IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, cilt.0, sa.0, ss.1-11, 2026 (SCI-Expanded, Scopus)
Urban micromobility systems require efficient battery collection and replacement strategies to maintain service continuity and sustainability. This study proposes an energy-aware fuzzy milk-run optimization model for e-scooter battery routing under traffic-induced time uncertainty. Travel times are represented by triangular fuzzy numbers derived from observed traffic variability, enabling flexible schedule compliance. The problem is formulated as a Fuzzy Mixed-Integer Linear Programming (FMILP) model minimizing operational cost, energy consumption, and time-window penalty costs through weighted coefficients (α, β). Rather than arbitrarily selecting these coefficients, a structured sensitivity analysis is conducted to evaluate their impact on routing performance. A real-world case study in Istanbul involving ten service nodes is used to validate the framework. Comparative experiments with a deterministic MILP baseline show an average 43.3% reduction in total cost and 14.97% reduction in energy consumption. To enhance robustness, multiple traffic scenarios are analyzed to assess model stability under varying uncertainty levels. Results indicate that the fuzzy formulation improves schedule reliability while maintaining energy efficiency. Compared with the authors' earlier deterministic conference study, this journal version extends the framework by integrating fuzzy time-window modeling, energy-aware calibration, and quantitative performance evaluation. The proposed approach provides a scalable decision-support tool for sustainable micromobility fleet management.