On the optimality of the optimal policies for the deterministic EPQ with partial backordering

In a note published in Omega [Zhang RQ. A note on the deterministic EPQ with partial backordering. Omega 2009;37(5):1036–8], the amended decision procedure for the Pentico et al.'s EPQ with partial backordering (EPQ-PBO) is proposed, by developing another critical value of the backordering rate. However, there is a case when a decision made with this amended procedure is not optimal, which will be shown in this paper. A new decision procedure will be proposed based on the derived necessary and sufficient conditions for considering the policy of losing all sales or the policy to meet all demand as possible optimal decisions. The proposed decision procedure is adapted for one of the extensions of the EPQ-PBO.