An inventory model for the supply chain with partial backordering, carbon emissions, energy and imperfect process

Abstract

Sustainability is a highly relevant issue today. It is related to the inventory problem because a large part of the greenhouse effect gases (GHG) come from the industry. In the supply chain, both transport and production processes require a lot of energy that is converted into emissions of carbon that cause global warming at the same time. The government, therefore, has developed different policies that limit the amounts of emissions allowed to achieve a sustainable development. These regulations increase the costs of companies, so it is convenient for them to adapt and comply with the rules. In this research, a sustainable inventory model for the supply chain with partial backordering, lost sales, process quality and environmental costs is developed. From this inventory model, three inventory models are identified as special cases: a sustainable inventory model with process quality and environmental costs, an inventory model with process quality costs, and an inventory model with traditional inventory costs. The four inventory models address shortages with partial backordering, lost sales, energy usage, and some of them include other real topics such as environmental problems and imperfect quality. A solution algorithm is developed to determine the optimal values for the buyer’s order quantity (q), the buyer’s backordering quantity (B), the number of shipments of size q in a cycle (n), and the vendor’s production rate (P), which minimize total system costs. The optimal vendor’s production quantity (Qv) is computed considering the buyer’s order quantity (q) and number of shipments of size (n). The optimal values for the buyer’s backordering quantity satisfied (Bq) and buyer’s lost sales quantity (BLS) are determined taking into account the buyer’s backordering quantity (B). Numerical examples are presented and solved. Additionally, a sensitivity analysis is done with the aim to see if the parameters have a significant impact, and in turn, provide better tools and knowledge for decision-makers in companies. Finally, it is important to remark that it was found that the proposed inventory model in this research is more economical from one of Marchi et al. (2019)’s inventory model.