A sustainable supply chain network under the Stackelberg and Nash equilibrium policy in a reverse logistic model with multiple deliveries and a single distribution center

This paper presents a framework for reverse logistics aimed at managing reusable items within supplier-buyer relationships to promote sustainability and reduce environmental impact. In this model, the supplier produces and inspects items, shipping only perfect items to buyers, while recycling or disposing of imperfect ones. Returned items from consumers are categorized as either reusable or damaged at a collection center. The concept of a circular economy encourages the return and refilling of reusable items, while damaged items are recycled. Additionally, the model incorporates carbon emissions considerations across production, storage, transportation, and landfilling, emphasizing the importance of environmental factors. To evaluate the sustainability and economic efficiency of the supply chain network, both Stackelberg and Nash equilibrium strategies are employed. The paper provides a mathematical framework based on lemmas to analyze the impact of the network and promote sustainable supply chain practices. In this cycle, consumers use the items and eventually discard them. To support a zero-waste policy, the supplier labels the bottles with barcodes to identify used items upon collection. The supplier has two different rates at which they purchase used bottles from consumers. Refilled bottles are sent back for reuse, while damaged bottles are either repurposed as raw materials or disposed of. The research paper aims to develop a mathematical model that determines the buyer's cycle time and the number of deliveries from the supplier to the buyer, ensuring that the buyer's demand is met without shortages.