Consignment inventory management in a closed-loop supply chain for deteriorating items under a carbon cap-and-trade regulation

This paper studies an inventory management problem for a closed-loop supply chain that is operated under a consignment stock policy and subject to a cap-and-trade regulation. The supply chain makes both new products and remanufactured products, considering that new raw materials (NRMs), cores, and finished goods (FGs) suffer from deterioration. Mixed integer nonlinear programming models are established to jointly optimize the pro-duction sequence of new products and remanufactured products, number of shipments, shipment interval, batch size of FGs, and production cycle length to minimize the total of production, shipment, inventory, deterioration, and carbon emission costs per unit time. Exploring and using the structural properties of the models, a Taylor -series based method is designed to solve the models. Finally, numerical examples and sensitivity analysis are provided to show the effects of key factors on the operational decisions and on both the economy and envi-ronment. Results indicate that the deterioration of NRMs, cores, and FGs triggers the supply chain to run short production cycles while making more frequent shipments under the consignment stock policy. Both the economic and environmental costs increase with the deterioration rates. In addition, raising the carbon-trading price can reduce carbon emissions but increase the economic cost of the supply chain, rendering the urgency in reasonably determining carbon cap and trading price.