CwU 2007
December 10-12, 2007
IIASA, Laxenburg
Austria
Spatial Planning of Agricultural Production
under Environmental Risks and Uncertainties
G. Fischer, T. Ermolieva
International Institute for Applied Systems Analysis, Laxenburg, Austria
Background
This research is under the umbrella of two EU-sponsored
projects
CHINAGRO: Decision Support System for China's Agricultural Sustainable
Development (EU-ICA4-CT-2001-10085), 2002-2005.
CATSEI: Chinese Agricultural Transition: Trade, Social and Environmental
Impact (EU FP6 Project 44255), 2007-2009.
Broad range of factors determining spatio-temporal heterogeneity of demand
and supply of agricultural products:
•
•
•
•
•
•
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Demographic change
Urbanization
Overall economic growth
Availability of farmland; irrigated land
Technological progress in agriculture
Trade policies
Conditions on international markets
Research question
 Growing demands for meat, intensification trends, concentration
of production according to “increasing returns” principle.
 Main risks:
- environmental pollution (manure combined with chemical fertilizers)
- livestock related diseases and epidemics
- market risks
- demand uncertainties and instabilities
 A continuation of current intensification trend would bring in high
risks for the future.
 Risk perspective suggests rationales for spatial diversification
and co-existence of large- and small-scale producers.
 Long-term planning needs to base on sustainability principles:
increasing returns in combination with enforced policies relying
on risk indicators.
Co-existence of heterogeneous producers:
a risk-hedging strategy
Absence of risks: Two producers with production costs c1 < c2 < b
minimize
solution
c1 x1  c2 x2
x1  x2  d x1  0
*
x1*  d x 2  0
x2  0
Risk exposure: a1 and a2 are random variables (shocks to production)
minimize
c1 x1  c2 x2
a1 x1  a2 x2  d
minimize
F ( x)  c1 x1  c2 x2  bE max{ 0, d  a1 x1  a2 x2 }
where bE max{0, d – a1x1 – a2x2} is the expected import cost if demand
exceeds the supply.
Ermoliev, Y., Wets, R. (Eds.) Numerical Techniques for Stochastic Optimization.
Computational Mathematics, Springer Verlag, Berlin, 1988.
Co-existence of heterogeneous producers
If Producer 1 is at risk: 0 < E a1 < 1, a2 = 1. Positive optimal decisions exist if:
Fx1 (0,0)  0 Fx2 (0,0)  0 Fx1 (0,0)  c1  bEa1 Fx2 (0,0)  c 2  b
i.e., less efficient producer 2 is active unconditionally: c2 – b < 0
The cost efficient producer 1 is active if: c1 – bEa1 < 0
The less-efficient producer 2 stabilizes the aggregate production and the market
in the presence of contingencies affecting the “most cost-effective” producer 1.
Market share of the Producer 2 (risk-free producer with higher production costs):
Take derivative
Fx2 ( x , x 2 )  c 2  bP[d  a1 x  x2 ]
Optimal production share
x 2*  0 of Producer 2 is defined by the quantile
P[d  a1 x1*  x 2* ]  c 2 / b
of the distribution function describing
contingencies of the Producer 1, i.e., a1 , and the ratio c2 / b.
Challenges of spatial livestock production
planning under risks and uncertainties
 Long horizons of problems related to production and risks.
 Spatially explicit framework:
2434 counties.
 Aggregate or insufficient data for estimation of spatially
“disperse” agricultural risks, indicators and constraints;
compound risks.
 Need for spatially-explicit stochastic LS production planning
model and data upscaling/downscaling, harmonization
procedures.
 Production allocation and intensification levels are projected
from the base year for:
- Pigs, poultry, sheep, goat, meat cattle, milk cows) and
- Management system (grazing, industrial, specialized, traditional.
