Multi-item single-source production quantity model for imperfect items with rework failure, inspection errors, scraps, and backordering

This paper represents a multi-item single-source (MISS) production quantity model for random imperfect items with repair failure, inspection errors, sales return, scraps, and backordering. In this study, it is assumed that some manufactured/produced goods might not be without fault and the first phase of inspection over the quality of goods might make some inspection errors through the classifying of imperfect/defective and perfect items. Besides, this model contains one or more steps of separation procedure that is after the rework time and there is no screening error in this period (i.e., error-free). The purpose of this investigation is to obtain the optimum cycle length and the optimal backordered quantity for each item to minimalise the total expected value cost. Finally, the numerical example is illustrated to explain and solve the studied model using our investigated innovative methodology, which is additionally clarified and explained over a sensitivity analysis.