FASOM

1
FASOM

• Hamburg
• January 17-19, 2007

2
Topics

• FASOM Basics
• FASOM Equations
• Analyzing FASOM
• Modifying FASOM

3
I FASOM Basics
4
Model Scope

• Natural Resources
• Agriculture
• Forestry
• Processing
• Food, Fibre, Timber, Energy Markets

5
Purpose and Objectives

• To study and advice policy makers about the
  agricultural and forestry sector response to
• Policies
• Environmental change
• Technical change
• Socioeconomic change

6
Policy Scope

• Climate and other environmental policies
• Research subsidies
• Agricultural policies
• Trade policies

Simultaneous assessment
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Structural Changes

• Policies
• Environmental change
• Technical change
• Socioeconomic change (population, preferences)

8
Methodology

• Partial Equilibrium
• Bottom Up
• Constrained Welfare Maximization
• Dynamic Optimization
• Integrated Assessment
• Mathematical programming
• GAMS

9
Model Structure
Limits
Limits
Resources
Land Use Technologies
Products
Markets
Inputs
Demand Functions, Trade
Processing Technologies
Environmental Impacts
Supply Functions
Limits
10
FASOM is a Large Linear Program
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Programming

• Declare and Assign
• Indexes
• Exogenous data
• Endogenous data
• Equations (endogenous/exogenous)
• Run Programs and Display Results

12
Major Indexes (Sets) (decl_basicsets.gms)

• Regions
• Periods
• Altitudes
• Species
• Resources
• Cohorts

• Farm sizes
• Farm types
• Technologies
• Products
• Substances

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Sets

• Identify scope
• Efficient, sometimes challenging
• Super sets, Sub sets, Tuples (Index maps)
• decl_basicsets.gms
• 2_activesets.gms
• calc_tuples.gms

14
Exogenous Data

• Resource endowments
• Technologies (Inputs,Outputs, Costs)
• Environmental Impacts
• Demand functions
• Policies
• Base Year Observations

15
Exogenous Data

• Parameters (Tables, Scalars)
• decl_parameters.gms
• Data_.gms

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Data Subdirectories

• EPIC
• FINDUS
• FADN others
• OSKAR
• FAO
• BIODIV

17
Endogenous Data

• Land use decisions (control variables), Impacts
  (state variables), Shadow prices of constraints
• Positive and Free Variables
• (Integer Variabales)
• 4_eufasom_model.gms

18
Equations

• Understanding them is
• to understand FASOM

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Equations

• Objective Function
• Resource Restrictions
• Technological Restrictions
• Environmental Accounts
• Others

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Major ParametersFOREST_DATA (PERIOD,REGION,SOILT
YPE,SOILSTATE,SPECIES,FARM,AGE,ALLTECH,ALLITEM)P
EREN_DATA (PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIE
S,FARM,AGE,ALLTECH,ALLITEM)CROP_DATA
(PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,ALL
TECH,ALLITEM)ECO_DATA (PERIOD,REGION,SOILTYPE,SO
ILSTATE,ALLTECH,ALLITEM)LIVE_DATA
(PERIOD,REGION,ANIMAL,ALLTECH,ALLITEM)FEED_DATA
(PERIOD,REGION,PRODUCT,ALLTECH,ALLITEM)PROCESS_D
ATA (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_D
ATA (PERIOD,REGION,ALLRESOURCE,SDITEM)STOCK_DATA
(PERIOD,REGION,PRODUCT,ALLITEM)LUC_DATA
(PERIOD,REGION,SOILTYPE,SPECIES,ALLCHANGE,ALLITEM)
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Major VariablesRESOURCE_VAR (PERIOD,REGION,RESOU
RCE) FOREST_VAR (PERIOD,REGION,SOILTYPE,SOILSTAT
E,SPECIES,OWNER,AGE,FORTECH) PEREN_VAR
(PERIOD,REGION,SOILTYPE,SOILSTATE,SPECIES,FARM,AGE
,CROPTECH) CROP_VAR (PERIOD,REGION,SOILTYPE,SOIL
STATE,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)
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Major EquationsOBJECTIVE_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,CHA
NGE) 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)
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Managing the Model Scope

• 2_active_sets.gms
• index elements on/off
• decl_scope.gms
• components on/off

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FASOM File Structure

• Main directory (full access)
• Data subdirectories (restricted access)
• Agriculture (FADN)
• Crop environmental impacts (EPIC)
• Bioenergy (ENFA)
• Nature Reserves (HABITAT)
• Forest Stands (OSKAR)
• Forest Industry (FINDUS)
• FAOSTAT
• Dynamics

