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All content in this area was uploaded by Ernest Ameyaw Effah on Jul 14, 2018
Content may be subject to copyright.
Improving equity in intermittent water supply systems
Ernest Effah Ameyaw, Fayyaz Ali Memon and Josef Bicik
ABSTRACT
The problems of limited financial resources and water scarcity in urban areas of developing countries
are of concern to water managers following growing demand–supply imbalance. As a result, an
intermittent supply is widely adopted as a measure for controlling water demand among consumers.
However, ensuring equitable water distribution at low cost in intermittent water supply systems
becomes a challenge. Most intermittent water supply systems fail to achieve both objectives and
how to improve equity remains a complex task for water managers. There is little research in this
area and therefore a need to develop more appropriate optimisation techniques that recognise this
unique feature of intermittent systems in developing countries. The paper proposes a simple multi-
objective optimisation model to measure and improve equity and minimise cost in intermittent
distribution networks, under water scarcity condition. A simple network is subjected to intermittent
supply to demonstrate the model, in which both locations and capacities of source tanks/reservoirs
are subject to optimisation. A simulation model is used to model intermittent systems as pressure-
dependent through the use of consumer storage tanks. The paper reveals that equity under
intermittent supply conditions is measurable and can be improved through optimal location and
sizing of elevated source reservoirs.
Ernest Effah Ameyaw (corresponding author)
Department of Building and Real Estate,
Hong Kong Polytechnic University,
Hong Kong
(Formerly of Centre for Water Systems,
University of Exeter, UK)
E-mail: myernest2010@yahoo.com
Fayyaz Ali Memon
Josef Bicik
Centre for Water Systems,
University of Exeter,
UK
Key words |EPANET2, equity, GANetXL, intermittent supply, multi-objective optimisation, tanks
INTRODUCTION
Following acute financial constraints and water scarcity in
urban areas (Arnell ;Clarke & King ) of many
developing countries, intermittent water distribution has
widely been adopted as a measure for controlling water
demand among consumers (McIntosh & Yniguez ;
Hardoy et al. ). Consumers ability to collect water is lim-
ited by being physically cut-off for several hours of the day,
or even days in some countries. Under water scarcity con-
ditions, efforts are made to distribute the scarce water
resource efficiently, dividing the water distribution network
into zones (Marchis et al. ). Each zone is supplied with a
percentage of the available amount for a fixed period of time
less than 24 hours. Consumers are encouraged by the nature
of supply to use over-sized household storage tanks to cope
with service intermittency (Criminisi et al. ), with the
intension to store as much water as possible when supply
resumes. Hence, node water demand relates to pressure at
outlets but not actual user consumption, which is the
major difference between continuous and intermittent
systems.
Intermittent water supply is prevalent among developing
countries, such as south Asia, Latin America and other Afri-
can countries. In south Asia, for example, it was estimated
that at least 350 million people receive water service as
little as a few hours daily while 91% of water systems in
south-east Asia are intermittent (WHO et al. ). Vairava-
moorthy et al.()reported that all Indian cities operate
intermittent systems and that two or three hours of water
supply a day is considered ‘good’. In Mumbai, for example,
water supply is not only intermittent but inequitable: 4% of
the population receive water more than 8 hours/day; 33%
receive water more than 4 hours/day; 42% receive water
552 © IWA Publishing 2013 Journal of Water Supply: Research and Technology—AQUA |62.8 |2013
doi: 10.2166/aqua.2013.065
for just 3 hours/day, and 21% receive water less than 3
hours/day (Vairavamoorthy ). This reinforces the argu-
ment that service intermittency is a notable management
problem: water service providers cannot guarantee custo-
mers equal access to limited water resource. Choe &
Varley ()reported that in Latin America, more than 50
million residents in ten of its major cities receive rationed
supplies. A study conducted in four Indian cities to evaluate
influence of service intermittency on domestic water con-
sumption revealed that both duration and timing of water
supply under intermittent mode have a significant impact
on litres per capita per day (lpcd), demand is never satisfied
(Subhash & Prakash ). In summary, problems of inter-
mittent water supply include (Rajiv ;Marchis et al.
