Download Checking Misbehaving Mathematical Programs

The European Forest and
Agricultural Sector Optimization
Model (EUFASOM)
Uwe A. Schneider
Research Unit Sustainabilty and Global Change
Hamburg University
FASOM History
US (1993)
EU (2004)
Global (2006)
FASOM
Partial Equilibrium Model
Maximizes sum of consumer and producer
surplus
Constrained by resource endowments,
technologies, policies
Spatially explicit, discrete dynamic
Integrates environmental effects
Programmed in GAMS
Purpose and Objectives
To advice policy makers about the
agricultural and forestry sector response
to structural changes
a) Policies
b) Environmental change
c) Technical change
d) Socioeconomic change
Policy Scope
Climate and other environmental policies
Research subsidies
Agricultural policies
Trade policies
Simultaneous assessment
Food
Timber
Fiber
Carbon
Sinks
Bioenergy
Biomaterial
Land use
competition
Sealed
Land
Nature
Reserves
Objective Function
Price
Supply
Consumer
Surplus
P*
Resource
Rents
Demand
Q*
Quantity
Surplus Maximization
Land Supply
Forest Inventory
Processing Demand
Water Supply
CS
Labor Supply
PS
Implicit Supply and Demand
Animal Supply
National Inputs
Domestic Demand
Import Supply
Feed Demand
Export Demand
Commodity Demand
• 4 general cases (above)
• For all final products
• For all regions
• Domestic Use, Export
Model Structure
Limits
Limits
Resources
Inputs
Supply
Functions
Land Use
Products
Markets
Processing
Technologies
Demand
Functions,
Trade
Technologies
Environmental
Impacts
Limits
Model Structure
Cropland
Water
Labor
Forest
Inventory
Forestry,
Nature,
Crop
production
Markets
Domestic
demand
Export
Processing
Import
Other Inputs
Livestock
production
Pasture
Feed
mixing
Spatial Resolution
Soil texture
Stone content
Altitude levels
Slopes
Soil state
Political regions
Ownership
(forests)
Farm types
Farm size
Many crop and tree
species
Tillage, planting
irrigation, fertilization
harvest regime
Homogeneous
Response Units
Altitude:
1. < 300 m
2. 300-600 m
3. 600-1100 m
4. >1100 m
Texture:
1. Coarse
2. Medium
3. Medium-fine
4. Fine
5. Very fine
Stoniness:
1. Low content
2. Medium content
3. High content
Slope Class:
1. 0-3%
2. 3-6%
3. 6-10%
4. 10-15%
5. …
Soil Depth:
1. shallow
2. medium
3. deep
DE11
DE12
DE13
DE14
EUFASOM Dynamics
5 (to 20) year time steps
State of forests (and soil organic matter)
Technical progress
Demand & industry growth
Resource and global change
Policy scenarios
State of the Art
Flexibility (resolve acc. needs)
Index notation
– millions of data, variables, and equations
with sparse programming statements
– ensures consistency (model development)
Extensive generic equation checks (30 checks
per equation)
Systematic solution analysis (symptom to
cause)
Positive Variables
RESOURCE_VAR (PERIOD,REGION,RESOURCE)
FOREST_VAR (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,OWNER,AGE,FORTECH)
PEREN_VAR (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,AGE,CROPTECH)
CROP_VAR (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,CROPTECH)
LIVE_VAR (PERIOD,REGION,ANIMAL,LIVETECH)
FEED_VAR (PERIOD,REGION,ANIMAL,PRODUCT,FEEDTECH)
ECO_VAR (PERIOD,REGION,SOILTYPE,SOILSTATE,ECOTECH)
PROCESS_VAR (PERIOD,REGION,PROCTECH)
LUC_VAR (PERIOD,REGION,SOILTYPE,SPECIES,CHANGE)
DEMAND_VAR (PERIOD,REGION,PRODUCT)
SUPPLY_VAR (PERIOD,REGION,PRODUCT)