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FASOM File Naming (Main Dir)

• Data files (data_.gms)
• Declaration files (decl_.gms)
• Input calculation files (calc_.gms)
• Program files (_.gms)
• GAMSCHK files (.gck), Solver option files
  (.opt)
• Report files (rep_.gms)
• Special program files (z_.gms)
• description
• 1,2,...,k

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FASOM Sub Directories

• Store original data files in provider format
• Convert data to FASOM format (names, resolution,
  unit consistency)
• Automated programs, slow, infrequent use
• Protect main FASOM directory from information
  floods
• Confidentiality (FADN), IPR

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FASOM Execution

• 1_load_data.gms (primary data files)
• 2_active_sets.gms (determine model size)
• 3_precompute.gms (calculation files)
• 4_eufasom_model.gms (equations)
• 5_base_report.gms (base solution report)
• 6_scenario.gms (repeated solves)
• 7_results.gms (scenario differences)

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Save / Restart

• When using GAMSIDE, each program segment must
  restart from previous one and save for the next
• 1_load_data.gms (save .\t\a1)
• 2_active_sets.gms (restart .\t\a1 save .\t\a2)
• 3_precompute.gms (restart .\t\a2 save .\t\a3)
• 4_eufasom_model.gms (restart .\t\a3 save .\t\a4)
• 5_base_report.gms (restart .\t\a3 save .\t\a4)
• ...

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1_load_data.gms

• Indexes
• include decl_basicsets.gms
• include decl_foresttuple.gms
• offlisting
• Load Data
• include data_crop2000.gms
• include data_faowood.gms
• include data_faocrop.gms
• include data_faoworldcrop2002.gms
• include data_oatsprice.gms
• include data_feed.gms
• include data_land.gms
• include data_cropsupply.gms
• include data_averagecropemission.gms

• include data_euepic.gms
• include data_euluc.gms
• include data_uscrops.gms
• include data_peat.gms
• include data_forprocess.gms
• include data_forproduct.gms
• include data_formarket.gms
• include data_treelog.gms
• include data_rotlength.gms
• include data_forestrent.gms
• include data_forest_set.gms
• include data_forest_nor.gms
• include data_forest_lrg.gms
• include data_forest_sml.gms

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2_active_sets.gms

• Define active set elements
• Region
• Period
• Product
• Cohort
• Can limit model scope to 1 Region, 1 Period, 1
  Product

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3_precompute.gms

• Assumptions and Definitions (Discounting)
• Deal with Data Gaps
• Calculations (Data, Tuples)
• Checks
• Calibrations (Zero Marginal Profits!)
• Experiments
• Check whether statements can be moved to
  subdirectory

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4_eufasom_model.gms

• Variable declarations
• Equation declarations
• On/off switches for some equations
• FASOM equations (see part II)
• First solve statement
• 4_eufasom_model.gck

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5_base_report.gms

• Declaration of report indexes and parameters
• Display of FASOM base solution
• Current period (?? observation)
• Future periods (?? econometric forecast)

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6_scenario_loop.gms

• Define scenarios
• Number (Set)
• Assumptions (Parameters)
• Declare report
• Loop over scenario set
• Restore all parameters to original values
• Implement scenario assumptions
• Solve
• Save solution

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7_scenario_report.gms

• Display scenario results
• Comparison between base line solution and
  scenario solution

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8_scenario_graphs.gms

• Display scenario results graphically
• Need gnupltxy installed

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II FASOM Equations

• 4_eufasom_model.gms

38
Understanding FASOM Equations

• GAMS code (indexed equation block)
• DISPLAYCR output (individual equations)
• Display equation components

39
Condition(al)s

• Restrict cases (very important, many indexes)
• Use GAMSCHK to check
• PRODUCTBAL_EQU(REGION,PERIOD,PRODUCT)
• PRODUCT_TUPLE(REGION,PERIOD,PRODUCT)..
• calc_tuples.gms

40
Constrained Optimization

• Max z f(X) ... objective function
• s.t. G(X) lt 0 ... constraints

41
FASOM Large Linear Programs
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Objective Function(Normative Economics)

• Maximize
• Area underneath demand curves
• - Area underneath supply curves
• - Costs
• Subsidies / Taxes from policies
• Maximum equilibrates markets!

