A simple model for the basic (r,Q) inventory control model with return flow

In recent years, as a result of environmental legislation and an increasing interest in economics, many producers have been forced to implement the PTB (Products Tack Back) program. In this paper, we employ the basic (R, Q) model to control a single-item single-echelon inventory system with return flow. Based on the assumption that the return and the demand are independent Poisson processes, we derive a simple approximate algorithm to determine the optimal control parameters. The numerical examples show that the presented algorithm is more tractable than the exact algorithm and more accurate than other approximate algorithms, such as normal approximation.