An inventory model for imperfect production system with rework and shortages

This paper considers a production inventory model with planned backorders for a single product. The product is manufactured in a single stage manufacturing system. The manufacturing system generates imperfect quality products. All these defective products are reworked in the same cycle. This paper develops two inventory models for two operational policies. The first policy covers the case that the rework is done and the shortages are not permitted. The second policy covers the case that the rework is done and the shortages are permitted. The generation of defective items during most practical production processes is almost inevitable. These imperfect quality items can sometimes be reworked and repaired, hence the overall production costs can be reduced significantly. To achieve this objective, a mathematical model is developed. In particular, the optimal production lot size which minimises the total cost is derived. This model is developed for deriving the necessary and sufficient conditions for having a unique solution. An illustrative example is provided and validated. The validation of result in this model was coded in Microsoft Visual Basic 6.0.