A Simple Parallel Projection Optimization Algorithm Estimating a Large-size Input- Output Table for Environmental Impact Assessment Ting Yu, Julien Ugon,

A Simple Parallel Projection A Simple Parallel Projection Optimization Algorithm Optimization Algorithm

Estimating a Large-size Input-Estimating a Large-size Input-Output Table for Environmental Output Table for Environmental

Impact Assessment Impact Assessment

Ting Yu, Julien Ugon, Manfred LenzenIntegrated Sustainability Analysis, University of Sydney, Australia

School of Information Technology & Mathematical Sciences, University of Ballarat, Australia

What I will talk?• Environment Impact Assessment:

• Economic Input-Output Life Cycle Assessment (EIO-LCA)

• A parallel optimization algorithm estimating a large-size input-output table

Environment Impact Assessment

• Definition: – An assessment of the possible impact (positive

or negative) that a proposed project may have on the environment (consisting of the natural, social and economic aspects).

Purpose of EIA• EIA becomes a part of standard corporate

reports, the same as traditional accounting reports

• Encourage business and public to consider the environmental impact of their actions

• Government is able to implement its regulation• Investors are able to assess the impact of their

investment on the environment (consisting of the natural, social and economic aspects).

World Business Council for Sustainable Development (2002)

“Corporate sustainability reports and

sustainability ratings are increasingly used as key

information for investment and lending

decisions.”

“There is a growing awareness that

shareholders’ value is enhanced by

increased corporate social and

environmental responsibility.”

Dollar as intermediary• Tone for CO2, Litre for water usage,

Square metre for land usage, number of people for unemployment

• Universal and single measurement for all kinds of impacts

• Monetary measure for corporate reporting

Case 1: Investors & insurersneed to see hidden risks, eg. GHG emissions

Construction Pty

C

On-site emissions

Embodied emissions

from materials

Water supplier Pty

D

On-site emissions

Lower embodied emissions from

materials

Real-world complexities (1)

Trucost & Defra (May 2006)

Real-world complexities (2)

Organisation

Mining Legal SteelTrans. BankingElect.

•••

•••

•••

•••

•••

•••

•••

•••

•••

•••

M L E T S B M L E T S B M L E T S B M L E T S B M L E T S B M L E T S B

Supplier level:

∞....

2

1

On-siteBoundary

UpstreamDownstream

Product 2Product 1

Consumer Industry

The problem of quantification

“… there is still a lack of quantification in most reporting.

… the majority of reports lack depth, rigour or

quantification.”

“Most business will have supply chain impacts that they

should understand and consider reporting. There is no

single, quantifiable measure that companies can use as a

Key Performance Indicator for the effect of their upstream

supply chain on the environment.”

Trucost & Defra (May 2006)

Economic Input-Output Life Cycle Assessment (EIO-LCA)

• The EIA enables decision makers to evaluate a project by data and analysis rather than a feeling that the natural product is better

• A life cycle assessment (LCA) is the investigation and valuation of the environmental impacts of a given product or service caused or necessitated by its existence, and an evaluation of the environmental impacts of a product or process over its entire life cycle.– often thought of as "cradle to grave" and therefore as the most

complete accounting of the environmental costs and benefits of a product or service

• Economic Input-Output Life Cycle Assessment (EIO-LCA) method uses information about industry transactions - purchases of materials by one industry from other industries, and the information about direct environmental emissions of industries, to estimate the total emissions throughout the supply chain

(Hendrickson, Lave, & Matthews, 2006 )

Industrial interdependence in a modern economy: a “tree” of upstream production layers

