Optimal maintenance and production rates for a machine: A nonlinear economic control problem

Abstract

This paper derives qualitative properties (such as monotonicity and limiting behavior) of the optimal policy for a class of nonlinear optimal control problems. 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 for this is the problem of determining the optimal production and maintenance rates for a machine when the effectiveness of the maintenance expenditures is subject to decreasing returns to scale, and where the marginal deterioration is an increasing function of the production rate. A stability analysis in both of the phase planes state-costate and state-control is carried out and it is shown that the Jacobian determinants in both cases are identical. Also provided is a sensitivity analysis of the equilibrium. Furthermore other applications of the model in the areas of advertising and pollution control models are proposed.