On modelling non-linear quantity discounts in a supplier selection problem by mixed linear integer optimization

Applying traditional integer programming techniques in order to solve real logistic problems can be an important challenge. To ensure tractability, real instances are often either simplified in scope or limited in size, given rise to solutions that may not address realistic issues. In this paper we present a novel approach to solve a multicommodity capacitated network flow problem with concave routing costs, considering also outsourcing, overload and underutilization facility costs. It is derived from a real NP production and transportation problem concerning to the processing of biological samples in a large health-care network, with consideration of volume-based price incentives—i.e. economies of scale—on the shipping costs. It is a tactical level model providing the global view of network layout and the coordinating policy among facilities with realistic assessment of long-term operations costs. The goal is to find an efficient resolution procedure in order to integrate it into a Decision Support System used by planners. With this aim, we analyse three alternative methods of linearizing the involved modified all-units discount cost function. Performance of the different modelling techniques is shown through extensive computations.