A new model of inventory control with returns is considered, when it is possible for consumers to return (under certain conditions) the products they have purchased and a similar model of multi-channel controlled queueing system with switching of service channels. An optimal inventory control strategy in such a system turns out to be four-level. Then we investigate a model of a multilinear queueing system (QS) with channel switching under uncertainty and study the analogy of this model with the model of inventory control with returns.
