A general lot-sizing problem in a closed-loop supply chain with returns

We consider a stochastic version of the multi-product multi-level capacitated lotsizing and scheduling problem with sequence-dependent setups. A bottler needs to determine its production schedule over a finite horizon in order to satisfy a deterministic demand. The raw materials are supplied through two different sources: uncapacitated reserves of new bottles and the uncertain returns of used bottles. We present results for the single-item case