Bi-Level Dependent-Chance Goal Programming for Paper Manufacturing Tactical Planning: A Reinforcement-Learning-Enhanced Approach

Abstract

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.