IIASA model for livestock production planning
Model structure and inputs

Base year distribution of production activities/resources at county level
 Alternative demographic projections and
 Economic scenarios
 Model derives estimates of:
- Demand for cereals and livestock products
- Spatial allocation and intensity levels of crop and
livestock production;
- Environmental pressure from agricultural production
- Health and environmental risk indicators
 Incorporates/compares:
Alternative production allocation criteria;
Procedures: Rebalancing/dowscaling &
stochastic optimization
Livestock production allocation under
risks and uncertainties
d i is the expected national supply increase in the livestock product i
xijl is the unknown portion of the supply increase i related to location j and
management system l
In its simplest form, the problem is to find xijl satisfying the following system
of equations:
 xijl  d i ,
(1)
xijl  0 ,
(2)
 xijl  b jl , l  1 : L , j  1 : n , i  1 : m ,
(3)
l, j
i
where b jl is aggregate risk constraint restricting the expansion of production
in system l and location j .
Apart from b jl , there may be additional limits imposed on xijl , xijl  rijl ,
which can be associated with legislation, for example, to restrict production i
within a production “belt”, or to exclude from urban or protected areas, etc.
Thresholds b jl and rijl may either indicate that livestock in excess of these
values is strictly prohibited or it incurs measures such as taxes or premiums,
for eradication of the risks, say, livestock diseases outbreaks or environmental
pollution. In this sense, they are analogous to the risk constraints from the
catastrophe and insurance theory. Values b jl and rijl may be reasonably
treated in priors.
Sequential rebalancing procedure
 yik  d i
Demand for product i; production in location k
k
 yik  bk
i
yik  0
Aggregate constraint on meat production at
location k
k qik  1 - prior, reflects alternative “behavioral” allocation principles
yik0  qik d i - expected initial allocation of demand to location i and system k
But y
0
ik
Derive relative imbalance
zik0
yiks
 k0  bk / i yik0
may not satisfy the constraint
Calculate
0
 y  bk
may not satisfy the constraint
 i0  d i / k zik0
can be represented as
i
ik
and update
zik0  yik0  k0
0
k zik  d i
and update
y1ik  zik0  i0


yiks  qikk d i qiks  qik  ks 1 /  j qik  ks 1

Sequential rebalancing procedure
The procedure can be viewed as a redistribution of required supply increase di
s 1
s
s
s 1
by applying sequentially adjusted qik : qik  qik  k / i qik  k ,
e.g., by using a Bayesian type of rule for updating the prior distribution,
qik0  qik .
The procedure converges to the optimal solution maximizing
the cross-entropy function
 yij ln
yij
qij
For Hitchcock-Koopmans transportation model the proof is in:
Bregman, L.M. “Proof of the Convergence of Sheleikhovskii’s Method for a Problem with
Transportation Constraints”, Journal of Computational Mathematics and Mathematical Physics,
Vol. 7, No. 1, pp191-204, 1967 (Zhournal Vychislitel’noi Matematiki, USSR, Leningrad, 1967).
For more general constraints and using duality theorem the proof is in:
Fischer, G., Ermolieva, T., Ermoliev, Y., and van Velthuizen, H.,
“Sequential downscaling methods for Estimation from Aggregate Data”
In K. Marti, Y. Ermoliev, M. Makovskii, G. Pflug (Eds.)
Coping with Uncertainty: Modeling and Policy Issue, Springer Verlag, Berlin, New York, 2006.
Alternative production allocation scenarios
1. Demand Driven Scenario: Production increase in locations is
proportional to demand potential (people, rural/urban, income)
2. Sustainable Scenario: trade-off between development and risks.
 Economic, social, environmental risk and sustainability indicators
and constraints reflect location-specific conditions and limitations
such as water and land scarcity, livestock density, urbanization level.
 Allocation of livestock beyond specified constraints may lead to
disastrous consequences related to water and air pollution,
hazards of livestock disease outbreaks, threats to
human health, which may incur high costs.
