On robust design for a class of failure prone manufacturing systems

Abstract

This paper concerns itself with the development of robust production and maintenance planning in manufacturing systems. Taking robustness into consideration, a new model for failure prone flexible manufacturing system with machines subject to breakdown and repair is proposed and analyzed. 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. Under suitable conditions, it is shown that the value function is locally Lipschitz and satisfies a Hamilton-Jacobi-Isaacs (HJI) equation. A sufficient condition for optimal control is obtained. Finally, an algorithm is given for solving the optimal control problem numerically.