;Vairavamoorthy et al. ): inability to practise effec-
tive supply and demand management; operational
inadequacies; customer inconvenience and coping costs;
water quality problems; inequitable water distribution.
Water distribution should be equitable and efficient
(Chambers ;Molden & Gates ). However, under
intermittent supply conditions many difficulties arise, and
achieving equitable water distribution in a cost effective
manner becomes difficult, if not impossible. Traditionally,
water distribution system design has focused on continuous
water supply for 24 hours a day. Yet, in many developing
countries, existing continuous water distribution systems
are operated as intermittent systems. Therefore, the network
pressure often becomes inadequate and unable to provide a
satisfactory level of service to all consumers (Marchis et al.
). The resulting effect is that water distribution is inequi-
table, affecting temporal and spatial distribution
(Fontanazza et al. ). Given pressure variations in distri-
buting water, distant consumers do not receive a sufficient
amount of water, as supply is limited to consumers close
to the supply nodes. Limiting distribution to nearby users
could reduce distribution losses, particularly in networks
with high leakage rates, but such a distribution is not equi-
table (Indra et al. ).
Intermittent water distribution has been analysed by
many researchers (McIntosh & Yniguez ;Vairava-
moorthy et al. ;Tokajian & Hashwa ;Fontanazza
et al. ;Rosenberg et al. ;Andey & Kelkar ;
Marchis et al. ), but how to measure and improve
equity in existing intermittent water distribution networks
has been less investigated. Typically, the operation of inter-
mittent systems is based on experience of a water utility,
analysis of supply and demand, and the search for a compro-
mise (Twort et al. ) rather than on equity issues. In the
literature, very few models have been proposed considering
equity issues in intermittent water systems. Vairavamoorthy
and co-authors (Vairavamoorthy & Lumbers ;Vairava-
moorthy & Elango ;Vairavamoorthy et al. ,)
have proposed models for the design and control of intermit-
tent water systems. However, the models have been found to
be flawed by some authors. Tzatchkov & Cabrera-Bejar
()argued that the models are more academic than prac-
tical and that water distribution models must be functional
and practical to be able to produce reliable results to guide
decision-makers. Moreover, the models proposed by Vaira-
vamoorthy and co-authors are more sophisticated and
require specialised software (Ingeduld et al. ). Ease of
use of water distribution network models is fundamental
in developing countries (Tzatchkov & Cabrera-Bejar ).
A simple two-objective optimisation model for measuring
and improving equity and minimising cost in intermittent
distribution networks is described.
THE CONCEPT OF EQUITY IN WATER SUPPLY
SYSTEMS
The ‘concept of equity’is both very simple and complex: it is
simple because everybody is aware of it and complex
because there is no single best measure of equity (Sampath
;Indra et al. ). Equity of water distribution refers
to the ‘delivery of a fair share of water to users throughout
asystem’(Molden & Gates , p. 806). They further
argued that equity is a complex objective to measure given
that many factors determine the meaning of a ‘fair share’,
and because authors often interpret a fair share in a subjec-
tive manner.
In intermittent water systems in developing countries,
the issue of inequity (in terms of water quantity) among con-
sumers is a well known problem, but, as mentioned earlier,
the academic literature on equity in intermittent water
supply systems is scarce. This seems to be due to the fact
that drinking water systems are designed for a 24/7 supply.
However, most of these systems are later operated as
553 E. E. Ameyaw et al. |Equity in intermittent water supply systems Journal of Water Supply: Research and Technology—AQUA |62.8 |2013
intermittent systems following various challenges. At the dis-
tribution level, inequity among users results from the two
transitional phases of intermittent systems (Marchis et al.
