1. Daniel L Sandars, Eric Audsley
Centre for Environmental Risks and Futures
Dept. of Environmental Science and Technology
School of Applied Science
Analysing the efficiency of
energy use on farms using
Data Envelopment Analysis
(DEA)
43rd Meeting of the
Agricultural Research Modellers’ Group
15th April, 2011
The Royal Society, 6-9 Carlton House Terrace, London

2. Research question
• Are some farms using fertiliser or diesel or
feed more efficiently than others?
• We used Data Envelopment Analysis
(DEA) as a method to quantify the
technical efficiency with which inputs
are converted into useful economic
activity within a sample of the UK
agricultural industry

3. Environmental efficiency
j
ijij
j
Energy
Outputsweights
E
}{}{
InputOutputEfficiency /
inputsweightedoutputsweightedEfficiency _/_
outputsunwantedinputsinputswantedoutputsEfficiency _/_

4. The DEA concepts
• Let each DMU chose its best weights to give it an
efficiency of 1,
• subject to those same weights applied to any other
DMU must not result
• in an efficiency >1. If your best weights give you an
efficiency of <1 then some DMU
• is doing a similar job better. That is quite damning
evidence.
• In DEA we think of Decision Making Units (DMU)
and here they are farms + farmers

5. DEA frontier and virtual composite
DMUs

6. 2007/08 Defra FBS Energy Module
• Fuels used on farm?
• Fertilisers usage?
• Contracting operations?
• Purchased animal feed?
• Purchased fodder & straw?
• Purchased bale wrap and silage
sheet?
• Woodland area?
• Grassland area
ploughed/planted?
• Organic manures
imported/exported?
• Baling of silage and straw
(proportion)?
• Ventilation of housing
(proportion)?
• Inventory of self-powered
machinery?
http://www.farmbusinesssurvey.co.uk/index.html

7. Activity data to emissions and energy
usage
• Cranfield’s David Parsons,
Kerry Pearn & Adrian Williams
extracted and processed the
raw data into useable values for:
• Direct and indirect Energy, MJ
• Direct and indirect Global Warming Potential (GWP
100 years) kg CO2 eqv.
• The method used life cycle thinking and thus includes
upstream energy and emissions sequestered in farm
inputs -www.agrilca.org

8. Output Vectors
• Cereals (t),
Oilseeds (t),
Combinable legumes (t),
Potatoes (t),
Sugar beet (t),
Horticultural revenue (£)*,
Milk (hectolitres),
Eggs (no),
Cattle Liveweight (kg),
Sheep Liveweight (kg),
Pig Liveweight (kg), and
Poultry Liveweight (kg).

9. Energy Module, farm numbers
Farm Type Large Medium Small
Very small
(part-time) Grand Total
Organic? FALSE TRUE FALSE TRUE FALSE TRUE FALSE
Cereals 31 1 29 21 1 83
Dairy 28 6 24 3 16 77
General cropping 41 2 23 2 9 77
Horticulture 73 15 12 2 2 104
LFA grazing livestock 9 1 6 2 1 19
Lowland grazing livestock 18 2 13 1 4 2 1 41
Mixed 20 1 11 2 11 2 47
Other 1 1
Specialist pigs 6 5 9 20
Specialist poultry 16 1 12 1 9 2 1 42
Grand Total 243 14 138 9 93 7 7 511

10. Energy Module, farm numbers
Farm Type
East
Midlands
East of
England
North
East
North
West
South
East
South
West
West
Midlands
Yorkshire
& the
Humber
Grand
Total
Cereals 14 23 6 2 18 6 4 10 83
Dairy 8 3 3 16 6 23 11 7 77
General cropping 17 27 4 6 6 7 10 77
Horticulture 13 24 6 29 17 7 8 104
LFA grazing
livestock 1 7 3 3 1 4 19
Lowland grazing
livestock 3 4 2 2 8 13 7 2 41
Mixed 6 5 2 4 7 10 8 5 47
Other 1 1
Specialist pigs 2 6 1 2 2 2 5 20
Specialist poultry 1 11 1 5 4 9 7 4 42
Grand Total 65 103 21 44 80 89 54 55 511

