Risk-averse bi-level optimization under dependent interval uncertainty for sustainable closed-loop production systems
摘要
This study develops a risk-averse interval bi-level programming framework for sustainable closed-loop production systems operating under dependent uncertainty. Correlated ambiguities in demand, return rates, and operational costs are represented through a structured mean–radius interval formulation with a common dependence factor, while heterogeneous uncertainty attitudes of the leader and follower are incorporated using a preference-based scalarisation approach. The lower-level interval optimisation problem is transformed into a deterministic nonlinear programme via KKT-type optimality conditions, yielding a KKT-based single-level reformulation that is valid under the stated convexity and constraint qualification assumptions. To solve the resulting complementarity-constrained nonlinear model, a hybrid evolutionary–NLP algorithm is proposed that combines global exploration with local refinement. A stylised closed-loop production example is presented to illustrate the applicability of the proposed framework and to examine the influence of uncertainty-width aversion and dependent uncertainty on production, remanufacturing, disposal, and policy decisions. The numerical results indicate that changes in uncertainty attitudes primarily affect the valuation of interval uncertainty, while the system’s operational structure remains comparatively stable across the tested scenarios.