); first, network filling up –where the quantity of
water entering the network does not reach users at the
same time, which can last for several hours in large net-
works. Consumers located far away from supplying
sources (nodes) become disadvantaged. Second, emptying
process –the generation of peak flows greater than antici-
pated in intermittent supply pipelines creates increasing
pressure losses denying users located faraway adequate
supply. Overall, the issue of inequity at distribution level is
mostly associated with water scarcity; when water supply
is limited, competition is generated among users.
Different ways of measuring equity (or inequity) of water
distribution have been suggested in the water management
literature, where many of these studies focused on irrigation
water systems (e.g., Garces ;Sampath ;Elawad ;
Indra et al. ). Range, relative mean deviation, variance,
coefficient of variation (CV), Gini coefficient (based on
economic literature on equity in income) and Theil’s infor-
mation measure are some useful positive measures of
equity measures (for irrigation system performance evalu-
ation) reported by some authors (Sampath ;Fuard
et al. ). These statistical measures are fairly easy to deter-
mine and could be used by decision or policy makers. The
CV of spatial distribution of water to farm plots was
employed as a measure of inequity in irrigation systems
(Molden & Gates ). By this measure, the target value
is 0.00 and a small (minimised) value of CV indicates an
improved water distribution to all farm plots. Indra et al.
()also evaluated 1 –CV as a measure of equity in irriga-
tion systems, in which a value close to 1.00 represents
improved water distribution. Both approaches produced
good results.
Similarly, the above measures of dispersion could be
adapted to evaluate equity issues in intermittent water
supply systems. Equity measures for intermittent systems
should be designed with the kind of situation at hand (e.g.,
water-deficient system). The objective of any equity measure
for intermittent systems must seek to determine the devi-
ations in actual quantities of water delivered to users
throughout a distribution network.
METHODOLOGY
Example distribution network and model formulation
The example network (Figure 1) is from the literature and its
data can be found in Gupta & Bhave ()and Ang &
Jowitt (). The network has been used by researchers to
demonstrate pressure-dependent demands in water distri-
bution. The network consists of a source tank, four
demand nodes at 1,000 m apart and four pipes in series,
and total length of 4,000 m. The source tank has an
elevation of 100 m above ground level. In this study, the net-
work is modelled as an intermittent system using a
Figure 1 |The baseline scenario.
554 E. E. Ameyaw et al. |Equity in intermittent water supply systems Journal of Water Supply: Research and Technology—AQUA |62.8 |2013
simulation tool. Node demands are modelled through the use
of ‘equivalent tanks’(discussed later), where T2, T3, T4 and
T5 represent original node demands of 2,877.12, 2,885.76,
4,320.00 and 1,442.88 m
3
, respectively. As shown in Figure 1,
T2–T5 refers to consumer (or private) tanks. Water is sup-
plied from the main supply tank to all four nodes, each
representing a group of consumers of specified population
with a demand allocation of 100 L h
–1
d
1
for a fixed supply.
The required amount of water to satisfy daily demands is
11,525.76 m
3
, but a fixed volume of 8,640 m
3
(i.e., 74.963%
of 11,525.76 m
3
) is assumed to be available for supply, caus-
ing a deficit of 2,885.76 m
3
. This assumption is applicable
for this study because the emphasis is on supplying limited
water under a water scarcity scenario. Therefore, water is
supplied intermittently, creating problems of competition
and inequitable delivery. Figure 1, the base scenario,
shows the percentage of ‘demand satisfaction’at each
node. Demand satisfaction in this context is the quantity
of water delivered to each consumer node, expressed as a
percentage of 8,640 m
3
. A value of 100% means that
demand at a node is fully satisfied and a lower percentage
indicates a poor satisfaction level. The need for strategies
to improve the situation and ensure equitable supply there-
fore arises, which is an optimisation problem.
