On A State-Constrained Control Problem in Optimal Production and Maintenance

Abstract

We consider a control problem introduced by Cho, Abad and Parlar (1993) which “incorporates a dynamic maintenance problem into a pro- duction control model”. For a quadratic production cost function we present a detailed numerical study of optimal control policies for differ- ent final times. The maintenance control is either composed by bang- bang and singular arcs or is purely bang-bang. In the case of a linear production cost, we show that bothproduction and maintenance con- trol are purely bang-bang. A recently developed second order sufficiency test is applied to prove optimality of the computed controls. This test enables us to calculate sensitivity derivatives of switching times with respect to perturbation parameters in thesystem. Furthermore, nu- merical results are presented in the case where a state constraint on the number of good items is added to the control problem.