Robust production and maintenance planning in stochastic manufacturing systems

In this paper the authors consider a preventive maintenance and production model of a flexible manufacturing system with machines that are subject to breakdown and repair. The preventive maintenance can be used to reduce the machine failure rates and improve the productivity of the system. The control variables are the rate of maintenance and the rate of production; the objective is to choose a control process that optimizes a robust cost of inventory/shortage, production, and maintenance. The value function is shown to be locally Lipschitz and to satisfy a Hamilton-Jacobi-Isaacs equation. A sufficient condition for optimal control is obtained. Finally, an algorithm is given for solving the optimal control problem numerically