An inventory model for imperfect items under inflationary conditions with considering inspection errors

This paper represents a discounted cash-flow approach for an inventory model for imperfect items under inflationary conditions with considering inspection errors. The previous imperfect quality inventory studies, however, have mostly had the emphasis on developing cost-minimizing models that do not consider imperfect inspection processes and related defect sales return issues despite their practical significance. In this paper, we assume that some produced items might not be perfect and the first stage inspector of product quality control might make some inspection errors during the separation of defective and perfect items. Thus, this study proposes a profit maximizing inventory model with incorporating both imperfect production quality and two-way imperfect inspection, i.e., Type-one inspection error of falsely screening out a proportion of no defects and disposing of them like defects and Type-two inspection error of falsely not screening out a proportion of defects, thereby passing them on to customers, resulting in defect sales returns. In addition, this model includes one more stage of inspection that is after the rework process and there is no inspection error in this stage. The purpose of this model is to determine the important factors of an inventory system to optimize the present value of the total profit in the finite time horizon. Finally, a numerical example is provided to solve the presented inventory model using our proposed innovative approach, which is further clarified through a sensitivity analysis.