A two - stage production / inventory system with admission control of product returns ⋆

We consider a two-stage production-inventory system. Each stage is made of an exponential production server and an output inventory. The downstream inventory faces a Poisson demand and each inventory receives product returns that can be either accepted or rejected. The objective is to find a production/admission policy minimizing the expected discounted costs over an infinite horizon. We consider linear holding, backorder, production, admission and rejecting costs. We show that the optimal policy is characterized by state-dependent base-stock levels and state-dependent disposal thresholds. We also obtain monotonicity results for these switching curves. Interestingly, our results can be transposed to an hybrid singleechelon system with a production facility and a remanufacturing facility, both with exponential leadtimes. Finally, we design heuristics to control production and disposal and we carry out a numerical study to investigate their performances.