Model formulation
Analytical procedures comprising simulation (EPANET2),
optimisation (GANetXL), and visual basic (VBA) program-
ming are applied to select desired solution(s) regarding two
objectives: equity and cost. GANetXL is used with
EPANET2 to evaluate the fitness of solutions for a given
set of decision variables and EPANET2 exposes its appli-
cation programme interface (API) in the form of a dynamic
link library (DLL) to invoke its functions from the VBA.
GANetXL is a decision support system (DSS) generator for
multi-objective optimisation of spreadsheet-based models,
which addresses some of the difficulties associated with the
development and application of model-based DSS in water
engineering practice (Savic
´et al. ). The relevance of
GANetXL and EPANET2 to the modelling is discussed in
the sections ‘Simulation model’and ‘Multi-objective optimis-
ation’, respectively.
Optimisation model
Equity of water distribution
Equity refers to a measure of spatial distribution of (drink-
ing) water over a distribution network (Elawad ).
Equity must be well defined to enable existing intermittent
systems to be rehabilitated well. This study defines equity
as being quantification of actual volume of water delivered
at specific locations (i.e., nodes that represent consumers),
and any deviation among the nodes measures the level of
equity. This is a measure of spatial uniformity, describing
the extent of variability in relative water delivery from
node to node over a water distribution network. To
ensure equitable water delivery, minimisation of variation
(inequity) among consumer nodes which is equivalent to
maximisation of equity is a main objective function. The
proposed equity measure is expressed as:
DE¼Min X
n
i¼1
j(%Qav %Qs)j(1)
where D
E
(%) ¼deviation of equity. It represents the
absolute value of summation of deviations (variations in
water delivery) of percentage of total water supplied to
each consumer node from the percentage average. This
sum represents inequity among consumer nodes in the dis-
tribution of the 8,640 m
3
of water. Therefore, the closer
the value of D
E
is to zero, the greater the level of equity
in water distribution. nis the number of consumer
nodes in the water distribution network. Qs(%) is the
volume (m
3
) of water delivered to each consumer node
expressed as a percentage. It is the ratio of actual
amount of water received to the amount required. Qs is
a supply indicator which is computed for each consumer
node.
Qav (%) is the percentage average volume of water deliv-
ered to all consumer nodes in the network. Thus, Qav is
expressed as the average of %Qs for all consumer nodes.
Qav is what every consumer node should be getting for
the fixed supply. Thus, as a good level of equity is achieved
(say D
E
¼0%), consumers receive the same level of demand
satisfaction and vice versa (see Table 2).
555 E. E. Ameyaw et al. |Equity in intermittent water supply systems Journal of Water Supply: Research and Technology—AQUA |62.8 |2013
Cost
The cost of each feasible solution includes the capital and
installation costs of elevated source tank(s). The cost of a
tank is expressed as a function of volume and is from
Centre for Water Systems (). Intermediate tank sizes
are considered in this approach, and corresponding costs
can be interpolated from tank sizes and costs. To generate
affordable solutions, minimisation of cost which is
expressed as a non-linear function, is considered as the
second objective function:
C¼Min[164377ln(v)789739] þn(2)
where C¼total cost of tank(s) in US dollars ($); ln ¼natural
log; v¼size (m
3
) of tank; n¼cost of transportation and
installation, and is likely to be variable and site specific.
The proposed multi-objective optimisation model
considers both objective functions: minimise D
E
and mini-
mise C.
Constraints to the model
The above model is limited by the two following constraints,
supply constraint and tank status constraint.
Supply constraint
The quantity of water distributed to the consumer nodes in
the network cannot exceed the total quantity of water
available for supply. The constraint is a mass balance
which must be satisfied for any feasible solution:
X
n
i¼1
Vi¼Aw(3)
where n¼number of source tanks optimised; V
i
¼total
volume (m
3
)ofnfor any solution; A
w
¼major constraint:
maximum availability of water for daily supply (m
3
).
