A Markov decision model to evaluate outsourcing in reverse logistics

One of the most important decisions regarding reverse logistics (RL) is whether to outsource such functions or not, due to the fact that RL does not represent a production or distribution firm's core activity. To explore the hypothesis that outsourcing RL functions is more suitable when returns are more variable, we formulate and analyse a Markov decision model of the outsourcing decision. The reward function includes capacity and operating costs of either performing RL functions internally or outsourcing them and the transitions among states reflect both the sequence of decisions taken and a simple characterization of the random pattern of returns over time. We identify sufficient conditions on the cost parameters and the return fraction that guarantee the existence of an optimal threshold policy for outsourcing. Under mild assumptions, this threshold is more likely to be crossed, the higher the uncertainty in returns. A numerical example illustrates the existence of an optimal threshold policy even when the sufficient conditions are not satisfied and shows how the threshold for outsourcing decreases while the probability of crossing any fixed threshold increases with the return fraction.