Determination of optimal inspection sequence within misclassification error bound

► We integrate a branch & bound and Lagrangian relaxation model to minimize two major types of inspection errors and their subsequent misclassification penalties for the benefits of both producers and consumers. ► The results show the proposed model is effective and computationally feasible when adopted to select the optimal inspection sequence from a group of viable sequences. ► This model can be expected to generate significant contributions to both the academic field and the real-world practice of quality control.