 The indicators and constraints are treated within priors or as explicit
constraints/goals.
 Individual “weights” of indicators/constraints reflect the critical tradeoffs, limitations and goals in locations.
Resource Constraints:
Intensity of cultivated and orchard land
(percent of total land in county) in 2000.
0 (%)
3-5 (%)
6-10 (%)
11-15 (%)
16-20 (%)
21-25 (%)
26-30 (%)
31-35 (%)
36-40 (%)
41-45 (%)
46-50 (%)
51-55 (%)
56-60 (%)
61-65 (%)
66-70 (%)
71-75 (%)
76-80 (%)
81-85 (%)
86-90 (%)
91-95 (%)
96-100 (%)
Population distribution
(persons per square kilometer)
Meat demand by income
Meat demand by sector
100000
1.2
80000
0.8
60000
0.6
1000 mt
Income Elasticity
1.0
0.4
0.2
Urban
40000
20000
Rural
0.0
6
7
8
9
0
10
2000
log(Incom e)
2010
2015
2020
2025
2030
Meat demand by type
Pigs by type of production system
600
100000
500
80000
Poultry
400
60000
Large
300
Spec
Trad
200
1000 mt
Millions
2005
40000
Pork
20000
100
Othe r meat
0
2000
2005
2010
2015
2020
2025
2030
0
2000
2005
2010
2015
2020
2025
2030
Hot-spots of high intensity of confined livestock
(livestock biomass in kg/ha cultivated land)
0
1-150
151-300
301-600
601-1000
1001-1500
>1500
0
1-150
151-300
301-600
601-1000
1001-1500
>1500
2000
2030
Hot-spots of manure nutrients from confined
livestock, (kg nitrogen/ha cultivated land), year
0
1-25
26-50
51-100
101-150
>150
0
1-25
26-50
51-100
101-150
>150
2000:
2000
2030:
a.
a. Demand-driving
b. Risk-adjusted
0
1-25
26-50
51-100
101-150
>150
33: Zhejiang
44: Guandong
Hot spots of fertilizer consumption (kg nitrogen/ha cultivated land)
2000
0
1-50
51-150
151-250
251-350
351-500
>500
2030
0
1-50
51-150
151-250
251-350
351-500
>500
Nutrient balance calculations.
County-specific nutrient balances compare nutrients from livestock
manure and fertilizers with the requirements and uptake capacities of crops.
Thus, calculated total nutrients losses include:
 nutrient losses from livestock housing, from manure storage facilities as well
as total liquid manure (largely unused),
 losses stemming from non-effective manure and fertilizers,
 losses due to over-supply of nutrients from fertilizers and manure to crops,
 non-effective manure nutrients produced by pastoral livestock systems.
Nutrient (nitrogen) losses per unit
area, kg/ha
2030
2000
0
1-25
26-50
51-100
101-150
151-250
>250
0
1-25
26-50
51-100
101-150
151-250
>250
A
B
Number of counties
2000
100%
100%
100%
80%
80%
80%
60%
60%
40%
40%
20%
20%
0%
0%
1600
60%
1200
40%
800
20%
400
0
0%
1-25
26-50
51-100 101-150 151-250
>250
Intensity of nitrogen losses per unit land (kg/ha)
Percentage of counties
Percentage of population
2400
1-25
26-50
51-100 101-150 151-250
>250
Intensity of nitrogen losses per unit land (kg/ha)
Cumulative percentage of population
Frequency distribution of:
a. Number of counties, and
b. Population, with regard to the intensity
of nitrogen losses per unit of land area.
Two scenarios are compared with respect to
number of people in China’s regions exposed to
different categories of environmental risks
NW
NW
SW
SW
S
S
C
C
E
E
NE
NE
N
N
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Figure 3. Relative distribution of population according to classes of severity
of environmental pressure from livestock, 2030: (a) demand driven scenario,
(b) environmentally friendly scenario.