Hybrid Fuzzy Optimization Integrating Sobol Sensitivity Analysis and Monte Carlo Simulation for Retail Decarbonization: An Investment Framework for Solar-Powered Coffee Machines in Taiwan’s Convenience Stores

This study develops a carbon emissions reduction strategy for solar-powered coffee machines in Taiwanese convenience stores, aiming to strike a balance between profitability and decarbonization. An integrated framework of the fuzzy nonlinear multi-objective programming (FNMOP) model, Sobol sensitivity analysis, and Monte Carlo simulation was applied to quantify uncertainties in electricity supply, consumer demand, and investment costs. Solar-powered machines reduce annual CO₂ emissions by 172–215 kg per store. Allocating 0.49–0.61% of coffee profits as subsidies shortens payback to [6.5, 9.375] years. Monte Carlo simulation confirms robustness with a 95% confidence interval of [5.8, 11.2] years, while urban stores achieve payback 18–25% faster. Sobol analysis identifies annual savings and net profit margins as key drivers. The framework demonstrates scalability and international applicability, providing empirical evidence for policymakers and retailers to accelerate the adoption of renewable energy in consumer-facing operations. Its methodological integration and consumer-side focus offer a replicable model for convenience store chains in high-density retail markets worldwide, with potential multiplier effects across sectors and supply chains.