Lenzen & Murray, 2003

Production layers and structural paths: Example: Australian aluminium

Lenzen & Murray, 2003

FRGESFRGESFRGESFRGESFRGES

•••

•••


•••

•••


•••

•••


•••

•••


•••

•••

4

3

•••

F RG E SF RG E S F RG E S F RG E S F RG E S 2

Aluminium for use

Food Resources EnergyGoods Services

0

1

Shipping to smelter

Manufacture of ship

Iron ore for steel

Energy foriron ore mining

Steel for ship

10 top upstream paths: energy use• Electricity> Al> exports 46.57 PJ (46.29%)• Alumina> Al> exports 14.48 PJ (14.39%)• Al> exports 8.24 PJ (8.19%)• Electricity> Alumina> Al> exports 1.40 PJ (1.39%)• Electricity> Al> stocks 0.78 PJ (0.78%)• Petroleum and coal products> Al> exports 0.40 PJ (0.40%)• Electricity> Bauxite> Alumina> Al> exports 0.34 PJ (0.34%)• Bauxite> Alumina> Al> exports 0.29 PJ (0.29%)• Iron and steel> Al> exports 0.26 PJ (0.26%)• Alumina> Al> stocks 0.24 PJ (0.24%)

0.1

1.

10.Employment

Income

Land disturbance

Water use

Primary energy

GHG emissions

Gross operating surplus

Imports

Exports

Government revenue

Banking

Electricity supply

0.1

1.

10.Employment

Income

Land disturbance

Water use

Primary energy

GHG emissions

Gross operating surplus

Imports

Exports

Government revenue

Electricity Supply

Why we need input-output table?

Input-output table

The structure of the economy

e.g. total emissions (direct plus indirect)

e.g. direct (on-site) emissions

e.g. purchases of a company

Integration

National Input-Output Tables

Physical & social

data

Input-output Table

Into domestic production Into domestic final

demand International exports

Total output

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

1…n 1…n 1…n 1…n 1…n 1…n 1…n 1…n 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 n

2 1 n

3 1 n

4 1 n

5 1 n

6 1 n

7 1 n

Out

of

dom

esti

c pr

oduc

tion

8 1 n

Domestic inter-industry transactions

trs

ij

)(

)( = industrial flow from

sector (i) in region (r) to sector (j) in region (s).

Domestic final uses

frs

i

)(

)(= final demand

of region (s) for the output of sector (i) in region (r).

International exports

err

i

)(

)(= international

exports out of sector (i) in region (r).

[ 0)()(

)(sre

rs

i]

Gross State

Output of industrial sectors

Xr

i

)(

)(

1 1

2 1

3 1

4 1

5 1

6 1

7 1

Val

ue a

dded

8 1

Domestic primary inputs to domestic production

prs

j

)(

)(= primary inputs from

region (r) into sector (j) in region (s).

Domestic primary inputs into domestic

final uses

prs

f

)(

= primary

inputs from region (r) into final demand of region (s).

International exports of domestic

primary inputs

prr

e

)(= international

exports of primary inputs from region (r).

[ 0)()(

srprs

e]

Gross State

Production

Pr )(

1 1

2 1

3 1

4 1

5 1

6 1

7 1

Inte

rnat

ion

al

imp

orts

8 1

International imports

mss

j

)(

)( = international

imports into sector (j) in region (s).

[ 0)()(

)(srm

rs

j]

International imports into

domestic final uses

mrr

f

)(= international

imports into final demand in region (r).

[ 0)()( srm

rs

f]

International re-exports

mrr

e

)(= international

re-exports in region (r).

[ 0)()( srm

rs

e]

Intern. state

imports

Mr )(

Total input

Gross State Input into industrial sectors

Xs

j

)(

)(

Gross State Expenditure

Fs)(

Intern. state exports

Es)(

Agriculture

Mining Manufacturing

Utilities Services

Agriculture

Mining

Manufacturing

Utilities

Services

Input to mining

Input to services

Output from mining

Output from Services

Input Coefficients

To Ag,For&Fish MiningManufact

uring

Utilities,Trade,Transport&Communica

tion Services

Ag,For&Fish 10.9 ¢/$ 0.0 ¢/$ 4.5 ¢/$ 0.4 ¢/$ 0.2 ¢/$

Mining 0.1 ¢/$ 8.3 ¢/$ 4.5 ¢/$ 1.2 ¢/$ 0.1 ¢/$

Manufacturing 16.5 ¢/$ 10.6 ¢/$ 23.8 ¢/$ 15.2 ¢/$ 6.1 ¢/$

Utilities,Trade,Transport&Communication 13.5 ¢/$ 12.8 ¢/$ 9.8 ¢/$ 17.1 ¢/$ 9.8 ¢/$

