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| Model source/country | Model formulation/benefits | Applied constraints/drawbacks |
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| Parker et al. [4] (2010, United States) | (i) Mixed-integer LP†
(ii) Maximizes annual revenue
(iii) Considers feedstock handling efficiency/loss, conversion cost and efficiency,and transportation costs
(iv) Simulates industry-wide fuel production at fixed price, for generating regional and/or state level exploring supply-cost curve under different feedstock mixes
(v) Model links with explicit feedstock spatial distributions | (i) Assumes value of all fuels have equal energy content
(ii) Other than transport, does not consider many aspects of supply logistics (i.e., pretreatment, collection, storage)
(iii) Impact of associated supply risks due to weather/climate-related variability and extremes not taken into account
(iv) Intraannual (i.e., within-year) supply dynamics not considered
(v) Net greenhouse gas benefits of biofuel production from feedstock mixes not considered, yet potentially has large effect on future crop production feedstock/resource base |
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| Dunnett et al. [5] (2008, United Kingdom) | (i) Single-commodity, discrete (i.e., grid-based) noninteger LP
(ii) Minimizes annual production costs and system logistics (i.e., supply distance/time specific to each feedstock type)
(iii) Considers rural, semirural, and urban region types, with assumed “industry of scale” cost reduction function
(iv) Considers pretreatment efficiency, transfer speed, and loading/unloading time for each feedstock supply logistics
(v) Flexible framework for including range of processing tasks, logistical modes, coproducts, and regional policy constraints as dynamic extensions for real-world case study | (i) Assumes 10% fractional availability of cropland as resource base
(ii) No link to explicit feedstock spatial distribution considers idealized crop spatial distributions as regional typologies: centralized and corner point
(iii) Lignocellulosic ethanol processing only currently simulated |
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| “BioTrans” Van Tilberg et al. [6] (2005, European Union) | (i) Multicommodity, multistage, mixed-integer LP
(ii) Annual time step, minimising production costs and system logistics
(iii) Considers macroeconomic and technological projections in finding minimal cost allocations for supply chains
(iv) Detailed consideration of conversion processes | (i) Operates on a country aggregation level. Input and projections can be set at national level and costs and production quantities determined
(ii) Requires each country to have a complete production and supply chain with one production or processing facility of each type, so difficult to apply at regional level
(iii) Impact of associated supply risks due to weather/climate-related variability and extremes not taken into account
(iv) Intraannual (i.e., within-year/in-season) supply dynamics not considered |
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| Huang et al. [7] (2010, United States) | (i) Multistage, mixed integer LP
(ii) Annual time step, minimizes annual production costs and system logistics
(iii) Considers transboundary of feedstock supply and associated outsourcing penalty costs
(iv) Considers explicit feedstock distributions
(v) Considers fixed candidate refinery locations
(vi) Allows for increases in biorefinery capacity over time | (i) Developed for first application to lingocellulosic ethanol/biomass resources
(ii) Landscape suitability/ratings specific to individual crops/feedstocks not currently considered, so only considers fixed set of candidate biorefinery locations
(iii) Impact of associated supply risks due to weather/climate-related variability and extremes not taken into account |
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| “IBSAL” Sokhansanj et al. [8] (2008, United States) | (i) Grid-based simulation
(ii) Integrated biomass supply analysis and logistics model (IBSAL)
(iii) Simulates the flow of biomass through collection, transport, storage, and preprocessing considers costs, energy, and net CO2 emissions multiobjectives considers weather impacts on supply-chain logistics | (i) Relies on calibration of empirical relationships and other detailed look-up table (LUT) logistics operation data, that is, primarily focused on the front end of the biofuels supply chain at the local level
(ii) No link to explicit feedstock spatial distribution
(iii) Enables sensitivity analysis of input data in relation to empirically derived logistical functions, but does not optimize, so lacks ability to explore more full supply-chain and regional-scale scenarios |
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| Newlands et al. [9, 10] (2010, Canada) | (i) Multicommodity, multistage, nonlinear LP
(ii) Implemented with a global parameter optimization scheme for enhanced robustness as model complexity increases (e.g., multiple chains, national-scale application)
(iii) Monthly time step, minimizes production costs and system logistics
(iv) Considers multiple feedstocks/mix, multiple collection and single to multibiorefinery systems
(v) Model links with explicit feedstock distributions
(vi) Considers weather/climate impacts as part of supply cost scenarios | (i) Developed for first application to lingocellulosic ethanol, subsequently being further applied/tested for forestry/agricultural cross-sector biomass and biodiesel supply chains
(ii) Landscape suitability/ratings specific to individual crops/feedstocks not currently considered, so only considers fixed set of candidate biorefinery locations
(iii) Does not currently include multicriteria as part of its optimization |
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