Presentation on theme: "Forest and Agricultural Sector Optimization Model (FASOM) Basic Mathematical Structure."— Presentation transcript:
Forest and Agricultural Sector Optimization Model (FASOM) Basic Mathematical Structure
Linear Programming FASOM can solve up to 6 Million Variables (j), 1 Million Equations (i)
Important Equations Objective Function Objective Function Resource Restrictions Resource Restrictions Commodity Restrictions Commodity Restrictions Intertemporal Transition Restrictions Intertemporal Transition Restrictions Emission Restrictions Emission Restrictions
ParameterDescription Technical coefficients (yields, requirements, emissions) Objective function coefficients Supply and demand functions Supply and demand function elasticities Discount rate, product depreciation, dead wood decomposition Resource endowments Soil state transition probabilities Land use change limits Initial or previous land allocation Alternative objective function parameters
VariableUnitTypeDescription CROP1E3 ha 0 Crop production PAST1E3 ha 0 Pasture LIVEmixed 0 Livestock raising FEEDmixed 0 Animal feeding TREE1E3 ha 0 Standing forests HARV1E3 ha 0 harvesting BIOM1E3 ha 0 Biomass crop plantations for bioenergy ECOL1E3 ha 0 Wetland ecosystem reserves LUCH1E3 ha 0 Land use changes RESRmixed 0 Factor and resource usage PROCmixed 0 Processing activities SUPP1E3 t 0 Supply DEMD1E3 t 0 Demand TRAD1E3 t 0 Trade EMITmixedFreeNet emissions STCKmixed 0 Environmental and product stocks WELF1E6 €FreeEconomic Surplus CMIX- 0 Crop Mix
IndexSymbolElements Time Periodst2005-2010, 2010-2015, …, 2145-2150 Regionsr25 EU member states, 11 Non-EU international regions SpeciessAll individual and aggregate species categories Cropsc(s) Soft wheat, hard wheat, barley, oats, rye, rice, corn, soybeans, sugar beet, potatoes, rapeseed, sunflower, cotton, flax, hemp, pulse Treesf(s) Spruce, larch, douglas fir, fir, scottish pine, pinus pinaster, poplar, oak, beech, birch, maple, hornbeam, alnus, ash, chestnut, cedar, eucalyptus, ilex locust, 4 mixed forest types Perennialsb(s)Miscanthus, Switchgrass, Reed Canary Grass, Poplar,, Arundo, Cardoon, Eucalyptus Livestockl(s)Dairy, beef cattle, hogs, goats, sheep, poultry Wildlifew(s)43 Birds, 9 mammals, 16 amphibians, 4 reptiles Productsy17 crop, 8 forest industry, 5 bioenergy, 10 livestock Resources/InputsiSoil types, hired and family labor, gasoline, diesel, electricity, natural gas, water, nutrients Soil typesj(i)Sand, loam, clay, bog, fen, 7 slope, 4 soil depth classes Nutrientsn(i)Dry matter, protein, fat, fiber, metabolic energy, Lysine Technologiesm alternative tillage, irrigation, fertilization, thinning, animal housing and manure management choices Site qualityqAge and suitability differences Ecosystem statex(q)Existing, suitable, marginal Age cohortsa(q)0-5, 5-10, …, 295-300 [years] Soil statevSoil organic classes StructuresuFADN classifications (European Commission 2008) Size classesz(u) = 100 all in ESU (European Commission 2008) Farm specialtyo(u) Field crops, horticulture, wine yards, permanent crops, dairy farms, grazing livestock, pigs and or poultry, mixed farms Altitude levelsh(u) 1100 meters Environmente16 Greenhouse gas accounts, wind and water erosion, 6 nutrient emissions, 5 wetland types PoliciespAlternative policies
Objective Function Maximize +Area underneath demand curves -Area underneath supply curves -Costs ±Subsidies / Taxes from policies The maximum equilibrates markets!
Economic Principles Rationality ("wanting more rather than less of a good or service") Law of diminishing marginal returns Law of increasing marginal cost
Demand function Area underneath demand function Decreasing marginal revenues uniquely defined by constant elasticity function observed price-quantity pair (p 0,q 0 ) estimated elasticity (curvature) price sales Demand function q 00 p0p0 q0q0
Duality restrictions (r,t,u) Prevent extreme specialization Incorporate difficult to observe data Calibrate model based on duality theory May include „flexibility contraints“ Past periods Observed crop mixes Crop Mix Variable No crop (c) index! Crop Area Variable
Miscellaneous GAMS Systematic Model Check Linearization Alternative Objective Function
Solution Decomposition Insights Why is an activity not used? How do individual equations contribute to the variable‘s optimality?
Current work Land management adaptation to policy & development Externality mitigation (Water, Greenhouse Gases, Biodiversity, Soil fertility) Stochastic formulation (extreme events) Land use & management change costs Learning and agricultural research policies Investment restrictions