Influence of dependency between demands and returns in a reverse logistics system

We consider two reverse logistics systems where returned products are as good as new. For the first system, the product return flow is independent of the demand flow. We prove that the optimal policy is of base-stock type and we establish monotonicity results for the optimal base-stock levels, with respect to the system parameters (arrival rate, production rate, return rate, production cost, lost-sale cost, return cost and holding cost). We also provide an efficient algorithm to compute the optimal base-stock level. For the second system, demands and returns are strongly correlated: a satisfied demand induces a product return after a stochastic return lead-time, with a certain probability. When the return lead-time is null, we extend the results obtained for the first system. When the return lead-time is positive, the optimal control problem is more complex and we do not prove that the optimal policy is of base-stock type. However, we provide a framework to analyse base-stock policies. Finally, we carry out a numerical study on many scenarios to investigate the impact of ignoring dependency between demands and returns. We observe that ignoring this dependency yields to non-negligible cost increase.