The implications of batching in the bullwhip effect and customer service of closed-loop supply chains

Batching is a well-known cause of the bullwhip effect. Despite being very common in many industries to leverage economies of scale, it has been little explored due to its nonlinear complexity. This work examines how order-quantity batching affects the performance of closed-loop supply chains, which are gaining importance as a result of their environmental and economic value. Specifically, we analyse a hybrid system with both manufacturing and remanufacturing operations. We observe that, when an order-up-to policy is used in the serviceable inventory, bullwhip is always an increasing function of the batch size. Nevertheless, when a smoothing replenishment rule is used, the closed-loop supply chain behaves differently for low and high volumes of returns due to the different degrees of uncertainty they convey. In the high-volume case, batches should also be as small as possible. In contrast, in the low-volume case, bullwhip can be mitigated by setting the batch size to a divisor of the mean production rate. However, this may lower the customer service level achieved. We also find that reducing manufacturing batch sizes should be prioritised over remanufacturing ones when both are large. In the light of our results, we finally provide professionals with specific suggestions on how to better manage closed-loop supply chains where goods are produced and delivered in batches.