An imperfect production model with shortage and screening constraint under time varying demand

This study presents an imperfect production inventory model in which shortages occur depending on the screening rate of the produced items in the manufacturing system. Since in the system, there may exist some unplanned events, such as machinery faults and labor issues etc., so the screening rate cannot be predicted by the manufacturer. Henceforth, here it has been considered as a variable because of disruptions in the screening process which creates complexity in the manufacturer’s demand fulfillment process. Now, on the basis of screening rate, there may exist two cases. In the first case, the screening rate of perfect items is higher than the demand rate, that means, there is no shortage during the demand fulfillment process. On the other hand, the screening rate of perfect items is lower than the demand rate. In this case, shortages may occurred in the system. In this investigation, a time dependent non-linear demand function has also been considered. Additionally, the screening cost of the product depends on the screening rate. The objective of this study is to find the optimum values of the production rate, screening rate, and business period in such a way that the manufacturer’s profit is maximized. Compairing two cases, we find that imperfectness and shortages have a negative impact on the average profit. The screening fraction parameter has positive impact on the average profit of the manufacturer. Also, sensitivity analysis is provided and some managerial insights are concluded for two cases.