The newsvendor pricing problem with supplier discounts

We consider the constrained newsvendor pricing problem where the suppliers provide all unit quantity discounts. The problem is to determine the optimal acquisition quantities and selling prices so as to maximize the retailer´s expected profit, subject to a budget constraint. We present a mixed integer nonlinear programming (MINLP) model to formulate the problem, and develop a Lagrangian based solution approach. A numerical example is presented to verify the approach.