The Sustainable Supply Chain Network Design Problem (SSCNDP) is to determine the optimal network configuration and resource allocation that achieve the trade-off among economic, environmental, social, and resilience objectives. The Sustainable Supply Chain Network Design Problem (SSCNDP) involves determining the optimal network configuration and resource allocation that allows trade-off among economic, environmental, social, and resilience objectives. This paper addresses the SSCNDP under hybrid uncertainty, which combines objective randomness got from historical data, and subjective beliefs induced by expert judgment. Building on chance theory, we formulate a dependent-chance goal programming model that specifies target probability levels for achieving sustainability objectives and minimizes deviations from these targets using a lexicographic approach. To solve this complex optimization problem, we develop a hybrid intelligent algorithm that combines uncertain random simulation with Reinforcement Learning-enhanced Salp Swarm Optimization (RL-SSO). The proposed RL-SSO algorithm is benchmarked against standard metaheuristics—Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and standard SSO, across diverse problem instances. Results show that our method consistently outperforms these techniques in both solution quality and computational efficiency. The paper concludes with managerial insights and discusses limitations and future research directions.

The paper manufacturing industry faces significant challenges in coordinating production and distribution decisions under uncertain market conditions. This research presents an integrated production–distribution planning model for paper manufacturing that addresses demand uncertainty through fuzzy set theory. The model considers multiple paper grades, production facilities, warehouses, and customer zones while minimizing total supply chain costs. A hybrid intelligent algorithm combining genetic algorithms with fuzzy simulation is developed to solve the complex optimization problem. The approach handles fuzzy demand parameters using credibility theory and employs Monte Carlo simulation for fuzzy variable evaluation. Computational experiments demonstrate the effectiveness of the proposed methodology, achieving cost reductions of 12–18% compared to traditional deterministic approaches. The results indicate that the fuzzy–genetic algorithm approach provides robust solutions that perform well under various uncertainty scenarios, making it suitable for practical implementation in paper manufacturing supply chains.

Tactical production–distribution planning in paper manufacturing involves hierarchical decision-making under hybrid uncertainty, where aleatory randomness (demand fluctuations, machine variations) and epistemic uncertainty (expert judgments, market trends) simultaneously affect operations. Existing approaches fail to address the bi-level nature under hybrid uncertainty, treating production and distribution decisions independently or using single-paradigm uncertainty models. This research develops a bi-level dependent-chance goal programming framework based on uncertain random theory, where the upper level optimizes distribution decisions while the lower level handles production decisions. The framework exploits structural symmetries through machine interchangeability, symmetric transportation routes, and temporal symmetry, incorporating symmetry-breaking constraints to eliminate redundant solutions. A hybrid intelligent algorithm (HIA) integrates uncertain random simulation with a Reinforcement-Learning-enhanced Arithmetic Optimization Algorithm (RL-AOA) for bi-level coordination, where Q-learning enables adaptive parameter tuning. The RL component utilizes symmetric state representations to maintain solution quality across symmetric transformations. Computational experiments demonstrate HIA’s superiority over standard metaheuristics, achieving 3.2–7.8% solution quality improvement and 18.5% computational time reduction. Symmetry exploitation reduces search space by approximately 35%. The framework provides probability-based performance metrics with optimal confidence levels (0.82–0.87), offering 2.8–4.5% annual cost savings potential.

The paper manufacturing industry faces increasing challenges in balancing operational costs with service quality under uncertain market conditions. This research presents a bi-objective credibility-based expected value model for integrated production–distribution planning that simultaneously minimizes total costs and maximizes service-level performance. The model considers multiple paper grades, production facilities, warehouses, and customer zones while handling demand uncertainty through credibility theory. Three additional constraints are introduced: service time limitations, capacity expansion decisions, and quality assurance requirements. The Torabi–Hassini (TH) method is employed to solve the bi-objective optimization problem effectively. Computational experiments demonstrate the model’s capability to provide balanced trade-off solutions between cost efficiency and service quality, achieving service-level improvements of 8–13% with cost increases of 5–9% compared to cost-only optimization, and cost reductions of 10–15% compared to service-only optimization. The results show that the credibility-based expected value approach provides robust and practical solutions for paper manufacturing supply chain optimization.