摘要：Abstract This paper deals with the simultaneous production planning and quality control problem in manufacturing systems with unreliable single machine responding to a single product type demand. The machine is subject to random failures and repairs, and deteriorates with its age while in operation. This deterioration manifests by imperfect repairs and is characterized to increase the failures rates and decrease the quality of the parts produced. Because the availability and the quality of the parts of the machine decrease with repair activities, the introduction of the option to replace the machine will be taken to completely restore the age of the machine. When the replacement action is selected, the machine is replaced by a new identical one. The objective of this research is to find the simultaneous production and replacement policy under quality and failures deteriorations. The optimal solution is established in order to minimize the discounted total cost including the inventory holding, backlog, production, repair and replacement costs over an infinite planning horizon and satisfy the customer demand. Due to imperfect repairs, the semi-Markov processes are more appropriate to describe the systems subject to deteriorations caused by the machine aging. Optimality conditions are developed using the optimal control theory based on stochastic dynamic programming. Numerical methods are used to obtain the optimal control policies (production rate and replacement policies). Finally, an illustrative example and a sensitivity analysis are provided to confirm the structure of the obtained optimal control policies.
