Fuzzy interval programming for energy and environmental systems management under constraint-violation and energy-substitution effects: A case study for the City of Beijing

In this research, a fuzzy interval-parameter approach considering constraint-violation and energy-substitution effects (FIP-CVESE) was developed for planning municipal energy systems, which was an integration of interval linear programming (ILP) and fuzzy linear programming (FLP), as well as methods of constraint-violation and energy-substitution analyses. The proposed method was then applied to a real-world case for supporting the planning of the energy system in Beijing. The developed FIP-CVESE method could not only tackle uncertainties expressed as both interval numbers and fuzzy sets, but also allow several given levels of tolerable violations of system objective and constraints to expand the model's decision space, facilitating the improvement in solution robustness. The obtained results could provide a series of desired decision alternatives at preferred satisfaction degrees, including schemes related to energy resources allocation, technology adoption, facility capacity expansion, transportation device identification, and environmental pollution mitigation. Also the substitution solutions among multiple energy resources can be generated by combining energy substitution effects with the violation levels of resources demands constrains through the introduction of violation variables. The acquired solutions could also help decision makers gain insights of trade-offs between the economy and environment, as well as support decision-making for the planning of the energy system in Beijing.