era lecture 8 case studies

8/6/2019 ERA Lecture 8 Case Studies

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Environmental Risk Analysis: Methodsand Applications

'2008/2009Lecturer- Prof. Eugene Levner

.8LectureOperations Research Tools in ERA.

Case studies.


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OUTLINE

1. Descriptions of Two Environmental Problems

2.1

The Jordan River Problem. 2.2. The Dead Sea Problem.

2. Two OR models 3.1. Risk mitigation planning for the Jordan River Problem

(the facility layout and multiple-choice knapsack problems)

3.2. Environmental risk minimization for the Dead SeaProblem (the multi-portfolio choice model).


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Environmental Risk Definitions

Risk is a likelihood that a course of actions (a lack of thereof) will

result in an undesired event (US EPA 1998,2002).

Environmental Risk is defined as a two-dimensional array

consisting of: (1) a probability of a threat to human health, to the

natural environment - air, water, and land - upon which life

depends, and to health of flora and fauna, and (2) a magnitude of

losses (Levner and Proth 2003,2005, Ganoulis and Levner,2007).


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Qualitative Risk MatrixQualitative Risk MatrixAmount of PollutionAmount of Pollution

& Probability of Damage& Probability of Damage

Probability

of Damage

20 40 100

0.1

0.3

0.5

0.7

0.9

Impact = Amount of

Pollution

The matrix serves to rank the risks: the green tier denotes low level, grey acceptable, yellow - high, red very high. The matrix has the capability toevaluate the effectiveness of risk mitigation measures; white ell ipsescorrespond to three different situations defined by three different risk-aversionstrategies: a passive strategy leaves the risk level very high, a moderate policy

decreases it to high, while an active strategy makes it acceptable.THIS COLORINGIS OUR FIRSTMAIN ASSUMPTION


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Integrated Eco-Risk Estimation


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Integrated Eco-Risk Index

R=7j=1,, 57r=1,, RwjrRjr,

where j is index of ecological risk classes j=1,5(human

health, crops, animals, nature, infrastructure), and r is index of

risk subclasses (age, diseases, professions, areas, etc.)

wjris weight, or importance

RandRjrare damage value (in physical or monetaryunits, or rating scale)

[THIS SUMMATION IS OUR SECOND MAIN ASSUMPTION]


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.1

1.5. Integrated Risk-Cost Analysis using a

combination of the environmental

supply chain and house-of-risks.

Modeling with the help ofOR tools

(Knapsack problem)


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ouse o s souse o s s

for defining integrated risk magnitudefor defining integrated risk magnitude

Weights

0.8

0.05

0.05

0.05

0.05

Risk R1

Risk R3

Risk R4

Risk R5

Risk R2

Absolute risk value

Costs

Transport Consumers Irrigation SewageWater

Quality

Water

QuantityFood ExposureRisk factor

1

Risk factor

2Risk factor

M

Rows depict Risk classes. Columns Risk factors, Risk sources


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An Illustrative Example

An ecological map of Tenerife, Canarian

Islands, designed together with Dr.David Alcaide Lopes de Pablo,University of La Laguna, Spain


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Results of computationsResults of computations


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2. Descriptions of Two

Environmental Problems in Israel 2.1 The Jordan River Problem.

2.2. The Dead Sea Problem.


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The Jordan River ProblemThe Jordan River Problem

In modern times the waters are 70 to90% used for human purposes andthe flow is much reduced. Moreover,the river is heavily polluted and in itslower part, just raw sewage andrunoff water from agriculture are

flowing into the river. Most pollutedis the 60-mile downstream stretch -a meandering stream from the Sea

of Galilee to the Dead Sea.


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In the early 1960s, the Jordan Rivermoved 1.3 billion cubic meters (46billion cu ft) of water every year fromthe Sea of Galilee to the Dead Sea.

But dams, canals and pumpingstations built by Israel, Jordan and

Syria to divert water for crops anddrinking have reduced the flow bymore than 90 percent to about 0.10

billion cubic meters (3.5 billion cu ft).


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Environmentalists say the practice hasalmost destroyed the river'secosystem.

The Jordan River will disappear ifnothing is done soon. More than halfof it is raw sewage and runoff water

from agriculture. What keeps theriver flowing today is sewage -Friends of the Earth, Midddle East.


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Specific Objectives:

To design the water balance for all main water sources andprovide a list of water saving strategies in the Jordan RiverBasin, (including innovative technologies for waste water

treatment, alternative agricultural and irrigation techniques,desalination and water treatment stations, intensiverainwater harvesting, etc.)

