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298 Biofuels for a More Sustainable Future

Other studies have used fuzzy mathematical programming (FMP) to
address uncertainties (Mula et al., 2010). In SP, the uncertainty of indepen-
dent variables is modeled using probability density function which could be
hard to determine due to the lack of data. In FMP, uncertainties are modeled
by fuzzy numbers with fuzzy intervals, which could be helpful to character-
ize uncertain parameters (Tong et al., 2013; Roubens and Teghem, 1991;
Inuiguchi and Ramik, 2000; Lodwick et al., 2000). For example, in the
MILP model developed by Tong et al. (2013), the data related to the con-
version rate from intermediates to end products, capital costs, and opera-
tional costs were limited, and the probability functions of feedstock
supply and product demand were unkown. In this situation, fuzzy numbers
could be helpful in modeling those uncertain parameters with limited data.
Another example the MILP model developed by Yilmaz Balaman and Selim
(2014) that incorporated fuzzy constraints and fuzzy goal programming to
address uncertainty.

4.1.3 Geographical information system (GIS)-based BSC design
Given the intensive computation loads of most optimization models, it is
challenging to design BSC at a high spatial resolution (e.g., 10km by
10km). Many previous optimization models used low-resolution spatial data
(e.g., county level without considering real routes of different transportation
infrastructure), as presented in Table 10.3. Geographic Information System
(GIS) is a powerful tool specifically used to process, visualize, and analyze
geographic data, and it has been used and integrated with optimization
models for BSC design. In most of previous studies, GIS has been used to
provide geographic information that is needed for parameters in optimiza-
tion models (Kim et al., 2011; Parker et al., 2010; Bowling et al., 2011;
Nardi et al., 2007).
Lin et al. (2015) developed a GIS-enabled model to optimize the BSC
using GIS to generate data on biomass availability, production costs, and dis-
tances for the optimization model. He-Lambert et al. (2018) proposed a
GIS-MILP combined model to decide the biomass supply and facility loca-
tions at a high spatial resolution where GIS provided the information of
cropland locations and areas, potential plant sites, and road transportation
network. Zhang et al. (2016b) developed a GIS and optimization model
where GIS was employed to choose biofuel facility locations by inputting
the geospatial information including county boundaries, transportation
network, water body dispersion, and city locations. In other studies, GIS