Optimal batch quantity models for a lean production system with in-cycle rework and scrap

In a manufacturing system, reworking of the defectives and management of waste or scrap are important issues that call for immediate attention to meet the basic objectives and requirements for lean production system. This paper deals with a manufacturing process where finished goods are occasionally produced along with undesirable defective items and scrap. As the system is not always perfect, some scrap is produced during the manufacturing and/or rework processes. A rework process is necessary to correct the defective items into good finished products. The manufacturing process considered in this research deals with the process of rework that is performed 'within' the cycle. Also, three types of scrap detection scenarios are considered: (i) detection 'before' rework, (ii) detection 'during' rework, and (iii) detection 'after' rework. In order to avoid shortage of finished products due to scrap production, finished-product buffers have been considered to fulfil the customers' timely demand. The required finished products for these buffers are ordered from different suppliers. Based on the observations in shop floors, a number of inventory models are developed for a single-stage production process wherein defective items are reworked, and scraps are detected and discarded during entire process. For the stated detection procedures, the total cost functions for a single-stage imperfect manufacturing system are developed with 100% inspection to find the optimum operational policy for manufacturing batch sizes and economic storage of inventories. Numerical examples are used to demonstrate these models, and an analysis is performed to study the sensitivity of different system parameters on several measures of performance.