Tank status constraint
The status of all the source tanks (T6–T9) cannot be off (0)
during the genetic algorithm (GA) runs (Figure 2). The status
of the source tanks are simulated using a binary variable, an
integer taking the values 1 (on –tank is used) or 0 (off –
tank not used). Both values (1, 0) refer to the same node
(location); a tank is either on or off during the GA run. A
GA generates a population of potential solutions to the optim-
isation problem via iterative randomised processes of
selection, crossover and mutation (see Goldberg ;Savic
´
et al. ). In this way, a GA optimises the objective functions.
The formulated model is a multi-objective nonlinear
optimisation model, which can be solved using a GA. GAs
have poor ability to handle constraints when applied to
water distribution networks (Prasad & Park ). Con-
straints such as mass balance equations are best handled
externally by a hydraulic solver. For this reason, the hydrau-
lic analysis of the network is performed using EPANET2, by
linking it to GANetXL.
Figure 2 |Optimisation scenario.
556 E. E. Ameyaw et al. |Equity in intermittent water supply systems Journal of Water Supply: Research and Technology—AQUA |62.8 |2013
Simulation model
The simulation model models the simple serial network
(Figure 1) for intermittent supply.
Modelling demand
EPANET2 is a complex hydraulic solver with powerful func-
tions which is adjusted to function as pressure-dependent to
model demands under intermittent supply (Ingeduld et al.
). The hydraulic solver has specified demands at junc-
tion nodes. In this study, the approach employed to model
node demands is based on an ‘equivalent tank’which rep-
resents the total demands at a node to ensure pressure-
dependency at nodes of the network. A tank will fill up
based on the existing pressure at the tank and it is possible
to visualise tank fill levels and the development of pressure
(and hence the amount of water delivered) at each consu-
mer tank. As tanks of shallow depths offer good results
(Trifunovic & Abu-Madi ), all consumer tanks are there-
fore limited in height to 2 m, giving large surface areas.
EPANET2 scales pressure between 0 and 2 m. Tank
capacities (in m
3
) are estimated based on the total demand
(i.e. population to be served) at each node. For a cylindrical
tank with a varying diameter but a constant height of 2 m:
V¼πr2h(4)
V¼πd2
4h(5)
d¼ffiffiffiffiffiffiffi
V4
h:π
r(6)
where d¼tank diameter (m); V¼volume of consumer tank
(m
3
); h¼tank height (m).
Decision variables and coding
There are three types of decision variables for water distri-
bution network models of fixed layout: pumps, pipes, and
tanks (Vamvakeridou-Lyroudia et al. ). In this study,
source tanks are the only decision variables considered.
To achieve reliable results, the following approach is used
to model and optimise the problem. Up to four elevated
source tanks are considered by the model and the height
(depth) and diameter are defined to determine a tank’s
capacity. Therefore, all nodes are potential locations for
new source tanks. The decision variables for tanks are:
status and diameter of each tank, giving a total of eight
decision variables for the problem.
New source tanks that are introduced into the water dis-
tribution network are simulated and optimised with the use
of integer numbers, referring to status and diameters of
tanks. As explained earlier, the status of tanks are simulated
using binary variables of 1 and 0. The nodes and tanks are
defined by their respective indices using EPANET2 pro-
grammers toolkit. Tank diameters are simulated using
integer values, between 2 and 20, which are scaled to corre-
spond to the supply constraint. This helps to obtain the
realistic diameter for each tank, and avoid infeasible sol-
utions. In summary, the optimisation applies to the
number, location and capacities of elevated source tanks
in the network.
Multi-objective optimisation
A multi-objective optimisation is performed for equity and
total cost. In most instances, water engineering decision-
making problems –water system designs, rehabilitation/
improvement, and operation –need to achieve multiple
objectives. This usually involves conflicting objectives such
as maximisation of benefits, minimisation of cost, minimis-
ation of risks, maximisation of reliability, etc., which
should be optimimised simultaneously (Haimes ;Wal-
ters et al. ;Farmani et al. ).
