Worst-case performance of power-of-two policies for serial inventory systems with incremental quantity discounts

This study presents power-of-two policies for a serial inventory system with constant demand rate and incremental quantity discounts at the most upstream stage. It is shown that an optimal solution is nested and follows a zero-inventory ordering policy. To prove the effectiveness of power-of-two policies, a lower bound on the optimal cost is obtained. A policy that has a cost within 6% of the lower bound is developed for a fixed base planning period. For a variable base planning period, a 98% effective policy is provided. An extension is included for a system with price dependent holding costs.