Sustainable economic production quantity models for inventory systems with shortage

Recently, new economic order/production quantity models have shifted away from focusing only on economic issues and towards combined economic-environmental concerns because of sustainable development goals. Despite this shift, only a few works have addressed sustainable Economic Production Quantity (EPQ). The theoretical sustainable EOQ and EPQ models are basic models that ignore many real-life conditions such as the possibility of stock-out in inventory systems. In this paper, we develop four new sustainable economic production quantity models that consider different shortage situations. To find optimal values of inventory system variables, we solve four independent profit maximization problems for four different situations. These proposed models include a basic model in which shortages are not allowed, and when shortages are allowed, the lost sale, full backordering and partial backordering models can be selected by operations managers depending on the manufacturer's motivation to improve service levels. We have also proposed an algorithm for determining optimum values of the decision variables for these sustainable economic production quantity models. Finally, the formulated models are explained with some different examples and the obtained results have been analyzed and discussed. These results show that the sustainable economic production quantity with partial backordering model is a general and more realistic model that can be used in many real cases with a reasonable profit amount, compared with the three other proposed models.