43
Alternative Objective Function

• To get technical potentials from land use for
  alternative objective u, simply use
• Maximize
• u s.t. all constraints
• Examples u Carbon Sequestration, Wheat
  production, Mire area

44
Is FASOM linear?

• Input prices increase with increasing input use
  (scarcity of resources)
• Output prices decrease with increasing output
  supply (saturation of demand)
• Hence, FASOM has non-linear objective function
  but is solved as Linear Program using linear
  approximations

45
Linear Approximation?

• For well behaved functions yes
• Concave benefit / convex cost functions
• Decreasing marginal utilities
• Increasing marginal costs
• For ill behaved no, need integer variables
• Fixed cost (Investment)
• Minimum habitat requirements (Biodiversity)

46
Linear Approximation in FASOM

• Use step variables (xi) ... with i steps
• Convexity Restriction
• Sum(i, xi) 1
• Identity Restriction
• Sum(i, aixi) x
• DEMAND_VAR(REGION,PERIOD,PRODUCT)
• DEMAND_STEP(REGION,PERIOD,PRODUCT,STEP)
• DEMAND_CONVEXITY(REGION,PERIOD,PRODUCT)
• DEMAND_IDENTITY(REGION,PERIOD,PRODUCT)

How many steps?
47
Correct Convex Combination?

• Model will automatically choose closest neighbor
  points

48
Constraints
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PRODUCTBAL_EQU

• Very important
• Multi-input, Multi-output
• Negative coefficients - Inputs
• Positive coefficients - Outputs

50
RESOURCEBAL_EQU

• Sum resource uses over all technologies, species,
  farm structures into an accounting variable
• RESOURCE_VAR(REGION,PERIOD,RESOURCE)

51
RESOURCEMAX_EQU

• Represent resource limits (endowments)
• RESOURCE_VAR(REGION,PERIOD,RESOURCE)
• RESOURCE_DATA
• (REGION,PERIOD,RESOURCE,Maximum)

52
LUC_EQU

• LUC_EQU(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE)
• LUC_TUPLE(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE
  )..
• Land use accounting equation
• Combines individual and aggregated accounting

53
LUCLIMIT_EQU

• LUCLIMIT_EQU(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE
  )
• (LUC_TUPLE(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE
  ) AND
• LUC_DATA(REGION,PERIOD,SOILTYPE,SPECIES,CHANGE,
  
• "MAXIMUM"))..
• Land use change limits
• Should be based on land characteristics
• Currently uses rough assumptions

54
FORINVENT_EQU

• Forest distribution this period depends on forest
  distribution in last period and harvest
  activities
• Note
• Oldest cohort transition
• Initial distribution
• Harvested forests can immeadiatly be reforested

55
INTIALFOREST_EQU

• Thinning regime cannot be switched
• Initial thinning distribution unknown
• Let model decide, which thinning regime to use
  for initial forests

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REPLANT_EQU

• Restricts tree species that can be replanted
  after harvest (can have agricultural break
  inbetween)
• Regulated by tuple SPECIESSEQU_MAP(OLDSPECIES,SPEC
  IES)
• Currently restrictive

57
SOILSTATE_EQU

• To portray important unstable soil properties
• Carbon sequestration effect depends on soil
  carbon level
• Equations are implemented, EPIC data are not yet
  established
• SOILSTATE_EQU(REGION,PERIOD,SOILTYPE,SOILSTATE)

58
SOILSTATE_EQU

• To portray important unstable soil properties
• Carbon sequestration effect depends on soil
  carbon level
• Equations are implemented, EPIC data are not yet
  established

59
SOILSTATE_EQU

• Contains soil state transition probabilities
• Probability_Data(REGION,SOILTYPE,SOILSTATE,SPECIES
  , OWNER,COHORT,ALLTECH,POLICY,OLDSTATE)
• Transition probabilities are calculated from EPIC
  based carbon functions

60
Soil Carbon Transition Probabilities
No-till Wheat Fallow
61
Carbon Functions
Soil Organic Carbon (tC/ha/20cm)
62
STOCK_EQU

• STOCK_EQU(REGION,PERIOD,STOCK)
• (STOCK_TUPLE(REGION,PERIOD,STOCK) AND
• STOCK_DATA(REGION,PERIOD,STOCK,"DecompRate"))..
  
