An (s,S) inventory control model with return flows

With the growth of environmental concerns, the reuse of used products has received increasing attention so that a new field “reverse logistics” has emerged. To improve inventory management performance of reverse logistics, an (s,S) inventory control model is presented comprising random demands and returns. For this model, an optimal control policy is derived, optimal control parameters are computed and the solving steps are described in detail. Moreover, probability distributions of net demands in two different situations, namely dependent and independent Poisson demands and returns, are calculated respectively, and applications of the model in these situations are carefully illustrated. Experimental study shows that the optimal parameters in independent situation are often smaller than that in dependent situation, so it is meaningful to analyze the relationships of item demands and returns in real-life practice in order to design a suitable inventory strategy.