Multi-period multi-product acquisition planning with uncertain demands and supplier quantity discounts

In this paper, we address a multi-period multi-product acquisition planning problem where the retailer faces uncertain demand for the products and the suppliers provide all-unit quantity discounts. The problem is an extension of single period constrained newsvendor problem, which considers both the supplier discounts and multiple periods. We formulate the problem as a mixed integer nonlinear programming model and develop a Lagrangian relaxation based approach. Efficient solution procedures are presented to solve the decomposed sub-problems that are based on the properties of the problem. Computational results show that the Lagrangian method can quickly obtain very good solutions.