Many multi-objective optimisation models and tools for
treating water engineering/management problems have
been developed and applied (Farmani et al.).
GANetXL is one of these models (Savic
´et al. ).
GANetXL combines the power of single objective and
multi-objective optimisation using a GA with a graphical
user interface that allows users to easily create a DSS appli-
cation that employs a GA to define water engineering
optimisation problems, configure, and execute optimisation
runs and analyse generated results through visualisation
of Pareto-optimal solutions (Savic
´et al.). For
557 E. E. Ameyaw et al. |Equity in intermittent water supply systems Journal of Water Supply: Research and Technology—AQUA |62.8 |2013
multi-objective problems, GANetXL supports NSGA-II
algorithm (Savic
´et al.). The concept of GANetXL is
to produce a set of optimal solutions in a Pareto front –
largely called Pareto-optimal solutions –in objective and
decision spaces. Detailed discussion of GANetXL and its
application is provided by Savic
´et al. (). The necessary
installation package can be downloaded from the Centre
for Water Systems’website: http://cws/ganetxl/. In this
case, the optimisation scenario entails the possibility of sup-
plying water from up to four source tank(s) –T6, T7, T8 and
T9. Thus, a tank is used or not used based on its status and
that of the connection pipes, as illustrated in Figure 2.Itis
worth noting that the main supply tank is not open to
optimisation.
APPLICATION OF THE MODEL
The above methodology is applied to measure and to select
equity levels for water distribution in a simple water distri-
bution network (Figure 1). The degree of equity among the
consumer nodes is calculated based on the amount of water
delivered to each node and the locations and capacities of
source tanks. Simulation of source tanks for optimisation
within a GA is complex, involving several decision variables
(Walters et al. ), which have effect on the objective func-
tion value (Vamvakeridou-Lyroudia et al. ). In order to
simplify the optimisation problem the following assumptions
are made: (1) the source tanks (T6–T9) are cylindrical in
shape; (2) the height (depth) of each tank is fixed at 5 m;
(3) the volume of each new (elevated) source tank is effective
storage, which provides acceptable pressure in the network;
and (4) each source tank empties its contents within a 24-
hour extended period simulation.
These assumptions are applicable for this methodology
because the emphasis of the study is on equity in water deliv-
ery with respect to optimal location and capacities of source
tanks. However, the model will work fine with an increased
number of decision variables without a need for complex
coding.
The methodology for the optimisation problem defines
the objective functions, decision variables, constraints and
any relationships among these variables. An Excel spread-
sheet file with a worksheet named ‘Problem’(referred to
as Excel spreadsheet model) defines the optimisation pro-
blem, stating cell locations of the decision variables, the
objective functions and the constraint of the problem.
Microsoft Excel spreadsheet, as used in this study, offers var-
ious chart options to enable visualisation of the decision
space. During the optimisation run(s), visualisation of the
decision space is by an optimisation progress form which
displays generated solutions in the form of a chat containing
values of objective functions, penalty functions, and
decision variables. The simulation tab of GANetXL calls
EPANET2 to evaluate fitness of organisms through a VBA
macro. The water distribution network is simulated using
EPANET2 which determines the water levels (tank filling)
in the four consumer tanks. These water levels (equivalent
to pressures) are read into the ‘Problem’sheet of the excel
file during the optimisation process. From these water
levels, the amount of water delivered to each consumer
node is calculated, from which the equity objective is com-
puted automatically. Results from the optimisation run(s)
are automatically saved in a separate worksheet of the
same spreadsheet file at the end of each run.
Steps for model application
The steps for applying the proposed methodology to multi-
objective intermittent water distribution optimisation are
suggested as follows:
1. A number of solutions are produced at each generation
by the DSS generator, GANetXL.
