An integrated multi-echelon robust closed-loop supply chain under imperfect quality production

In this paper, we consider a novel closed loop supply chain design consisting of multiple periods and multiple echelons. The models are considered under imperfect quality production with multiple uncertainties to provide meaningful solutions to practical problems. In addition, we assume that the screening is not always perfect, and inspection errors are more likely to take place in practice. We measure the amount of quality loss as conforming products deviate from the specification (target) value. In our study, we develop three robust counterparts models based on box, polyhedral, and combined interval and polyhedral uncertainty sets. 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 paper is expected to provide more insights in managing this important problem.