Solving an EPQ Model with Rework and Service Level Constraint

This paper examines an economic production quantity (EPQ) model with rework and service level constraint. First, we prove that the expected overall costs for an imperfect EPQ model with backlogging permitted is less than or equal to that of the one without backlogging. Secondly, the relationship between “imputed backorder cost” and maximal shortage level is derived for decision-making on whether the required service level is achievable. Then an equation for calculating the intangible backorder cost is proposed for situation when the required service level is not attainable. By including this intangible backorder cost in mathematical analysis, one can derive a new optimal lot-size policy that minimizes expected total costs as well as satisfies the maximal shortage level constraint for the EPQ model with rework. Numerical example is provided to demonstrate its practical usage.