2. For each solution, the water distribution network is
solved using EPANET2 in order to select the number of
source tanks, compute the capacity of each source tank,
and compute the amount of water in the consumer tanks.
3. From step 2, the objectives of equity and total cost are
automatically calculated, using Equations (1) and (2),
respectively.
4. Steps 1, 2, and 3 are repeated for all solutions in any
single generation.
5. All solutions (say X) together with their respective total
cost (C) and equity (D
E
) values enter the trade-off pro-
cedure of the GA. This is to ascertain the Pareto-
optimal curve and selection for reproduction to the
next generation.
558 E. E. Ameyaw et al. |Equity in intermittent water supply systems Journal of Water Supply: Research and Technology—AQUA |62.8 |2013
6. Recombination and mutation occur, and a new gener-
ation of solutions is produced. GANetXL offers the
flexibility of selecting different mutation and crossover
operators and probabilities.
7. Start from step 1 for the next generation of solutions,
until termination criteria for GANetXL are met.
During the optimisation process, it must be noted that,
the worst case occurs when the water is distributed to only
three consumer/private tanks. In that case, those tanks
will be fully satisfied while the disadvantaged tank will
receive zero percent supply, giving the worst equity value
of 150%. For example, if the limited water (8,640 m
3
) is sup-
plied to only T2, T4 and T5, the worst equity value of 150%
is generated. This is undesirable. The optimisation method-
ology, therefore, tries to avoid this situation by minimising
this maximum value, as demonstrated in this study.
RESULTS AND DISCUSSION
Different equity measures and total costs are generated by
applying the above methodology. By optimising source
tanks’locations and capacities, some control is imposed
on the amount of water delivered to each consumer tank
(node), hence the determination of equity levels. Percen-
tages of water demand satisfaction of the four demand
nodes (T2–T5) of the water distribution network are
shown in Table 2 under both base and optimised scenarios.
Under the base scenario, when no control was imposed on
water distribution, the water delivery favoured consumer
nodes close to the main supply tank (Figure 1). But when
water distribution control is imposed in the application of
this methodology as in Figure 2, the distribution of the
scarce water resource (8,640 m
3
) tends to be more equitable
(see Tables 1 and 2).
Solutions of different values of equity and cost are
shown in the generated Pareto trade-off curve in Figure 3.
They are extracted from the Pareto-optimal curve generated
by the twin-objective optimisation. The details of the total
costs, equity values, and number of optimised tanks and
their respective capacities and locations of the solutions
are presented in Table 1. The ‘best’Pareto-optimal front in
Figure 3 is chosen following several test runs. It is produced Figure 3 |Equity vs. cost pareto-optimal.
Table 1 |Proposed solutions
Solution
Tank(s)/
capacities (m
3
)
Tank(s)
location
Equity
(%)
Total cost
($)
1T7–8640 J2 25.56 705,200
2T7–8273
T9 –367
J2
J4
21.59 883,897
3T7–7776
T9 –864
J2
J4
16.48 1,014,589
4T7–6912
T9 –1728
J2
J4
11.83 1,109,166
5T6–5530
T9 –3110
J1
J4
4.19 1,169,105
6T6–5359
T7 –371
T9 –2910
J1
J2
J4
3.68 1,344,598
7T6–5031
T7 –125
T8 –1129
T9 –2355
J1
J2
J3
J4
2.85 1,487,233
Table 2 |Demand satisfaction: optimised solution vs. base scenario
Optimised solutions (%)
Consumer tank Base scenario (%) 1 5 6 7
T2 89 76.90 75.47 75.31 75.16
T3 81 85.21 75.97 76.11 76.52
T4 66 69.45 73.31 73.50 73.74
T5 58 67.11 76.87 76.38 75.09
Qav 73.5 74.67 75.41 75.32 75.13
559 E. E. Ameyaw et al. |Equity in intermittent water supply systems Journal of Water Supply: Research and Technology—AQUA |62.8 |2013
from 2,000 generation runs, a population size of 100, simple
multi-point recombination operator with probability of 0.9,
and a simple gene mutation operator with probability of
0.125 (see Goldberg for discussion of terms).
