On the bullwhip effect in circular supply chains combining by-products and end-of-life returns

• The dynamics of a circular supply chain is investigated. • A threshold for the reverse and by-product flows sets a limit to maintain system stability. • Increasing the degree of circularity below the stability threshold improves the dynamic performance of the supply chain. • Implementing multiple circular strategies benefits the performance of all supply chain members. The move towards a circular economy represents an urgent need for production and distribution systems. For this reason, traditional supply chains must rearrange their structures and configurations to reduce virgin material extraction, as well as production and end-of-life products that are sent to landfill. However, many questions regarding the dynamic behavior of circular supply chains remain unsolved. The aim of this work is to contribute to the literature on circular supply chains by investigating their dynamics when there are several reverse loops, i.e., the products delivered to the final customer have been either produced from virgin materials, by the remanufacturing of end-of-life products, or by the use of by-products generated in another supply chain. Using a full factorial design of experiments and a difference equation modelling approach, a wide range of supply chain scenarios with different return and by-product usage rates are analyzed, and their dynamic and economic performance is evaluated. Our results suggest that there is a combined effect of the return rate and the by-product rate on the dynamic behavior of the supply chain. When their combination exceeds a stability threshold, the order amplification disappears, at the expense of unmanageable inventories. However, they also show that, below this threshold, circular supply chains can outperform traditional ones.