Quantifying the Bullwhip Effect in closed-loop supply chains: The interplay of information transparencies, return rates, and lead times

The Bullwhip Effect manifests itself in the form of an increased order and inventory variability in the uppermost nodes of the supply chain. This dynamic phenomenon is not yet well understood in closed-loop supply chain settings, despite their growing importance in modern societies pursuing circular economy opportunities. Indeed, the problem-specific literature has provided somewhat conflicting findings. To better understand the Bullwhip Effect in closed-loop systems, we obtain expressions for the order and inventory variance amplification in four archetypes that differ in the structure of information transparency. Interestingly, we observe that the impact of return rates and lead times on the system performance strongly depend on the degree of supply chain visibility. This perspective allows us to revisit discrepancies in prior works. We later move the study from the operational to the economic prism. Here we prove the existence of an optimal return rate, and we derive its expression in the four closed-loop supply chain archetypes. We show that the optimal rate is dependent on the node's cost structure, the lead times, and the variability of demand. Properties of the different closed-loop systems and relevant managerial implications are also discussed in our work.