Note：Proof of the Conjecture on the Consistent Advantage of the Newsvendor Model under Progressive Multiple Discounts

In this note, a recent work in Won (2011) which investigates properties of the newsvendor model under progressive multiple discounts is revisited and a complete proof is provided for the conjecture on the consistent advantage of progressive multiple discounts over no-discounts in terms of the expected profit. The proof considers the generalized newsvendor model under progressive multiple discounts extended with positive shortage cost and salvage value which have not been considered in the previous newsvendor models under progressive multiple discounts. Without relying on derivatives, we prove that the expected profit under progressive multiple discounts are consistently greater than or equal to the one under no-discounts for every order quantity as far as her multiple discounts do not decrease customer demand, and therefore, the optimal expected profit under progressive multiple discounts is always greater than or equal to the one under no-discounts. As by-products from the proof, some interesting features of the generalized newsvendor model under progressive multiple discounts are revealed.