Worst-case analysis of (R,Q) policies in a two-stage serial inventory system with deterministic demand and backlogging

The paper considers a two-stage inventory system where customer demand arises at stage 1, stage 1 replenishes its inventory from stage 2, and stage 2 orders from an outside supplier with unlimited stock. Customer demand is assumed to arrive continuously at a constant rate and is backlogged when stage 1 runs out of stock. There are economies of scale in transferring inventories from the outside supplier to stage 2 or from stage 2 to stage 1. We show that (R,Q) policies are 86%-effective. Numerical examples are provided to further demonstrate the cost effectiveness of (R,Q) policies.