraints on staff distributions, (ii) finite time horizon with constraints on final staff distribution, (iii) infinite horizon with constraints on staff distribution and (iv) problems with a nonstationary transient stage and an infinite stationary stage. In each case results developed in solving the simpler problems are useful in analyzing more complicated situations. In addition to providing computational procedures we apply the algorithms to a three rank model and discuss the possible uses and limitations of our procedure.

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