Production and preventive maintenance control in a stochastic manufacturing system

This paper considers the problem of production and preventive maintenance control in a stochastic manufacturing system. The system is subject to multiple uncertainties such as random customer demands, machine failure and repair, and stochastic processing times. A threshold-type policy is proposed to control the production rate and the preventive maintenance operation simultaneously. The explicit form of the stationary distribution of the system state is derived analytically and used to produce the formula for various steady-state performance measures. The optimal threshold values can then be obtained by optimising the relevant formula. Numerical examples demonstrate that the proposed threshold policy is indeed optimal or extremely close to the optimal policy in a range of scenarios.