In this paper, an economic production quantity model for an imperfect production system with reparation of non-conforming products is studied. The system allows shortages and a proportion of the shortages are backordered, following a last-in/first-out (LIFO) policy. It is assumed that the repair of non-conforming products cannot be carried out in the manufacturer's production system. Therefore, the company decides to have the repairs carried out in a repair centre. Depending on the time when the consignment of reworked items returns to the manufacturer's stocks, this study identifies three cases. The paper shows the derivation of the optimal solution for each case. The required conditions for the initial value of the backordering rate are developed in order to achieve optimal partial backordering. The model is also compared with a modified version that includes not only outsourcing repair of non-conforming products but also full backordering. The numerical examples comparing full backordering with partial backordering indicate that partial backordering is more profitable than full backordering when return of the repaired items to the system leaves a negative inventory level; that is, when there is a shortage.