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Over the past 20 years, integrated decision making for production systems has gained the interest of researchers and practitioners. Many studies have shown that integrated decision making can lead to substantial amount of savings. Yet, a few research work has been conducted on the areas of integrated maintenance, production and quality in dynamic environments. This paper provides an integrated multi-period, maintenance, production and quality-inspection scheduling model, which is formulated as a Markov decision process. The model minimizes the total expected maintenance, production and quality inspection costs. The structural properties of the proposed model are mathematically investigated and with using sensitivity analysis, practical insights are also provided. We mathematically provide conditions to guarantee that the optimal inspection policy is monotone non-decreasing in the state of the machine. Furthermore, we show that the optimal production policy decreases by one unit as the state of inventory increases by one unit. Sensitivity analysis demonstrates that the production parameters affect both, maintenance and inspection decisions. In addition, the maintenance parameters affect inspection decisions. Finally, it is found that among the inspection parameters (i.e., cost-of-inspection and inspection-errors), type-II error mainly affects maintenance decisions.

Dynamic Maintenance, Production and Inspection Policies, for a Single-Stage, Multi-State Production System