The newsvendor problem with capacitated suppliers and quantity discounts

We consider a seller who stocks an item in anticipation of a single selling season in which demand for the item is uncertain. The seller may order stock of the item from multiple suppliers, each of which offers a quantity discount pricing structure and has production volume limits. The seller seeks to minimize its total procurement plus expected overstock and understock costs, resulting in an objective function that is neither convex nor concave in the decision variables in general. We provide an algorithmic approach that permits solving this non-convex problem in pseudopolynomial time by solving a set of 0-1 multiple choice knapsack subproblems. We also provide an efficient heuristic solution algorithm and demonstrate the algorithm's asymptotic optimality in the number of suppliers under mild assumptions on the problem data and under certain quantity discount structures. The results of a set of computational tests demonstrate the superior performance of the knapsack-based algorithms when compared with a commercial solver.