Using the supply chain and House-of-Risks approach,evaluate the social, economical and ecological risks ofdifferent water resources utilization scenarios, at present

and in the future. Provide a comprehensive ORbased optimization model as a

flexible tool for scientifically motivated and fair waterallocation between all the water stakeholders in the JordanRiver Basin.



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The Dead Sea ProblemThe Dead Sea Problem

Main Threats to the Dead Sea - water pumping from Lake Kinneret and

the Yarmouk River for water supply hascreated a water deficit about 800 millioncubic meters per year;

- industrial solar evaporation ponds atChemical Works are responsible for about

20% of the total evaporation of Dead Seawaters;

-additional threats come from theuncoordinated tourism industry, hotels,transport, road building, etc.


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The Dead Sea ProblemThe Dead Sea Problem

The overal goal is:

To develop an OR-based multi-

criteria optimization model forintegrated management of waterresources for the Dead Sea

Basin


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RiskRisk--Oriented Optimization ModelsOriented Optimization Models Which risk-mitigating strategies to select? Which water treatment facilities to use?

Which water/wastewater technologies to use?in order

TO MINIMIZE INTEGRATED REGIONAL RISK IMPACTSTO MINIMIZE INTEGRATED REGIONAL RISK IMPACTSTO MINIMIZE TOTAL COSTSTO MINIMIZE TOTAL COSTS

TO MINIMIZE UNCERTAINTYTO MINIMIZE UNCERTAINTY ((variance of returnsvariance of returns fromfromthe portfolio of chosen strategies, facilities andthe portfolio of chosen strategies, facilities and

technologiestechnologies xx ))..

under budgetory, technological, resource, legal andunder budgetory, technological, resource, legal andsocial constraints.social constraints.

A General Framework forA General Framework forTwo ProblemsTwo Problems


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PROBLEM FORMULATIONPROBLEM FORMULATION(Facility Location Problem)(Facility Location Problem)

Input A set ofwater stakeholders or demand

points D,

A set of water/wastewater treatmentfacilities Fwith facility creating cost fi ,

Connection cost Cij(not necessarily obeythe triangle inequalities),

Environmental risk imposed Rij.Output A subset of facilities Fd An assignment of demand points from D to

facilities in F

ijijxR


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Facility Location ProblemFacility Location Problem

Objectives

(1) Minimize the total cost (facility

building + connections)

(2) Minimize the environmental risk involved

)involvedrisksntal(environmemin

costs)connectioncostscreating(min


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Asimple case: The bi-criteria FLPThe ILP Formulation

FiDjyx

FiDjyx

Djxts

xRMin

yfxCMin

iij

iij

Fi

ij

Fi Dj

ijij

Fi Dj Fi

iiijij

e

!

,}1,0{,

,

1..

Each demand point should be assigned to one facility.

Demand points can only be assigned to created facilities.


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PROBLEM FORMULATIONPROBLEM FORMULATION(Facility Location Problem)(Facility Location Problem)

Input A set ofwater stakeholders or demand

points D,

A set of water/wastewater treatmentfacilities Fwith facility creating cost fi , Connection cost Cij(not necessarily obey

the triangle inequalities),

Environmental risk imposed Rij.Output A subset of facilities Fd An assignment of demand points from D to

facilities in F

ijijxR


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Facility Location ProblemFacility Location Problem

Objectives

(1) Minimize the total cost (facility

building + connections)

(2) Minimize the environmental risk involved

)involvedrisksntal(environmemin

costs)connectioncostscreating(min


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FiDjyx

FiDjyx

Djxts

xRMin

yfxCMin

iij

iij

Fi

ij

Fi Dj

ijij

Fi Dj Fi

iiijij

e

!

,}1,0{,

,

1..




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FiDjyx

FiDjyx

Djxts

xRMin

yfxCMin

iij

iij

Fi

ij

Fi Dj

ijij

Fi Dj Fi

iiijij

e

!

,}1,0{,

,

1..




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Indices

k= water stakeholders in the SC in aregion, k= 1, K.

i = risk classes, i= 1, , I.

j = stressors (sources of waterpollution),j= 1,, J.

m = index of different water saving andrisk mitigating strategies andtechn l ies m =1 M.

AnotherAnother simplesimple case: The bicase: The bi--constrained knapsackconstrained knapsackThe ILP FormulationThe ILP Formulation


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Variables

xim - technological/management choice

variable :x

im =1, if the m-th riskmitigation strategy is chosen fordecreasing i-th risk;

xim =0, otherwise, m=1,, M.

