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Key issue, challenges, and status quo of models for biofuel supply chain design 287

those decisions are critical for BSC design. With the development of com-
puter science and mathematical programming theories, increasingly
complex BSC models have been developed to address large-scale and multi-
dimensional challenges in BSC design. In this section, two main aspects of
modeling techniques for BSC design, optimization and simulation, are dis-
cussed and reviewed.

4.1 Optimization models
Optimization is a mathematical process aiming at finding the maximum or
minimum value of objective functions which are subject to constraints
(Dantzig, 2016; Fang and Puthenpura, 1993). An optimization model
consists of three parts, decision variables, constraints, and objective func-
tions. Generally, the constraints can be equalities, inequalities, and integer
restrictions. Depending on the mathematical structureand thesizeof
models, different algorithms are needed to solve optimization problems
(Fang and Puthenpura, 1993; Rajasekera and Fang, 1991).

4.1.1 Types of BSC optimization objectives
The objective functions in the BSC optimization models are typically related
to three aspects of sustainability: economic, environmental, and social impli-
cations. Economic effectiveness is the most common objective function in
BSC optimization studies (Corsano et al., 2011). In recent years, environ-
mental objective functions such as minimizing GHG emissions and energy
footprints and social implications (e.g., job creation) have been included in
more and more articles (You et al., 2012; Corsano et al., 2011). Previous
studies are reviewed and categorized based on their considerations related
to economic, environmental, and social aspects as shown in Table 10.3.
Economic viability is one of the most common objectives used in pre-
vious BSC optimization studies. Common indicators related to economic
viability used in previous studies include expected net profit, Internal Rate
of Return (IRR), and Net Present Value (NPV) (Lea ˜o et al., 2011; Palak
et al., 2014; Alex Marvin et al., 2012; Dal-Mas et al., 2011). The economic
objective function can be designed for whole or part of the BSC (e.g., profit
of biorefinery or NPV of the entire supply chain) (Azadeh et al., 2014; Alex
Marvin et al., 2012). Depending on the specific economic indicators chosen
as the objective functions, economic and process data at different levels need
to be collected. For example, using robust optimization, Lin et al. (2012)
chose minimizing product unit cost as the objective function and collected
the data of fuel price. Ren et al. (2015) took the life cycle cost of the BSC as