Analysis of Reverse Channels in a Stochastic Closed-loop Supply Chain

We study a closed-loop supply chain in which used products can be collected by a manufacturer, a retailer, or a third-party for the purpose of recycling. Since the collection process can be noisy, the system dynamic is modeled by a stochastic differential equation. We formulate stochastic differential game models for each of the three reverse channels, derive their feedback control strategies, and compare the performance of the three reverse channels. We find that the manufacturer collection is the most efficient reverse channel. This is different from the known result in a static setting that has the retailer collection as the best channel. Furthermore, we extend our model to consider the impact of the reverse logistics cost and the collection cost coefficient. The retailer and the third-party collection could also be the best reverse channel when the retailer has the advantage of a low reverse logistics cost, or the third-party has the advantage of a high collection capacity, respectively