• Represents dynamics of dead wood (14 types)
• Linked to emission accounting

63
PRODUCTINVENT_EQU

• PRODUCTINVENT_EQU(REGION,PERIOD,PRODUCT)
• Represents different product life span of forest
  products
• Linked to carbon emissions from forest products

64
EMIT_EQU

• EMIT_EQU(REGION,PERIOD,SUBSTANCE)
• EMIT_TUPLE(REGION,PERIOD,SUBSTANCE)..
• Accounting equation
• Contains direct emissions and emissions from
  stock changes

65
POPULATION_EQU

• Computes the number of wild animals on suitable
  habitats
• POPULATION_EQU(REGION,PERIOD,ECOSYSTEM,ANIMAL)
• HABITAT_DATA(REGION,PERIOD,ECOSYSTEM,ANIMAL,"D
  ENSITY")..
• POP_VAR(REGION,PERIOD,ECOSYSTEM,ANIMAL)
• - HABITAT_DATA(REGION,PERIOD,ECOSYSTEM,ANIMAL,"DE
  NSITY")
• ( HABITAT_DATA(REGION,PERIOD,ECOSYSTEM,ANIMAL,"
  MINIMUM")
• HABSIZE_BINVAR(REGION,PERIOD,ECOSYSTEM,ANIMAL
  )
• HABITAT1_VAR(REGION,PERIOD,ECOSYSTEM,ANIMAL))
  
• L 0

66
HABITAT0_EQU, HABITAT1_EQU

• See presentation in wetland sub directory

67
Other Equations

• Crop mix
• Calibration constraints

68
III Analyzing FASOM
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Why Large Models?

• Land use is diverse and globally linked
• We want both high resolution and large scope
• More computer power tempts larger models
• Data availability better

70
Large Model Effects

• Indexed data, variables, and equations
• Dimensions need to be carefully conditioned
• More things can go wrong
• Less intuition in model drivers
• Causes of misbehavior difficult to guess
• Higher probability that some errors are not
  discovered

71
Pre-Solution Analysis

• Generic variable and equation checks
• About 30 different types
• Easy in GAMS through use of GAMSCHK, possible
  with other software

72
Example

• Nonnegative Variable Xj occurs only in lt
  constraints
• All aij coefficients are nonnegative
• All objective function coefficients (cj) are
  nonpositive
• ? Optimal Xj 0! (Maximization problem)

73
More Generic Checks
74
Generic Errors

• Caused by
• Missing/misspecified data
• Missing/misspecified conditions
• Missing/misspecified equations
• Correction (rule of thumb)
• All individual variables need the same condition
  in all individual equations

75
Generic Checks

• Large models frequently reveal unchecked generic
  errors
• Errors may or may not impact optimal solution
• Correction always increases model speed
• Detection and correction of generic errors also
  applicable to non-linear models

76
Post-Solution Analysisof Misbehaving Solutions

• Infeasible equations
• ? empty solution
• Unbounded variables
• ? objective reaches infinity
• Non-sensible solutions

77
Infeasibility

• Very easy to detect
• Easy to fix
• Use artificial variables
• Analyze equations with non-zero artificial
  variables
• Look for constraints with high shadow prices

78
Unbounded Solution

• Very easy to detect
• Easy to fix
• Add artificial bounds
• Look for high variable levels
• Examine equations coefficients of unbounded
  variables

79
Non-sensible solution values

• Detection requires context knowledge
• Problem analysis more challenging
• Large deviations easier
• Must employ post optimality checks
• Start at the symptom
• Go backwards alternating between variables and
  equations

80
Linear Program Duality
81
Reduced Cost
Shadow prices
Objective Function Coefficients
Technical Coefficients
82
Complementary Slackness
Opt. Slack Variable Level
Shadow Price
Opt. Variable Level
Reduced Cost
83
Reduced Cost Equality

• Links variables with individual equations
• Positive aijUi ? costs (Maximization)
• Negative aijUi ? benefits (Maximization)

84

Ex Reduced Cost Computation
85

Ex Row Summing
86
Fixing Non-sensible Models

• Zero/large variables look at cost and benefits
  of these variables in individual equations
• High shadow prices indicate resource scarcity
  (check endowments, technical coefficients, units)
• In general, analyst needs a combination of
  mathematical and context knowledge

87
Conclusions

• Large mathematical programming models are not
  necessarily black boxes
• Drivers for individual results can be traced and
  understood
• Generic misspecifications can and should always
  be corrected
• Systematic post-optimality analysis is by far
  better and faster than intuition and guesswork

88
IV Modifying FASOM
89
Possible Modicfications

• Data updates
• Data calculations
• Scenario anaysis
• Equation modifications

Easy
Difficult
90
Documentation

• Write log of changes in text file
• Place comments on purpose of programming
  statements in FASOM code
• Put ???? where you make preliminary
  modifications

91
Frequent Errors

• Units (Ex 5 vs. 1 years)
• Inconsistent conditions
• Ignorance of GAMSCHK