Abstract
This paper discusses a class of nonlinear optimal control problems for which qualitative properties of the optimal policy (monotonicity, limiting behavior) can be derived. The problem structure is characteristic of certain economic investment problems where two control instruments influence the rate of deterioration of a capital good. An example of an economic problem of this type is the determination of the optimal running speed and maintenance policy of a machine when the effectiveness of maintenance is subject to decreasing marginal efficiency and if the marginal attrition brought about by increasing the running speed is increasing.
By means of a stability analysis in the phase planes state-costate and state-control qualitative properties of the optimal policy are derived. The results for infinite horizon problems, for instance, indicate that the optimal decision rule is one where the maintenance expenditures (running speed) decrease (increases) with the quality level of the machine.
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© 1982 D. Reidel Publishing Company
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Hartl, R. (1982). Optimal control of concave economic models with two control instruments. In: Feichtinger, G., Kall, P. (eds) Operations Research in Progress. Theory and Decision Library, vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7901-7_18
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DOI: https://doi.org/10.1007/978-94-009-7901-7_18
Publisher Name: Springer, Dordrecht
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