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Key issue, challenges, and status quo of models for biofuel supply chain design  305


                 Different modeling approaches have been used to solve BSC optimiza-
              tion models. Among those approaches, MILP is found to be the most com-
              mon type of modeling technique. Binary variables are useful for modeling
              decisions related to locations or technologies. NLP can be employed when
              nonlinearity exists in models (e.g., production constraints). Both MILP and
              NLP are used for deterministic BSC. However, there are many sources of
              uncertainties in BSC, such as biomass availability, feedstock price, fuel
              demand, and selling price. To address uncertainty, SP and FMP are used
              in many previous studies. Uncertainties related to tactical and operational
              decisions were typically modeled in the second stage of multistage optimi-
              zation. Besides uncertainties in BSC, BSC design with high geographic res-
              olution can be challenging given the intensive need of geospatial
              information. GIS has been used by previous studies to process and provide
              the spatial data need by BSC design.
                 As another modeling approach for BSC design, simulation can offer a
              better understanding of the dynamic effects of design strategies and param-
              eter settings. In most of previous studies reviewed in this chapter, BSC
              design decisions was made by developing “what-if” scenarios in simulation
              models. Among different simulation techniques, ABM is a powerful tech-
              nique that has been employed by researchers to support BSC decision-
              making with a consideration of individual stakeholder behaviors and to
              understand emergent phenomena for risk management.
                 The uncertainty of different components in BSC design is challenging
              from both technical and modeling perspective. How to coordinate different
              component in BSC with a consideration of uncertainty is challenging and
              needs more efforts on the data collection and decision-making tool devel-
              opment. Effective algorithms are also needed for complex BSC models that
              take uncertainty into consideration. Some uncertainties are brought in by
              choices in methodology (e.g., LCA allocation methods). Those uncer-
              tainties are hard to be fully addressed, but transparent documentation and
              sensitivity analysis could be helpful.
                 Based on the review and challenges identified, future directions that need
              more efforts are summarized:
              (1) BSC design needs more integrated modeling tools to enhance decision-
                 making toward sustainable production and delivery of biofuels, espe-
                 cially on understanding and quantifying environmental and social
                 implications of different BSC design strategies.
              (2) Uncertainty challenges need to be addressed from technical, data, and
                 methodological  perspectives.  More  advanced  algorithms  and
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