## On optimal inventory control with independent stochastic item returns.(English)Zbl 1033.90002

Summary: To a growing extent companies take recovery of used products into account in their material management. One aspect distinguishing inventory control in this context from traditional settings is an exogenous inbound material flow. We analyze the impact of this inbound flow on inventory control. To this end, we consider a single inventory point facing independent stochastic demand and item returns. This comes down to a variant of a traditional stochastic single-item inventory model where demand may be both positive or negative. Using general results on Markov decision processes we show average cost optimality of an ($$s,S$$)-order policy in this model. The key result concerns a transformation of the model into an equivalent traditional ($$s,S$$)-model without return flows, using a decomposition of the inventory position. Traditional optimization algorithms can then be applied to determine control parameter values. We illustrate the impact of the return flow on system costs in a numerical example.

### MSC:

 90B05 Inventory, storage, reservoirs

### Keywords:

Inventory; Optimization; Reverse logistics
Full Text:

### References:

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