An adaptable robust optimization model for a dual-channel closed-loop supply chain considering cost and demand uncertainty

Most real-life optimization problems are subjected to uncertainty, and the robust optimization approach is one of the efficient techniques to deal with uncertain optimization problems. Supply chain optimization problems are highly sensitive to data perturbations mostly due to inappropriate estimation of the problems' parameters and the highly dynamic environment. In this study, we propose an adaptable robust optimization model for the dual-channel closed-loop supply chain (CLSC) and present two counterpart models; the first model is a mixed integer linear programming (MILP) model based on the adjustable box uncertainty set, while the second robust model is a mixed integer nonlinear programming (MINLP) model based on the adjustable ellipsoidal uncertainty set. We provide a novel approach for considering multiple uncertainty sets in the objective function, that provide flexibility and control risk based on the preferences of the decision-makers. This study aims at minimizing the total cost of the dual-channel CLSC network considering uncertain purchasing, transportation, fixed, and processes costs, in addition to uncertain customer demand. Intensive computational experiments are conducted on the two robust models using GAMS software. Robust solutions are obtained and sensitivity analysis is conducted on both models considering 10% perturbation of the uncertain parameters around their nominal values as well as probability guarantee for not violating the constraints.