An inventory model with single price break and convexity of cost function

The paper considers inventory management of a single commodity for a dynamic risk model when one discount is available during procurement. The discount can be afforded if a known minimum amount of the product is procured. The orders are to be placed at the beginning of periods with instantaneous replenishment and backlogging is allowed. To find the optimal ordering policy a single period setup has been considered with strictly convex cost function in stock height (or order quantity) for fixed procurement price. Under this setup a theorem has been derived subject to the conditions that the cost function is increasing and optimal stock height (or order quantity) is non increasing in procurement cost when respective other factors are constant.