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图与网络算法优秀论文211
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图与网络算法优秀论文211
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For office use only
T1
________________
T2
________________
T3
________________
T4
________________
Team Control Number
52849
Problem Chosen
E
For office use only
F1
________________
F2
________________
F3
________________
F4
________________
2016
MCM/ICM
Summary Sheet
(Your team's summary should be included as the first page of your electronic submission.)
Type a summary of your results on this page.
Do not include the name of your school, advisor, or team members on this page.
To address the “wicked problem” of water scarcity, our team adopted a three-pronged
interdisciplinary approach combining theoretical mathematics, statistics, environmental
science, physics, economics, cultural anthropology, geography, epidemiology,
computational science, and history to perform a fresh analysis of global water scarcity.
Using a systems-network model, an agent-based network model, and a particle-
optimization model, we characterized current forms of water scarcity, both physical and
economic, and analyzed possible interventions on a global scope. After gaining a
comprehensive analysis of the sources of the water crisis in the poorest country in the
western hemisphere, Haiti, we designed interventions that addressed this largely
economic crisis in a culturally-aware manner. Beginning with a systems-network model
created using Vensim, we characterized water flow across the global network, taking
into account locked, available, and potable water storage and its agricultural, industrial,
and residential uses. The resulting system of differential equations was then solved in
specification to Haiti, creating a comparison of the effects of possible interventions,
concluding that both physical and social infrastructure for transportation and
dissemination of potable water ought to be prioritized. Next, optimizing the distribution
of such water required considering societal structure and the behavior of individuals. To
model this, we created an agent-based network customized to Haiti using NetLogo
software, representing each individual as a node on the network connected to others by
links. We compared various distribution methods using metrics grounded in
mathematical philosophy like Rawlsian logic, concluding that building on existing
distribution centers that employ locals is the most efficient way to tailor distribution to
the entirety of the social network, especially in regards to future water scarcity. Then,
we adopted a broader perspective to general groundwater collection. A groundwater
flow analysis algorithm was constructed in Python that can determine water loss to the
ocean and hydraulic head in any region. The outputs of this algorithm, as well as
geographical and climactic data, were used as inputs in a particle swarm optimization
algorithm to determine optimal solutions to provide clean water at the minimum cost.
This analysis concluded that using localized rainwater collection is both sufficient and
most cost-effective to meet Haiti’s needs. All three models were tested for sensitivity
and robustness to ensure their broader viability, such that they can be adopted by
organizations in any region to analyze local water demands and intervention
possibilities.
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Where’s My Water?
Global Water Scarcity and Haiti’s Water Crisis
2016 Interdisciplinary Contest in Modeling
Team 52849
Problem E
Page 1
January 2016
1 Introduction
1.1 Problem
According to the the United Nations, 1.6 billion people experience water scarcity. There are two
components of water scarcity: economic and physical scarcity. Either the water exists in the region
but money to clean or transport the water is lacking, or the supply of water in the region is less
than the demand in the region.
In this paper, we use different models to determine a region’s ability to provide water on the
basis of multiple factors. We aim to use these models to understand the behavior of a specific
system currently and how it is projected to behave 15 years in the future. We then use this behavior
to propose an intervention plan and apply our models with intervention plans to determine whether
they are viable.
1.2 Analysis of the Problem
According to Dr. Brian Davidson of University of Melbourne, water management and distribution
should be classified as a “wicked problem” (1). “Wicked problems,” he writes, “do not have a
single, once-off, optimal solution. They have a temporary solution. And it is a solution that has
to change over time in response to changing circumstances.”
This wicked problem is dependent on the interplay of multiple factors and thus is inherently
interdisciplinary, as shown below.
1
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Team 52849 MCM/ICM Page 2 of 31
Discipline Relevance to Problem
Environmental Science Affects how much water is “available”
to take without hurting ecosystems
and incurring environmental cost (can
also be measured monetarily)
Economics Monetary availability constrains
the optimal solution
Cultural Anthropology, Psychology Accurate assumptions of behavior
behind models for the region, viability for
solution/intervention plan to be adopted
Epidemiology Disease affects demand and supply of water
History Understanding the reasons for the current
water crisis and past attempted solutions
can help in understanding constraints
of the region
To come up with viable models to create viable solutions, we must have models which not only
take into account environmental, economic, cultural, psychological and epidemiological perspec-
tives but which also are robust enough to adapt to changes in the systems they address.