Services 5.7 ¢/$ 6.2 ¢/$ 5.2 ¢/$ 14.8 ¢/$ 20.3 ¢/$

4.5c of agriculture is needed for every dollar’s worth of manufacturing

How much ghg does it take to provide $1000 worth of services (from this one supply chain)

0.4kg x 0.128$ut x 0.45$mi x 0.238$man x 0.061$man x $1000s

$util $mining $manuf $manuf $services

= 0.033kg

$1000 was the driver for this whole chain of reactions and its environmental consequences

For services

For manufa-cturing

For agricutlure

For utilities $100

0

Formining

ghg from utilities

You spend $1000 on a weekend away. You have muffins for breakfast. They are manufactured. The manufacturer needs blueberries. They are farmed. The farm needs electricity. The power plant needs coal. The coal mine needs gas. The gas provider emits ghg.

A Simple Example of a Matrix Used in Economic Study

23.01 X 2X

3X 4X

5X 6X

7X 8X

2008 China (1)

Shoe (1) Retail (2)

Australia (1)

NSW (1)

Sheep (1)

Oil (2)

VIC (2) Sheep (1)

Oil (2)

2009 China (2)

Shoe (1) Retail (2)

Australia (1)

NSW (1)

Sheep (1)

Oil (2)

VIC (2) Sheep (1)

Oil (2)

23.01 X 2X

3X 4X

5X 6X

7X 8X

Where to get the input-output table? Google it? Or Estimate it?

Answers•Survey, published by Australian Bureau of Statistics every 4 years

•Or estimate the Input-output table

- Purpose: populate the matrix by using available information, (matrix completion? With full rank?)

-Significance: matrices are widely used in economic study and transportation planning to represent the commodity or traffic flows between origin and destination.

-Difficulties: available information often is not completed, with a large amount of noise

Available Data• Data From Australian Bureau of Statistics:

– Australian National Accounts: State Accounts

– Environment and Energy– Economy, Industry, Value of Agricultural Commodities Produced

• Data from Australian business register• Data from Reserve Bank of Australia• Data from Sydney Water, and other private companies

From State accounts

Expenditure Components of GSP June 2005($m)

Note: GSE components= GSP Expenditure components +M-E NSW VIC QLD WA SA TAS NT ACT

1 2 3 4 5 6 7 8

GSE1HFC intra-state (aggregated into groups containing commodities i')

Food 17951 14346 10913 5787 4748 1328 746 1082

Alcoholic beverages and tobacco 7751 5067 3651 1997 1583 420 194 404Clothing and footwear 6586 5280 3837 1714 1412 397 136 407

Rent and other dwelling services 32761 21887 16684 8279 5946 1545 1095 1837

Electricity, gas and other fuel 2912 3666 1594 883 1088 291 73 238Furnishings and other household equipment 9118 7425 5655 3325 2099 666 283 642Health 8447 7616 5289 2826 1862 631 191 373Transport 21639 15900 11217 5902 4343 1404 511 1030Communications 5152 3776 2733 1416 1126 351 145 280Recreation and culture 21262 15304 11744 5692 4273 1474 772 1275Education services 6377 5269 3014 1655 1234 292 95 337

Hotels, cafes and restaurants 14999 8409 8403 2873 3116 709 403 670

Miscellaneous goods and services 24238 17660 13134 7065 4981 1639 809 1483



Total output

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

1…n 1…n 1…n 1…n 1…n 1…n 1…n 1…n 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 n