The problem is to choose the set of thecounter-pollution strategies, facilitiesandactivities so as to minimize the

integrated risk,or, equivalently,to

AnotherAnother simplesimple case: The bicase: The bi--constrained multiconstrained multi--choice knapsackchoice knapsack

The ILP FormulationThe ILP Formulation


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MC2KP

Maximize D = 7i=1,,N 7m=1,,MiDimxim(there are N risk groups, and Mi items in each group, totally M1 +M2 ++MN = M)

Subject to: 7i=1,,N 7m=1,,Mipimxim p0,(1)

The first constraint requires that the total probability of

damage does not exceed the allowed levelp0 .

7i=1,,N 7m=1,,Mibimxim B0, (2)The second constraint imposes the bound on budget

B0.

7m=1,,Mixim ki , i=1,,N (3)The third group provides the balanced choice between

different groups (classes) of environmental risks.


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The RiskThe Risk--based Water Resources Management Problem for thebased Water Resources Management Problem for the

Dead Sea as aDead Sea as aMMultiulti--portfolio Choice Problemportfolio Choice Problem

Given a m-dimensional vector budget(amount of money available toinvest, along with other tools, suchas human and information resources)and a list of management strategies1,, n requiring investment, how

can the vector budget be optimallydivided among the various waterresources management strategies for

the saving of the Dead Sea?


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The RiskThe Risk--based Water Resources Management Problem for thebased Water Resources Management Problem for the

Dead Sea as aDead Sea as aMMultiulti--portfolio Choice Problemportfolio Choice Problem

Denote by xij the amount of thejthcomponent of the m-dimensionalvector budget allocated to

management strategy i, for i=1,,n,j=1,, m. Then the nxm matrix x,that we call a multi-portfolio, is amulti-dimensional decision variable

for the problem. A goal of theoptimisation process is tocharacterise and find the optimumportfolio of management strategiesfor the develo ment of the Dead


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The RiskThe Risk--based Water Resources Managementbased Water Resources ManagementProblem for the Dead Sea as aProblem for the Dead Sea as aMMultiulti--PortfolioPortfolio

Choice ProblemChoice Problem

Let the total return from portfoliox be therandom variablev(x), and (x) = theexpected value of returnv(x) from portfolioxin a pre-specified period. It is a measure ofthe long term average return per period fromthe portfolio.

Note that in this approach, the returnv(x) isa vector function whose components reflect

separate economic, technical, environmentaland social returns (benefits, welfare) that arequantitatively estimated by using the utilityfunctions for each stakeholder.


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based Water Resources Managementbased Water Resources Management--The RiskThe RiskProblem for the Dead Sea as aProblem for the Dead Sea as aPortfolioPortfolio--ultiultiMMChoice ProblemChoice Problem

Finding an optimum portfolio of waterresources management strategies shouldmaximise the expected return andminimise the environmental risk; inother words these objectives should beachieved simultaneously.

Finding an optimum portfolio ofintegrated water resources managementstrategies is therefore a multicriterion

optimisation problem.


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Following a financial risk management approachproposed by Harry Markowitz in 1952, we mayassume that the environmental risk of a portfolio can

be quantitatively characterised by thevariance ofreturns from the portfoliox. Our Markowitzean approach is applicable to water

resources management and extends the basicMarkowitz model in that (1) the variable portfoliox isthenxm matrix rather than an-dimensional vector of

variable assets, and (2) each objective function (i.e.,the return and risk) is, in fact, a vector of severalfunctions,for different risks and differentstakeholders.


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The present multi-portfolio methodology

is more complicated and computationallyless tractable than the classicalMarkowitz model. However, it allowspowerful mathematical methods of

financial risk analysis (see, e.g.Rockafellar and Uryasev 2000 ) to beexploited for measuring and minimising

environmental risks .


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BibliographyBibliography1. K.-H. Elster, E.G. Golshtein, E. Levner, et al., Modern

Mathematical Methods of Optimization, Akademie Verlag,Berlin, 1993, 416 pp.

2. E.Levner, I. Linkov and J.-M. Proth, Strategic Management

of Marine Ecosystems, Springer, Berlin,2005, 313 pages,ISBN 1-4020-3157.

3. E.Levner, J.Ganoulis, I.Linkov, Y. Benayahu, Multi-objective risk/cost analysis of artificial marine systemsusing decision trees, in I. Linkov (ed.), Risk ManagementTools for Environmental Security, CriticalInfrastructureand Sustainability, Springer, 2007.

4. H. M. Markowitz,Portfolio selection,Journal of Finance, Vol. 7, No.1,

pp.77-91,1952.

5. Rockafellar, R. and Uryasev, S., Optimization of conditional Value-at-

Risk,Journal of Risk, No. 2, pp. 2142,2000.

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