Manufacturing system with immediate rework and partial backordering

This paper extends a manufacturing system with manufacturing capacity limitation, immediate rework, imperfect production processes and partial backordering in a multi–product single–machine manufacturing system. The primary aim of this research is to minimise the total cost by deriving the optimal periodic length, backorder, and order quantities. The objective function of the proposed model is proved to be convex, and two numerical examples are used to illustrate the proposed method. Finally, sensitivity analysis is performed to demonstrate the applicability of the proposed model in the real world environments and to provide some managerial insights for practitioners.