Sustainable inventory management for a closed-loop supply chain with learning effect and carbon emission under the multi-shipment policy

The key to the success of any supply chain is its strong coordination and sustainability among its supply chain partners. In recent epochs, the attention of big businesses is not only on gaining the maximum profit but also on attaining sustainability. To do so, the entrepreneurs are now focusing on sustainable cost-reducing practices. To achieve this, the present paper develops a closed-loop supply chain (CLSC) model in which the manufacturer produces and delivers the quantity to the retailer per the muti-shipment policy. The learning effect of holding reduces the retailer's holding cost at a constant rate. By adopting a multi-shipment policy, both the manufacturer and retailer can save their holding cost and maintain the product's freshness. Fresh products flow from the manufacturer to the retailer, fulfilling the customer demand. Further, this model also considers the carbon-emissions effect due to the production of items and their holding in the storage for better sustainability; the company collects the defective/used items and bifurcates them into remanufacturable and salvage options. Collecting such units has two benefits. The first is that if the units are remanufacturable, they can be utilized, which will reduce the load on raw material for manufacturing, and if they are not, then they can be disposed of properly. The developed model indicates that remanufacturing options for used items positively impact the environment and triple bottom line (TBL).