Stochastic manufacturing systems under unknown demand and robust control criteria

This paper is concerned with robust production and maintenance planning in stochastic manufacturing systems. The machine capacity is assumed to be a Markov chain with finite state space, whereas the demand rate is treated as a bounded disturbance that can be deterministic or stochastic as long as it is adapted with respect to the Markov chain representing the machine capacity. The control variables are the rate of maintenance and the rate of production, and the cost function has a minimax structure. It is shown that the value function is locally Lipschitz and satisfies a Hamilton-Jacobi-Isaacs equation. A sufficient condition for optimal control is obtained