Control of a two-stage production/inventory system with products returns

We consider a two-stage production-inventory system with demand at the down-stream stage and returns at each stage. We characterize the structure of the optimal policy which is a complex state-dependent Base-stock policy. We also investigate four classes of policies: Fixed buffer, Base-stock echelon, Kanban and Half-optimal. We compare the performances of these policies and exhibit that the maximal overcost for using the Half-optimal policy is of 0.35% on all the instances tested.