a linear programming model to optimize diets in
TRANSCRIPT
12/09/2018
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A linear programming model to optimize
diets in environmental policy scenarios
Paper by: L.E. Moraes, J.E. Wilen, P.H. Robinson, J.G Fadel
(2012)
Presented by: Dan Jensen
Advanced Quantitative
Methods in Herd Management
– 12/09 2018
Introduction
• Problem: (Dairy)-farming is messy!
• Goal: Tool for optimizing dairy cattle diet
• Status of this research: Preliminary!
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•Agriculture: 6.3 % total US GHG emissions (2009)
•Enteric fermentation (���): 20 % of US human GHG
•Also nitrogen, phosphor, etc.
•Effect of emission taxes
•Forced (assumed) reduction
•Sensitive to constraints. E.g. feed prices
Methods
General Background
• Linear Programming Model (LPM)
• Reminder - an LPM is:
• Method to achieve best outcome given certain
constraints
• Constraints are represented by linear
relationships
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Methods
The models
• Three scenarios – three models:
• BASEM: Cheapest possible feed (baseline)
• TAXM: what if there was an emission tax?
• … of 5 $ per tonne?
• … of 17 $ per tonne?
• … of 250 $ per tonne?
• REDM: what if you were forced to reduce emissions?
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Methods
The models, Assumptions 1
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�� − ��
Methods
The models, Assumptions 2
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Locally
collected
kg/kg DM $/kg DM − �� − �� − �
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Methods
The models, Assumptions 2.1
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Methods
The models, specifics
• BASEM/REDM:
Remember: j = feed
c = cost of feed
a = animal class
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Methods
The models, specifics
• TAXM:
Remember: j = feed
c = cost of feed
a = cow category
Notice: e = expected emission (tonnes)
p = tax price per tonne
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������
Methods
The models, Outputs
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55.65 MJ/kg• How big is the mess?
Feed composition – absorbstion� Excrete composition
5 minute breakMethods
The models, Constraints 1
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Nutrient req. Diet. Feed Limits
Methane Restrictions
DMI
Other Limits, 1
Diet. Barley LimitsOther Limits, 2
Diet. Forage Proportions
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Methods
The models, Constraints 2
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Nutrient req.
Remember: j = feed
a = cow category (7 kinds)
i = nutrient (14 kinds)
Amount
Nutrient
content
Requirement7 x 14 = 98 eq.
Methods
The models, Constraints 3
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Diet. Feed Limits
Remember: j = feed
a = cow category (7 kinds)
l = limit (for 10 kinds of j)
��� ≤ ��� ∙������
���
7 x 10 = 70 eq.
Methods
The models, Constraints 4
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Methane Restrictions
(REDM)
Total feed
(all cows, all feed)
1-Reduction
BASEM
emission
Max.
Emission
Total NDF Total MEMethane
prediction
Results
• REDM:
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Neutral Detergent Fiber
consumption given
Methane reductionMetabolisable energy
proportion given
Methane reductionCrude protein consumption
given Methane reduction
Results
• REDM:
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↓ ���→↓ ���� !∴↓ ���→ ↑ $�% !
Results
• REDM:
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Co
nsu
mp
tio
nE
xcre
tio
n
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Results
• Shadow prices, Feed stuff:
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�%&!��'()��*!%')�% !+:-.)��*!'*/���-0��!(1 *%�'+
Results
• Shadow prices, Methane emissions:
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Conclusions
• Cost of low emission diet exceeds cost of taxes
� TAXM ~ BASEM
• Reduction of ��� emissions yields increase in
Nitrogen-excretion
• Further studies are needed!
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