TRADE_VAR (PERIOD,REGION,REGION,PRODUCT)
Equations
OBJECTIVE_EQU
RESOURCEBAL_EQU (PERIOD,REGION,RESOURCE)
RESOURCEMAX_EQU (PERIOD,REGION,RESOURCE)
SOILSTATE_EQU (PERIOD,REGION,SOILTYPE,SOILSTATE)
FORINVENT_EQU (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,OWNER,AGE,FORTECH)
LUC_EQU (PERIOD,REGION,SOILTYPE,SPECIES,CHANGE)
LUCLIMIT_EQU (PERIOD,REGION,SOILTYPE,SPECIES,CHANGE)
STOCK_EQU (PERIOD,REGION,STOCK)
EMIT_EQU (PERIOD,REGION,SUBSTANCE)
PRODUCTBAL_EQU (PERIOD,REGION,PRODUCT)
MINFEED_EQU (PERIOD,REGION,ANIMAL,NUTRIENT)
MAXFEED_EQU (PERIOD,REGION,ANIMAL,NUTRIENT)
Data
FOREST_DATA (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,AGE,ALLTECH,ALLITEM)
PEREN_DATA (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,AGE,ALLTECH,ALLITEM)
CROP_DATA (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,ALLTECH,ALLITEM)
ECO_DATA (PERIOD,REGION,SOILTYPE,SOILSTATE,ALLTECH,ALLITEM)
LIVE_DATA (PERIOD,REGION,ANIMAL,ALLTECH,ALLITEM)
FEED_DATA (PERIOD,REGION,PRODUCT,ALLTECH,ALLITEM)
PROCESS_DATA (PERIOD,REGION,ALLTECH,ALLITEM)
PRODUCT_DATA (PERIOD,REGION,PRODUCT,ALLITEM)
MARKET_DATA (PERIOD,REGION,ALLITEM,SDTYPE,SDITEM)
TRADE_DATA (PERIOD,REGION,REGION,PRODUCT,ALLITEM)
RESOURCE_DATA (PERIOD,REGION,ALLRESOURCE,SDITEM)
STOCK_DATA (PERIOD,REGION,PRODUCT,ALLITEM)
LUC_DATA (PERIOD,REGION,SOILTYPE,SPECIES,ALLCHANGE,ALLITEM)
Pre-Solution Analysis
Identifies structural errors
– Missing data
– Misspecified data
– Wrong signs
More than 30 general variable and
equation checks
Mitigation Potentials
500
Carbon price (Euro/tce)
450
400
Technical
Potential
350
Competitive
Potential
300
250
200
150
100
50
0
0
100
200
300
400
500
Mitigation (mmtce)
600
700
800
Changes in Welfare
Accounts
8
6
4
Gross Ag-Producer Surplus
Billion Euros
2
Net Ag-Producer
Surplus
0
-2
Emission
Payments
-4
-6
Ag-Consumer Surplus
-8
-10
0
20
40
60
80
Carbon Equivalent (CE) Prices in Euros per Ton
100
GHG Mitigation and Markets
220
200
Fisher index
180
160
Crop prices
Livestock prices
140
120
Livestock production
100
80
60
Crop production
Net exports
40
20
0
50
100
150
200
Carbon price (Euro/tce)
250
300
Afforestation Potentials
Carbon price (Euro/tce)
500
400
300
Competitive
Economic
Potential
200
Economic
Potential
100
Technical Potential
0
0
50
100
150
200
Emission reduction (mmtce)
250
300
Forest Policy: Crop Emissions
15
Emissions (kg C/ha)
10
Irrigation Use
Nitrogen
Fertilizer
5
0
Fossil Fuel Use
-5
-10
-15
Ag-Soil Carbon
0
50
100
150
200
Carbon price (Euro/tce)
250
300
500
Carbon Price in Euro/mtce
450
400
350
Independent
Geographic
Potential
Competitive
Economic Potential
300
250
Simult.
Technical
Potential
200
150
Independent
Technical
Potential
100
50
0
0
100
200
300
400
500
600
700
800
Total Agricultural Greenhouse Gas Emission Abatement in mmtce
900
500
Crop
Area
Fixed
450
Carbon Price in Euro/mtce
400
Crop
Area
and
Prices
Fixed
350
300
Crop Area
and Prices
Endogenous
250
200
Prices
Fixed
150
100
50
0
0
100
200
300
400
500
600
700
Total Agricultural and Forest Greenhouse Gas Emission Abatement in mmtce
Power Plant Biomass Supply
Energy Crops (million hectares)
80
70
Unrestricted
Capacity
60
50
2050 Capacity
40
30
2030 Capacity
20
10
0
2010 Capacity
0
20
40
60
80
Carbon tax on energy (Euro/ton of carbon)
100
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