Cross-docking in retail: Sustainable EOQ-based models for multi-item inventory systems with imperfect quality and stockouts under carbon cap-and-trade

Cross-docking is a widely used strategy for inventory consolidation and distribution in complex retail supply chains involving multiple suppliers, products, and retailers. This strategy reduces the costs of managing inventory in retail operations by streamlining the supply chain from the point of origin to the point of sale. Environmental sustainability is a crucial concern in operations management, necessitating the monitoring of emissions generated by supply chain activities. Additionally, quality control is vital in retail supply chains to ensure consumer health is not compromised by the sale and consumption of poor-quality products. Taking these factors into account, this paper proposes a sustainable inventory model for a cross-docking system that includes multiple suppliers, retailers, and items with imperfect quality, all under cap-and-trade emissions regulation. Data from a retail company with a single warehouse and multiple stores is used to formulate the inventory system as a mixed-integer non-linear programming problem. The warehouse serves as a hub for cross-docking operations, consolidating inventory from multiple suppliers and distributing it to various stores. The results indicate that the fraction of imperfect quality items, carbon emissions cap, and price for emissions in the open carbon market significantly impact total inventory costs and emissions. Incorporating these variables results in a 9% increase in total costs compared to scenarios where they are excluded. However, this approach enables precise quantification of emissions. To explore the impact of stock shortages on retail operations, the model is extended to include backordering. The extension demonstrates that stock shortages adversely affect total costs.