Replenishment decisions under an all-units discount schedule and stepwise freight costs

0377-2217/$ see front matter 2008 Elsevier B.V. A doi:10.1016/j.ejor.2008.09.037 * Tel.: +90 312 2901702. E-mail address: [email protected]. In this study, we analyze the replenishment decisions under a general replenishment cost structure that includes stepwise freight costs and all-units quantity discounts. We first formulate a general model that accounts for a larger class of problems and prove several useful properties of the expected profit function. We later utilize these properties to develop a computational solution approach to find the optimal order quantity. As an application of the general results, we study the replenishment decisions in the single-period, i.e., the Newsboy, problem considering several scenarios that model the cost considerations either for the buyer or for both the buyer and the vendor. 2008 Elsevier B.V. All rights reserved.