Robust Green Supplier Selection with Risk-Aware Trade-offs using Bi-Level Programming

Abstract

This paper addresses the supplier selection and order allocation problem in a multi-product, multi-scenariosupply chain environment, subject to uncertainty. Traditional models often neglect critical factors such as supply risk andenvironmental impact, leading to suboptimal and unsustainable decisions. In this work, we propose a two-level decisionmakingframework where the upper level selects a subset of suppliers based on a set of criteria such as cost, reliability, risk,and environmental impact, while the lower level determines the optimal order allocation under multiple uncertain demandscenarios. The lower-level problem is reformulated using Karush–Kuhn–Tucker conditions to obtain a single-level mixedinteger linear programming model. A detailed numerical example illustrates the effectiveness of the approach and the impactof uncertainty on supplier selection decisions.The numerical study is further extended with larger-scale instances, a heuristicbaseline comparison, a big-M sensitivity analysis, and a discussion of the model’s computational and theoretical limitations.The proposed model can be viewed as a strong green supplier selection model with risk-aware trade-offs, and it is a practicaldecision-making tool for sustainable and resilient procurement strategies.