Real Options, Optimisation Methods and Flood Risk
Management
Michelle Woodward - HR Wallingford and Exeter University
Ben Gouldby – HR Wallingford
Zoran Kapelan – Exeter University
Soon-Thiam Khu – Exeter University
Objective of PhD
Title:
Real options based optimum selection of flood risk
mitigation options
Objective:
To investigate optimum flood risk intervention
strategies taking into account the possible
effects of climate change
Page 2
Presentation outline
• Overview of Risk Analysis tool
• Calculating Benefits of interventions
• Optimisation Techniques
• Evolutionary Algorithms
• Dynamic Programming
• Real Options
• Valuing flexibility for climate change adaptation
strategies
• Outline of computational framework
Page 3
Background to RASP
Risk Assessment for System Planning
Research Project funded by the UK Environment
Agency (2001-2004)
Page 4
RASP is a framework for flood risk analysis
National Level
National justification, regional prioritisation, long term outlook
Common
database
(NFCDD)
Catchment / Coastal Cell Level
Strategic planning
Development regulation
Common
input/output
Site / System Level
Scheme appraisal
Page 5
Conceptual model
Utilises a structured definition of the flood system
Page 6
The system model
Determining
depth versus probability
• Recognises that levees behave
as “defenceflood
systems”
Pathway
Receptor
The system model:
Source
• A flood depth versus probability distribution is established by
considering multiple combinations of storm loading and possible
levee failure
Page 7
Pathway
Receptor
All inundation scenarios
Source
A new super fast inundation
model (HR RSFM) enables
10000s of inundation
scenarios to be realised
Runtime: <0.1 sec
Model has been compared
to hydrodynamic models
like Infoworks-RS2D
Page 8
The system model
Estimating
flood damages
1. Depth damage curves are used to assess
the damage
Three steps are used to calculate risk
associated with each possible flood scenario
2. By combining the scenario damage with the probability
of the scenario occurring a scenario risk is estimated
3. By integrating across all scenarios the expected annual
damages (risk) is determined
Depth Metres
Depth Dam age Curve
High
Susceptibility
Band
3. 00
2. 75
2. 50
2. 25
2. 00
1. 75
1. 50
1. 25
1. 00
0. 75
0. 50
0. 25
0. 00
-0. 25
-0. 50
-0. 75
-1. 00
Low
Susceptibility
Band
Indicative
Susceptibility
0
250
500
750
1000
1250
1500
Dam age £/m 2
Source: Flood Hazard Research Centre, 2003
Page 9
Investigating intervention strategies
Risk profile through time for HLO 1, 2 and the P3 Policy
60
50
Risk(EAD £m)
40
30
20
P3
10
HLO1
0
2000
2020
2040
2060
Time (year)
Page 10
2080
2100
2120
Optimisation Techniques
-Dynamic Programming
Enumerative Scheme
-Evolutionary Algorithms
Inspired by Darwin’s theory of evolution
Survival of the fittest
Genetic operators
 Reproduction (crossover)
 Mutation
 Selection
Page 11
Structure of a Simple Genetic Algorithm
START
Generate
initial
population
Evaluate
objective
function
Application
Model
Are
optimisation
criteria
met?
Best
individual
Generate new population
RESULT
Mutation
Page 12
Crossover
Selection
Genetic Algorithm Operators
5
2
4
6
7
1
8
6
9
3
1
4
2
0
Two Parent
Chromosomes
5
2
4
6
4
2
0
6
9
3
1
7
1
8
Crossover
5
2
4
6
4
2
0
Mutation
6
Page 13
9
9
1
7
1
8
Two new
Offspring
Multi-objective optimisation
• Multi objective optimisation methods seek
solutions that are “optimum” with respect to all
objectives.
• Invariably a set of optimal solutions is
discovered (known as a Pareto set)
Page 14
Objective 2 (to be minimised)
The Pareto Front
Objectiv e 1 (to be minimised)
Page 15
Objective 2 (to be minimised)
The Pareto Front
Objectiv e 1 (to be minimised)
Page 16
Objective 2 (to be minimised)
The Pareto Front
Objectiv e 1 (to be minimised)
Page 17
Optimisation Problem
Objectives:
Maximise Benefit:
EADwithout interventions – EADwith interventions
n
Minimise total cost: ∑Ci
Ci = costs per intervention
i=1
Subject to: Realistic and available intervention
options
Page 18
Multi-objective optimisation
Identification of transition, where
significantly more investment yields little
benefit (incremental benefit cost)
Identification of
costs associated
with specified
benefit level
The Pareto Front
Benefit (£’s)
Identification of most
appropriate option/s given
fixed budget
Cost (£’s)
Page 19
Real options overview
“A Real Option is a choice that becomes
available through an investment opportunity or
action”
Page 20
Real Option Overview
Maximum height
increase for
widened defence
Plausible range of
future extreme
water levels
Maximum height increase
for current defence
Present Day
extreme water level
Current
Defence
Page 21
Widening of Base
Framework for Optioneering
Features include
• Analysis of Real Options
• Automated option searching techniques using evolutionary
optimization processes (multi-objective optimization)
• Automated option cost generation
• Economic discounting of benefits and costs
• Temporally evolving risk analysis (a fastRASP) – risk is a
function of future climate change scenario, future socioeconomic scenarios
• Range of decision making methods
Page 22
Overview of framework
Calculate NPV cost
(Cost functions)
No
Calculate option fitness for:
Multiple objectives
Multiple futures
(Single decision method)
Generate a (Real) option
(Optimisation method)
optimum solutions found
Yes
Calculate NPV Benefits
Multiple futures
(fastRASP)
Decision variables include:
Standard of maintenance
Raise crest level (Each defence)
Widen defence (each defence)
Non structural measures (flood
proofing)
Page 23
Output Pareto
Set of optimum
solutions
Thank you for listening
m.woodward@hrwallingford.co.uk
b.gouldby@hrwallingford.co.uk
Page 24