Inspection of the solutions along the proposed Pareto-
optimal front reveals that each potential solution has a
different number and location of new source tanks. This is
due to the competing objectives of equity and cost. Solution
1 is the best in terms of cost and solution 7 provides the best
equity function value. There is a sharper change in equity
function values from 25.56% in solution 1 to 4.19% in sol-
ution 5 (see Figure 3 and Table 1), indicating a good level
of equity. However, there is a marginal improvement
between solutions 5 and 7. Layouts of selected solutions
are shown in Appendix A (available online at http://www.
iwaponline.com/jws/062/065.pdf). ‘J’refers to junction
node as used in EPANET2.
Solutions 1, 5, 6 and 7 representing solutions on the extre-
mities and centre of the Pareto front are compared with the
base scenario and among themselves, in Table 2. The table
shows the percentage of demand satisfaction, indicating the
degree of variation among the demand nodes represented by
private/consumer tanks. It also suggests that water delivery
becomes more equitable as equity values near zero.
It must be noted that the optimisation problem is solved
assuming that the decision variables are discrete (i.e. integer
bounded). This limits the number of optimal solutions in the
Pareto-optimal set, allowing easy analysis of compromise
solutions in the set. Furthermore, the application of
GANetXL generates a set of optimal solutions to aid the
decision-maker to analyse and select the most optimal sol-
ution based on equity and budget allocation in this case.
In developing countries, cost is a major consideration, the
decision-maker may be interested in solutions that do not
offer maximum equity, however, meet the budget constraint.
The main differences in total costs of the solutions relate to
the level of equity and number of source tanks. Thus,
improved equity implies the use of more than one new
source tank which increases the cost of the solutions. A
tank’s cost is primarily a function of its capacity.
However, the emphasis is the ability of the methodology
to improve equity rather than putting too much emphasis on
cost in this case. This is because the costs of elevated tanks
(and tanks in general) are highly site-specific and the
comparison must be made on a case-by-case basis. In a prac-
tical situation, the choice of a solution must be balanced
with social concerns. Given that high inequity is a recipe
for social conflict (Indra et al. ), public anger and non-
payment of bills, the choice of a solution must guarantee a
good level of equity. In this model, the choice of a solution
means that the decision-maker becomes aware of the
amount of water to be delivered to each demand node
(four nodes in this case) and the number and capacities of
source tanks from the spreadsheet model or the simulation
model.
CONCLUSION AND FUTURE WORK
The paper describes an optimisation methodology for measur-
ing and improving equitable water distribution under
intermittent supply. A spreadsheet-based multi-objective optim-
isation model, GANetXL, for minimising inequity and cost is
illustrated. The paper also shows that EPANET2 can be
adjusted to model intermittent water systems successfully.
Theappliedmethodologyinthiscasesuggeststhatequity
among water consumers (inter-consumer equity) can be
improved through optimal location and capacities of elevated
source tanks in an existing intermittent water system. This
methodology offers a set of solutions to enable the decision-
maker to arrive at a final decision based on economic or
social factors. In this case, the best equity level is associated
with the highest total cost and vice versa. A balance must be
made between consumer concerns on equity and the water uti-
lity’sfinancial strength.
Future research would focus on application of the meth-
odology to a large and typical intermittent water supply
system, while adding other performance measures, includ-
ing reliability and efficiency of supply, water quality and
individual costs.
ACKNOWLEDGEMENT
The first author is grateful to the Commonwealth Shared
Scholarship Scheme (CSSS) for sponsoring his MSc study
at the University of Exeter, UK. This paper is based on the
author’s dissertation.
560 E. E. Ameyaw et al. |Equity in intermittent water supply systems Journal of Water Supply: Research and Technology—AQUA |62.8 |2013
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