Uncertain Quality and Quantity of Returns in a Closed-loop Supply Chain

In this work the design and planning of a Closed-Loop Supply Chain (CLSC) under uncertain conditions is considered and a two-stage scenario-based modeling approach is proposed in order to deal with this multi-product, multi-period problem. The network design and tactical plan are simultaneously optimized in a given time horizon, comprehending the raw material acquisition and the processing, storage and distribution of intermediates, returns and final products. Uncertainty is associated to the returns, both in terms of their quantity, which is customer dependent, and quality, which is determined at the sorting centers. Therefore, the ensuing mathematical MILP formulation considers the simultaneous integration of two important uncertainty sources, which represents an important modeling advantage, allowing a better understanding of the reverse network structure. For each probabilistic scenario, the model estimates the amount of products to be returned by customers and of returns to be remanufactured for each quality level, as well as the storage levels. Several tests based on a real sized example of a Portuguese glass company are undertaken in order to show the applicability of the developed approach. Based on these tests, the influence of the uncertain quality and quantity of returns on the design and planning of the CLSC is assessed.