Flows of returns due to recycling and reusing waste are developing in order to preserve the limited natural resources of our planet. These new flows interact with the traditional production flows. Therefore, in order to provide customers with the best service level and minimize the stock in the supply chain, the control of the return flows appears to be of highest importance. We address this problem by modeling a situation with a limited porduction capacity and we consider an operational production/inventory problem that incorporates flows of returns. We model three continuous-time production/inventory problems with limited produc- tion capacities, random lead times, and linear costs. In the first problem we take into account the probability that a product can be reused as a finished product or only as semi-finished product (by parts), in the second problem we include a step of remanufac- turing before reusing the returned product, and in the third problem we consider a system with product returns that are announced in advance by the customers. Apart from the caracterization of the optimal policies for these cases, the performance assessments of some heuristic policies and the study of the poduction capacity effect on these heuristic policies stand as main contributions. Throughout this work we have used existing tools to characterize optimal policies for different Markov decision processes. The last chapter aims to improve these tools and enable us to study the influence of several system parameters on its optimal policy.
