This paper proposes an optimal integrated production-inventory model with multiple discrete delivery and shortage to manage the step-wise delivery of the products to the retailers. The main objective of the model is to determine the optimal order and backorder quantities to obtain the minimum total cost. A novel smoothing strategy and an original heuristic algorithm have been introduced to cope with the non-linearity of the model and solve it. The encouraging and quite simple results obtained for practical purposes show the superiority of the proposed framework compared to the classical Economic Order Quantity (EOQ) model. These empirical findings lead to some managerial implications that enable the system to select the best modeling approach based on different amounts of cost.
