Optimal production schedule in declining market for an imperfect production system

This is a study about economic production in an imperfect production system. The imperfect production system means is a system in which the machine shifts from an ‘in-control’ state to an ‘out-of-control’ state. This may happen at any random time during the production period. The classical economic production lot size model is based on the assumption that the produced items are of perfect quality. However, this is not observed during the production phase. In the long run, the process shifts from the ‘in-control’ state to the ‘out-of-control’ state after certain time due to continuous usage of the machine. The proposed model is developed to study the optimal production when a certain percent of total product is of imperfect quality. These items are reworked to maintain the quality of the products. The production cost per unit item is convex function of production rate. The demand is assumed to be decreasing function of time. The total cost of inventory system per time unit is minimized. The development of the model is validated by numerical examples and its sensitivity analysis is carried out too.