Bayesian risk quantification for power battery closed-loop supply chain network design considering regional heterogeneity

Weiwei Xu; Lipu Zhang; Weiwei Xu; Lipu Zhang

doi:10.3934/jimo.2026103

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 6: 2817-2842. doi: 10.3934/jimo.2026103

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Research article

Bayesian risk quantification for power battery closed-loop supply chain network design considering regional heterogeneity

Weiwei Xu ^1,2,
Lipu Zhang ^{3,4
,
,}

1.
Zhejiang Institute of Social Governance and Communication Innovation, Communication University of Zhejiang, Hangzhou 310018, China
2.
School of Cultural Creativity and Management, Communication University of Zhejiang, Hangzhou 310018, China
3.
School of Media Engineering, Communication University of Zhejiang, Hangzhou 310018, China
4.
Key Lab of Film and TV Media Technology of Zhejiang Province, Hangzhou 310018, China

Received: 07 February 2026 Revised: 15 May 2026 Accepted: 19 May 2026 Published: 21 May 2026
90B06, 90C11, 90C15, 62F15, 68U20

The rapid surge in retired power batteries poses a critical challenge for designing cost-efficient and regionally adaptable closed-loop supply chain (CLSC) networks. This study developed a mixed-integer linear programming (MILP) model for a recycling network covering fifty major Chinese cities. The model introduces several novel decision and constraint structures, including differentiated spatial coverage constraints with regional reverse logistics radii (600 km in eastern regions and 1200 km in northwestern areas), a mandatory regional coverage constraint to ensure hub deployment in remote regions, and a conservative demand coverage constraint ensuring feasibility under a bounded 20% demand deviation. A carbon emission penalty term was embedded in the objective function via an auxiliary excess-emission variable linked to a quota allowance. Bayesian inference was used as a post-optimization risk quantification tool to evaluate cost uncertainty due to recovery-rate variability. Our results indicated a baseline system cost of 878 million CNY, driven primarily by forward logistics and facility investments, with limited structural impact from current carbon policies. Bayesian analysis yielded a 7.89 million CNY risk premium for recovery-rate uncertainty. Sensitivity analysis identified critical thresholds triggering network reconfiguration. The framework supports resilient CLSC design under regional and parametric uncertainty.
- power battery closed-loop supply chain,
- Bayesian risk quantification,
- network design,
- regional heterogeneity,
- optimization under uncertainty
Citation: Weiwei Xu, Lipu Zhang. Bayesian risk quantification for power battery closed-loop supply chain network design considering regional heterogeneity[J]. Journal of Industrial and Management Optimization, 2026, 22(6): 2817-2842. doi: 10.3934/jimo.2026103

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Abstract

The rapid surge in retired power batteries poses a critical challenge for designing cost-efficient and regionally adaptable closed-loop supply chain (CLSC) networks. This study developed a mixed-integer linear programming (MILP) model for a recycling network covering fifty major Chinese cities. The model introduces several novel decision and constraint structures, including differentiated spatial coverage constraints with regional reverse logistics radii (600 km in eastern regions and 1200 km in northwestern areas), a mandatory regional coverage constraint to ensure hub deployment in remote regions, and a conservative demand coverage constraint ensuring feasibility under a bounded 20% demand deviation. A carbon emission penalty term was embedded in the objective function via an auxiliary excess-emission variable linked to a quota allowance. Bayesian inference was used as a post-optimization risk quantification tool to evaluate cost uncertainty due to recovery-rate variability. Our results indicated a baseline system cost of 878 million CNY, driven primarily by forward logistics and facility investments, with limited structural impact from current carbon policies. Bayesian analysis yielded a 7.89 million CNY risk premium for recovery-rate uncertainty. Sensitivity analysis identified critical thresholds triggering network reconfiguration. The framework supports resilient CLSC design under regional and parametric uncertainty.

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