Scenario-Based Mathematical Modeling for Biofuel Supply Chain Design

Objective: This study aims to design and optimize a sustainable biofuel supply chain focusing on water resource management, uncertainty reduction, and enhancing economic, environmental, and social performance. Sustainable biomass, such as Paulownia trees, and recycled water are considered key inputs, providing an integrated solution to the challenges posed by fossil fuels and the urgent need for renewable energy development. Methods: A multi-objective mathematical model is proposed to minimize costs, satisfy demand, and mitigate environmental impacts. The model incorporates uncertainties in supply and demand using the LP-metric method and applies the Fuzzy Analytic Hierarchy Process (FAHP) to weight objectives, ensuring balance among conflicting goals. Sensitivity analysis examines variations in biomass supply, prices, and demand, while Pareto frontier analysis evaluates trade-offs across objectives.  Results: Results show that scenario-based modeling enables a comprehensive assessment of supply and demand impacts on supply chain performance. Incorporating wastewater and sewage sludge reduces pressure on natural resources and improves economic and environmental efficiency. The ε-constraint method generates Pareto-optimal solutions, offering decision-makers alternatives consistent with their priorities. Sensitivity analysis highlights that using Paulownia biomass and recycled water enhances flexibility, reduces risks, and promotes balance among economic, environmental, and social objectives, while lowering costs and unmet demand. Conclusion: This study provides a practical framework for designing and managing a sustainable biofuel supply chain by presenting a comprehensive and practical model. The findings can serve as a roadmap for developing renewable energy and resource efficiency in the energy sector. Additionally, the proposed model offers a robust decision-making tool under conditions of uncertainty and environmental and economic fluctuations. Its application can significantly support sustainable development policies and reduce dependence on fossil fuel resources.

Keywords:

Mixed-Integer Linear Programming (MILP) , Multi-objective optimization , biofuel supply chain , Uncertainty , Water Resource Management