Optimal reliability, production lot size and safety stock in an imperfect production system

This paper is concerned with the joint determination of optimal production lot size, safety stock and reliability parameter under the realistic assumptions that the production facility is subject to random breakdown of machinery system and also to change in the variable reliability parameter. Reliability of a machinery system is a decision variable that can be increased by more investment in production technology. In this model, preventive and corrective maintenance, safety stock for repair times and shortages are adopted to generalise the model. Except machinery breakdown, the manufacturing system may shift from in-control state to out-of-control state. During out-of-control state, a certain percentage of total production consists of defective items which can be reworked immediately at a cost to make as good as perfect quality items. The cost function is maximised by Khun-Tucker method. Numerical results are provided to illustrate both the study of the optimal solutions and sensitivity of different changes in key parameters.