Three-Echelon Sustainable Supply Chain for Deteriorating Items with Imperfect Quality Considering Inspection Scenarios and Carbon Emission Policies

This article integrates sustainability principles into a three-echelon supply chain for deteriorating items with imperfect quality, consisting of a single vendor, a third-party logistics enterprise (3PL), and a single buyer, with a focus on balancing economic efficiency with environmental responsibility. The vendor is assumed to operate an imperfect production system, resulting in products of imperfect quality. The 3PL undertakes all transportation activities, while the buyer conducts a quality inspection process to detect defective items, which is subject to Type-I and Type-II errors. Aside from that, the inventory model also assesses carbon emissions arising from various operational activities including energy usage during production, warehousing, and disposal processes, and fuel consumption in transportation, for which the above members of the supply chain are accountable. Afterward, carbon management policies such as a carbon tax and carbon cap-and-trade are considered to regulate total supply chain emissions. The objective is to minimize the joint expected total cost by simultaneously optimizing shipment frequencies and the replenishment cycle for the buyer within carbon emission constraints. An iterative solution procedure is developed to address the problem. A numerical example and sensitivity analysis are provided to demonstrate the model’s applicability and to explore the influence of critical parameters. Finally, the study presents managerial insights, along with conclusions and recommendations for future research directions.