Location-Allocation of a Biorefinery Based on Linguistic Mixed Integer Nonlinear Mathematical Modeling

Significant research is currently being conducted to explore renewable energy sources, such as biomass fuel, in response to recent fluctuations in fossil fuel prices and environmental concerns. However, utilizing biomass energy poses challenges due to the widespread distribution of feedstock and the need to transport multiple low-energy-density materials to conversion facilities. In this investigation, a Linguistics Mixed Integer Nonlinear Programming (LMINLP) approach with Z-number computations was employed to analyze the optimal allocation of locations for a bio-refinery supply chain network. This proposed method significantly impacted the product process, time value for plutocrats, installation investment costs, and transportation network. This research aims to construct an LMINLP model to determine the optimal position of a single installation within a bio-refinery. The primary goal was to make well-informed investment decisions regarding technologies, facilities, capacities, and site selections. A firefly algorithm incorporating a piecewise linearization approach was utilized to solve the model and achieve global optimality. The model’s effectiveness was demonstrated through numerical examples, including those from the ethanol industry.