2 1 n

3 1 n

4 1 n

5 1 n

6 1 n

7 1 n

Out

of

dom

esti

c pr

oduc

tion

8 1 n


trs

ij

)(



Domestic final uses

frs

i

)(

)(= final demand



err

i

)(

)(= international


[ 0)()(

)(sre

rs

i]

Gross State


Xr

i

)(

)(

1 1

2 1

3 1

4 1

5 1

6 1

7 1

Val

ue a

dded

8 1


prs

j

)(




final uses

prs

f

)(

= primary



primary inputs

prr

e

)(= international


[ 0)()(

srprs

e]

Gross State

Production

Pr )(

1 1

2 1

3 1

4 1

5 1

6 1

7 1

Inte

rnat

ion

al

imp

orts

8 1


mss

j

)(

)( = international


[ 0)()(

)(srm

rs

j]


domestic final uses

mrr

f

)(= international


[ 0)()( srm

rs

f]


mrr

e

)(= international


[ 0)()( srm

rs

e]

Intern. state

imports

Mr )(

Total input


Xs

j

)(

)(


Fs)(


Es)(



Total output

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

1…n 1…n 1…n 1…n 1…n 1…n 1…n 1…n 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 n

2 1 n

3 1 n

4 1 n

5 1 n

6 1 n

7 1 n

Out

of

dom

esti

c pr

oduc

tion

8 1 n


trs

ij

)(



Domestic final uses

frs

i

)(

)(= final demand



err

i

)(

)(= international


[ 0)()(

)(sre

rs

i]

Gross State


Xr

i

)(

)(

1 1

2 1

3 1

4 1

5 1

6 1

7 1

Val

ue a

dded

8 1


prs

j

)(




final uses

prs

f

)(

= primary



primary inputs

prr

e

)(= international


[ 0)()(

srprs

e]

Gross State

Production

Pr )(

1 1

2 1

3 1

4 1

5 1

6 1

7 1

Inte

rnat

ion

al

imp

orts

8 1


mss

j

)(

)( = international


[ 0)()(

)(srm

rs

j]


domestic final uses

mrr

f

)(= international


[ 0)()( srm

rs

f]


mrr

e

)(= international


[ 0)()( srm

rs

e]

Intern. state

imports

Mr )(

Total input


Xs

j

)(

)(


Fs)(


Es)(

2003-2004

2002-2003

Temporal-Spatial Estimation with Conflicting Information (1)

• Time series of Input-output tables• Spatial information from national or regional government,

private cooperate, and research institutes, for example: – Total commodity trade of given industries between regions– Total green house gas emission of the given industry of a

region within the current year• Conflicting information:

– Caused by the data noise: error from the process of data collection

– Change of underlying structure: non-stationary– Without considering the confliction, the problem

becomes unsolvable.


• IO table is estimated as a vector X• Main algorithm:

subject to

where X is the target vector to be estimated, X0 is the vector of the previous year which is known, E is a vector of the error components (uncertainty)

dis is a distance metric which quantifies the difference between two vectors.

G is the coefficient matrix for the local constraintsC is the right-hand side value for the local constraints.

])(

[1

2

1

i

ieXXdisMin

CEGX

2)(),( ii XXXXdis


• The reason why the vector E is introduced is to solve the conflicting information.

– the vector E is introduced to balance the influence between the conflicting information, and reaches a tradeoff between the conflicting information.

• Assumption: – the temporal stability, which assumes the industry structure of a certain region keeps

constant or has very few changes within the given time period. This assumption is often required to be verified for long time period. Within the short time periods, dramatic change of the industry structure is relatively rare.

• The datasets often contain the temporal patterns between years, such as the trend of the total output of certain industry sections, and also much spatial information regarding the total emission within a certain region such as national total emission and state total emission.

• On the other hand, it is very common that either of datasets is not comprehensive and imperfect and even the conflicts between the datasets exist. Thereby, the estimation algorithm is required to consolidate the conflicted datasets to uncover underlying models.

