Multiproduct EPQ model with single machine, backordering and immediate rework process

Production systems with scrapped and rework items have recently become an interesting subject of research. While most attempts have been focused on finding the optimal production quantity in a simple production system, little work appears on a joint production environment. In this research, two joint production systems in a form of multiproduct single machine with and without rework are studied where shortage is allowed and backordered. For each system, the optimal cycle length, the backordered and production quantities of each product are determined such that the cost function is minimised. Proof of the convexity of the involved objective functions of each model is provided and numerical illustrations are given to demonstrate the applicability of the proposed models. Furthermore, the results obtained by solving the models with and without rework of defective items are compared. Sensitivity analysis and some managerial insights based on the numerical illustration are provided at the end.