Sustainable inventory model with environmental impact for non-instantaneous deteriorating items with composite demand

Global warming and climate change become a sensitive issue worldwide, and many countries try to control the CO2 emissions by investigating in many projects. This study proposes a sustainable inventory model to reduce carbon emission. It is generally assumed that demand is increasing at starting of an inventory level and decreasing at ending for a particular newly launched product. In this situation, demand is usually represented by Normal distribution or imprecise fuzzy demand. However, in reality, those assumptions do not always hold. In most of the inventory models, it is seen that demand is a linearly increasing function of time before starting deterioration; then, the demand decreases inversely proportional to the deterioration rate after starting the deterioration. To describe the possible situations more clearly, we introduce here a new type of demand, called as composite demand. Most of the products have a fixed life span for maintaining the quality in original condition which is known as non-instantaneous deterioration. Therefore, we design an inventory model for non-instantaneous deteriorating items with composite demand function. The deterioration rate is assumed to follow an exponential distribution; the holding cost is considered as time dependent. The model is formulated based on retailer's perspective and, thereafter, the total cost for the retailer is calculated. Numerical examples are provided for better understanding of this model. The results show that the total profit for non-instantaneous deteriorating items is higher than for instantaneously deteriorating items. A sensitivity analysis is conducted based on the important parameters. Finally, the paper ends with conclusions and an outlook to future research.