Parallel Projection Method (1)

• Why parallel computing is needed? – A large amount of variables are estimated: a

2000-by-2000 matrix has 4,000,000 variables to be estimated

– A large amount of available information is available to be utilized and need to be processed efficiently.

• Available supercomputing facility

Supercomputer at NCI


• Original formula has to be rewritten:

subject to:

where

• Linear constraints and quadratic objective function => Convex function

• Partition the formula into many sub-problems:

])(

[2

PP

Min

0

C P*G

X

])(

[2

PP

Min

nn CPGts *..

])(

[2

PP

Min

0.. Xts

E][X, P

])(

[2

PP

Min

11 *.. CPGts

......

......


• Iterative process and convergence:

where L is the relaxation parameter,

and projection

• Covex combination , where is the solution of i-th subproblem

])(Pr[1 nniinn PPwLPP

)(Pr nii PwZ )(Pr ni P

)()(Pr 1ini

Tinni CPGGPP

Test of Convergence

The constraints converges to zero.

the objective function converge to a constant level after the same number of iterations as the constraints are satisfied.

CGPn

Performance• A medium size optimization problem consists of 25,070

variables, 219 constraints. The optimization runs 5,000 iterations over 16 CPUs (or nodes). The whole process takes 01:15 minutes and uses 918MB memory totally.

• A large size optimization problem consists of 3,340,800 variables, over 3,100 constraints. The optimization runs over 2,000 iterations over 16 CPUs (or nodes). The whole process takes 37:29 minutes and uses 2,280MB memory totally.

• Available memory is update to 3GB*8*64 = 1,536 GB at the supercomputing facility.

Experiments (1)• Direct evaluation of a large-size matrix is a rather

difficult task. – A thousand-by-thousand matrix contains up to ten million

numbers. Simple measurements such as the sum do not make too much sense, as the important deviation is submerged by the total deviation which normally is far larger than the individual ones.

• Indirect evaluation:– Estimate the impact of the change of matrix elements on the final

output in the whole economic system– It is more suitable when researchers are more interested to find out

how sensitive the system is regarding the error of the estimation.

Direct evaluation

Experiments (2)• Indirect evaluation: sensitivity analysis by calculating the

multipliers

• How to calculate the multipliers:

where M is the multiplier, I is the identity matrix, D is the change in the final output, and A is the technique coefficients matrix, each entry of which is the ratio:

X is a value from the matrix estimated by the previous

mining algorithm

1)( AIDM

n

iii XX

1

/

Change of Underlying Structure

0

0.5

1

1.5

2

2.5

3

3.5

4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

estimate

real

•Basically two series basically follow the same pattern.

•The estimated multipliers are more volatile than the true underlying multipliers. This phenomenon indicates the estimated multipliers amplify the errors.

Conclusion• Running over a supercomputing facility and reducing the

computational time to 1.5 hours for estimating a 3000-by-3000 Input-output table. More importantly, the size of input-output table can be increased to 15,000-by-15,000, which is enough for the table representing global economic structure (150 countries).

• A large-size Input-output table enables to analysis the environmental impact from a global perspective. The ISA will publish the first version of global Input-output table very soon.

• Future development: – Speed up the algorithm– Vertically split the estimation algorithm

Sustainable Development is not a cover up!

European Union Emissions Trading System 2008-2013 & 2013 -2020

•Second phase 2008-2013•5% cut in 2005 levels•polluters still avoid cuts by investing in CDMs•free permits mean huge windfall profits.

•Third phase 2013 to 2020•permits to emit decided on EU-wide basis, rather than through national allocations

Power producers to buy permits at auction www.guardian.co.uk/environment/2008/jan/04/em

What ML and DM can do?

ISA @ The University of Sydney

http://www.isa.org.usyd.edu.auwww.bottomline3.com

Documents

A Simple Parallel Projection Optimization Algorithm Estimating a Large-size Input- Output Table for Environmental Impact Assessment Ting Yu, Julien Ugon,