Design of reverse supply chains under uncertainty: the lexicographic R* criterion for exploring opportunities

Reverse supply chains (RSCs) have been increasingly implemented in recent years to manage the growing flow of solid waste generated by end-of-life (EOL) products and to minimise their environmental impact. Furthermore, recent research has shown that the implementation of RSCs benefits job creation, enables savings in raw materials, and creates income from the sales of re-manufactured products. However, designing RSCs requires dealing with many sources of uncertaintydue to the reverse flow of EOL products. To model these uncertainties, we consider a set of equally possible scenarios. In previous models for scenario sets, the decision often has been influenced by negative scenarios while neglecting opportunities. We propose a new risk/opportunity approach based on the $R_* $R∗ criterion to give more weight to positive scenarios in the decision-making process. This criterion is used in order to distinguish zones of risk and opportunity and guide the decision-making process accordingly to the existing zones. We develop a lexicographic approach for the consideration of existing scenarios, and propose two methods to compute the optimal solution for lexicographic $R_* $R∗ ( $LexiR_* $LexiR∗) criterion: one in the form of an algorithm and another in the form of a mixed-integer program (MIP). The performance of the developed approaches is demonstrated in a case study for a reverse facility location problem.