11. The spread of efficiencies amongst
farms
0
10
20
30
40
50
60
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Numberoffarms
DEA techical input efficiencies: histogram category, mid-points
GWP100
Energy

12. The efficient set
DMU No. Type Organic No. times a model
336 Cereals 6
359 Cereals 18
441 Cereals 162
283 General cropping 4
222 General cropping 7
196 General cropping 12
333 General cropping 15
215 General cropping 36
426 General cropping 39
320 Horticulture 23
381 Horticulture 104
47 LFA grazing livestock Y 67
62 Lowland grazing livestock 38
332 Lowland grazing livestock 128
304 Mixed 26
214 Mixed 48
303 Specialist poultry 20
321 Specialist poultry 26

13. An inefficient DMU and its models
Peer Energy Cattle Sheep
DMU No proportion GJ t lwt t lwt
145 660 19 12
332 0.73 170 18 0
47 0.48 320 13 25
145′ 280 19 12
This is the projection of 145 onto the efficient frontier using its two model farms

14. An inefficient DMU and its peers
0
100000
200000
300000
400000
500000
600000
700000
800000
32197 35653 + 2970
Energy,MJ(scaled)
DMU (332 and 47 are efficient and scaled to 145)
Purchased Sheep
Purchased OtherCattle
Bought feeds
FertWrap
Contracting operations
manufacturing costs
Implied manufacturing costs of
farm machinery
Contracting operations diesel
RedDiesel
Fossil fuels (-red diesel)
Electricity

15. Wonder?
0
2000000
4000000
6000000
8000000
10000000
12000000
14000000
16000000
18000000
20000000
35647 35621
EnergyMJ(scaled)
DMU (321 is efficient and scaled to 331)
Purchased Poultry
Bought feeds
Implied manufacturing
costs of farm
machinery
Fossil fuels (-red
diesel)
RedDiesel
Electricity331 321

16. Positives
• Empowerment – DEA does help to make these
issues more tractable
• Wonder – DEA does find interesting questions -
Chance? Outlier? –we are naturally curious (if not
stressed)
• Acceptance & Belonging DEA shows that many
farmers seem to have something to learn and to
improve and DEA helps identify appropriate models.
• Affirmation – DEA could identify you and your farm
as a peer to many others

17. Some challenges
• Onerous data demands and access to IT –more
burdensome for some farmers
• Heterogeneity – making it hard to identify true like for like
comparators – farms are more than can be measured!
• Another shove on the technology treadmill – with the
financial benefits of win-wins soon negated in the market
place.
• Non disclosivity - making it hard to literally identify and
approach your farm’s peers
• Wonder turning to Frustration - not finding the answers
• Implied Criticism at the farmer - ‘tough love messages’

18. The End -Thanks
• This work was funded by Defra Project code RMP
5465 http://www.defra.gov.uk/
• For further information contact:
Daniel Sandars, Cranfield University
+44(0)1234 750111 ext 2742
Daniel.sandars@cranfield.ac.uk

19. DEA by 2 stage Linear Programme
Take a set of N DMUs (j=1….N) using m inputs to generate r outputs where xij and
yrj are the levels of the ith input and rth output respectively. The technical efficiency
of DMU j0 is defined as k0 and is determined by the following linear programming
model:
Where λj is weight each DMU (j=1…N) will have in calculating the inputs and
outputs of the composite DMU j0*. Each of the criteria can have a slack
denoted by and ,which represents the distance from the constraint

20. The End -thanks
Centre for Environmental Risks and Futures,
Building 42a>>>>>
http://www.cranfield.ac.uk/
Daniel.sandars@cranfield.ac.uk

21. This work was funded
by Defra
Project code RMP 5465
http://www.defra.gov.uk/

22. Global warming, mitigation & climate
change

23. Complex world
• More history - the consequences of past choices catch
up
• Know more about the relationships, interactions,
causes and effects
• More stakeholders.
• = A more challenging decision environment

24. That matters to people