Affinely adjustable robust optimization under dynamic uncertainty set for a novel robust closed-loop supply chain

In this paper, we propose a novel closed loop supply chain design with multiple periods, echelons and uncertainties. The model assumes that the quality of the produced lot size is imperfect. Thus, the amount of quality loss as conforming products deviate from the specification (target) value is measured. In addition, we assume that the screening is not always perfect, and inspection errors are more likely to take place in practice. The affinely adjustable robust formulation based on “wait and see” decisions is presented. That is, the decisions are made over two sequential stages where multiple uncertainties are included. Moreover, we propose a budget dynamic uncertainty set to mimic the dynamic behavior of the market demand over time. The introduced dynamic uncertainty set is formulated according to Vector Autoregressive (VAR) models where the temporal and spatial correlations of customer demand zones are captured. Also, we utilize different a priori probability bounds to approximate probabilistic constraints and provide a safe solution. The objective is to minimize the total cost of the supply chain network. Finally, numerical examples are provided to illustrate the proposed models. The proposed approach can significantly improve the market demand forecasting and produce less conservative robust solutions. Also, our findings provide to the decision maker an overview of a conservatism comparison between the introduced uncertainty set under different probability bounds.