Sustainable Supplier Selection under Quantity Discounts: An Epsilon-Constraint Model for Cost and Water Footprint Reduction

This paper presents a multi-objective mixed-integer nonlinear optimization model for sustainable supplier selection under quantity discounts. The model minimizes total procurement cost and water footprint across a multi-echelon supply chain by integrating purchasing, processing, and transportation costs with blue, green, and grey water footprint components. To address the resulting nonlinearity, the e-constraint method is used to reformulate the multi-objective problem into a sequence of single-objective models. Numerical experiments show that the proposed approach identifies Pareto-optimal solutions that clearly illustrate the trade-of between cost and environmental performance. In particular, the results indicate that slight relaxations of water footprint constraints can lead to substantial reductions in total cost.