A fuzzy technique for supply chain network design with quantity discounts

This paper proposes a hierarchical technique for Supply Chain Network (SCN) efficiency maximisation under uncertainty composed of three steps. The first step extends a previous fuzzy cross-efficiency Data Envelopment Analysis approach, originally intended for suppliers' selection, in order to evaluate and rank all the actors in each SCN stage under conflicting nondeterministic criteria. Afterwards, a fuzzy linear integer programming model is stated and solved for each pair of subsequent SCN stages to determine the quantities required from each stakeholder to maximise the overall SCN efficiency while satisfying the estimated demand and respecting the nodes capacity. Finally, a heuristics is applied to limit the exchange of small quantities in the SCN, in which the trade is not economically convenient according to quantity discounts. An illustrative example from the literature shows the technique effectiveness.