To respond to the adoption of carbon pricing regulations, researchers and industry are developing low carbon inventory models that can meet emission reduction targets while maintaining company profits. The challenge is getting tougher when the company is still facing problems related to imperfect product quality. This research solves this problem by developing an economic order quantity (EOQ) model by considering several sources of carbon emissions, as well as the influence of the defective rates, different demand rates, selling price and holding cost for defective products, and shortages backorder. The objective function of the formulated mathematical model is to minimize the total costs which include the emission costs. A numerical example is developed to illustrate the model based on the previous data set. Sensitivity analysis is also carried out to validate the model and to learn more about the system characteristics. The total emissions are calculated and the affecting factors are identified.

Traditional economic production quantity (EPQ) model assumes that the production products are perfect. However, this assumption does not hold for many real production systems due to several weaknesses. This paper considers production inventory model with defective items for deteriorating items. In this paper, production rate is considered to be greater than demand rate. Mathematical model is developed for finding optimal order quantity, cycle time and total profit. Moreover, a numerical example is provided to illustrate the proposed model. Next, sensitivity analysis is established to demonstrate the model developed. Finally, some conclusions and future research directions are proposed.