1.3 General Metric
Multiple requirements must be met for a solution to be considered viable and effective, as mea-
surable by the following general metric.
success = (m
i
− m
s
− m
e
) + as + bc
where m
s
and m
e
represent the direct cost of the solution and the environmental cost of the
solution respectively, m
i
represents the money available to the region, s represents the ability of
the solution to be self-sustainable, and c represents the ability of the solution to be culturally
adopted/socially viable. These factors were considered in the formulation of each model, which
each has its own metrics for effective comparison within model solutions.
2 Haiti: A Case of Extreme Economic Water Scarcity
Once, it was the wealthiest colony in the world. Now, 300 years later,
it’s the poorest country in the western hemisphere with the lowest
access rates to improved water and sanitation.
2.1 From Riches to Rags: The Historical Sources of Haiti’s Water
Crisis
Haiti was once the world’s wealthiest colony, but a series of revolutions that made Haiti the world’s
first free slave nation sparked Haiti’s present poverty and declining infrastructure. In exchange
for Haitian freedom, France extorted an “independence debt” amounting to $21 billion in today’s
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Team 52849 MCM/ICM Page 3 of 31
dollars. Experts say the crushing burden of the debt is the principal historic cause of Haiti’s un-
derdevelopment, directly responsible for today’s grinding poverty, but as France continues to resist
pressure to repay Haiti, there is little evidence of poverty in Haiti declining in the near future.
(33) This fundamental inability of the Haitian government to significantly invest in water infras-
tructure will continue if the situation does not change. Moreover, water infrastructure destruction
was perpetuated by a series of US-supported Haitian dictators that enforced water-controlling
regimes, using militias to cut off pipe access to locals. (36) This lack of pipe access for water still
persists, compounding reliance on external water sources.
2.2 Current Situation
Figure 1: A) The UNEP characterized multiple regions in Haiti as moderately exploited or over-
exploited based on Water Stress Indicators (WSI) in 2004. (5) B) According to the UNEP, “This
2008 update of the ‘Vital Water Graphics’ is aimed at giving an overview of the state of water
resources in the world.” As shown, Haiti is the only country in the western hemisphere where less
than 65% of the population has access to an improved water source. (6)
Haiti’s water crisis was exacerbated by the 2010 earthquake (which ruptured most remaining
water piping systems) (8) and the cholera epidemic, compounding both physical and economic
scarcity, such that Haiti now has the lowest rates of access to improved water and sanitation
infrastructure in the western hemisphere (7). Moreover, water-borne diseases like cholera are
the leading cause for mortality of children in Haiti, linked to 50% of overall deaths (9). This
has drawn tens of thousands of non-governmental organizations (NGOs) to Haiti, which is now
known as the “Republic of NGOs” because there are more NGOs there per capita than anywhere
else in the world, providing 80% of the country’s basic services (10). These organizations often
alleviate short-term burdens, but since most do not train locals, they are often un-sustainable
as other issues break out around the world and the NGOs Haitians have grown dependent on
leave. Furthermore, due to the lack of coordination between NGOs, there is frequent duplication
of work and inefficient use of resources (11). It’s clear that this model is inefficient and a long-
term solution should involve coordination by a central authority. Because the current water and
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Team 52849 MCM/ICM Page 4 of 31
sanitation situation has evolved over decades of limited attention and resources, it will take a long-
term, sustained effort to improve the situation. Sanitation and clean water is key in the long-term,
although short-term methods also need to be improved until the former is fully developed.
2.2.1 Comparison of Current Common Interventions in Haiti (2)
Intervention Cost Maintenance Sustainability Culturally Accepted? Impact
Water Sachets $ none none yes individual
Purification Tablets $ none none yes individual
Passive Solar
Disinfection (in bottles) $ low high yes individual
Boiling $$ medium medium very homes
In-Situ Filtration Wells $$ low high yes commune
Chlorinators $$$ some high yes commune
3 Models
3.1 Systems-Network Model
Figure 2: We created a systems model for water usage systems using Vensim software (3). Global
water systems involve agriculture, industry, and residential water usage, with adjustable rates
based on inputted variables. This model can be customized to fit any region.
3.1.1 System Flow Based on Model
Change in agricultural water:
d(agricultural)
dt
=
d(funnel)
dt
−
d(runof f
a
)
dt
−
d(runof f
l
)
dt
Change in industrial water:
d(industrial)
dt
=
d(transport
i
)
dt
−
d(contamination)
dt
−
d(waste
i
)
dt
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