Optimal production lot sizing with rework, scrap rate, and service level constraint

This paper studies the optimal lot-sizing decision for a production system with rework, a random scrap rate, and a service level constraint. In most real-life manufacturing settings, generation of defective items is inevitable. Reworking of defective items may significantly reduce overall costs. We derive an optimal operating policy and prove that the expected overall cost of such a production system with backlogging permitted is less than or equal to that of the same model without backlogging. Then the relationship between the ‘imputed backorder cost’ and maximal permitted shortage level is derived for decision-making on whether the required service level is achievable. In the case that the required service level is not attainable, an equation for calculating the intangible backorder cost is proposed. This enables us to derive a new optimal lot-size policy that minimizes expected overall costs as well as satisfies the service level constraint. A numerical example is provided to demonstrate its practical usage.