Ben-Gurion University of the Negev Jacob Blaustein Institutes for ...

Ben-Gurion University of the Negev
Jacob Blaustein Institutes for Desert Research
Albert Katz International School for Desert Studies
A water distribution system in Sicily: optimization options
for the provinces of Siracusa and Ragusa
Thesis submitted in partial fulfillment of the requirements for the degree of
“Master of Science”
By: Salvatore Campisi
January 2009

Ben-Gurion University of the Negev
Jacob Blaustein Institute for Desert Research
Albert Katz International School for Desert Studies
A water distribution system in Sicily: optimization options for
the provinces of Siracusa and Ragusa
Thesis submitted in partial fulfillment of the requirements for the degree of
"Master of Science" (or “Master of Arts”)
By Salvatore Campisi
Under the Supervision of Prof. Gideon Oron
Department of Environmental Hydrology & Microbiology
Zuckerberg Institute for Water Research (ZIWR)
Author's signature …………….……………………… Date …………….
Approved by the Supervisor…………….……………. Date …………….
Approved by the Chairman
of the Graduated Program Committee …….………… Date ………

Abstract
I
The Sicilian water balance, on a yearly base, shows a substantial equilibrium between
the total water demand and total water supply. Nevertheless a closer analysis, at basin
level reveals a local situation of dramatic shortages both in terms of spatial and
temporal distribution of water resources.
Given an unbalanced allocation of water resources in the provinces of Siracusa and
Ragusa, South East Sicily, this work seeks the optimization of inter-basin water
distribution through the analysis of several theoretical aqueduct schemes.
The methods used for this study belong to the disciplinary area of operational research
with special focus on linear programming of transportation problems. In practice, two
different mathematical models were built: a transportation model and a transshipment
model. They were solved using commercially available software. The research started
from the collection of data in order to assess demand and supply of water at basin scale,
then data where processed and used in the model.
Results show that the study area is in fact supplied with a total amount of water
sufficient to meet total water demand. Nevertheless, water resources are distributed
unevenly. The model determines which branches of a theoretical aqueduct should be
used and how much water should be transported such that the total transportation cost is
minimized and each and every demand is satisfied.
This work provides a first approximation of feasible routs and directions of
transportation of water in the study area. The working procedure can be easily applied
to different and larger areas. The results obtained do not take into consideration
investment costs and are not meant to inform any decision but they can support to
taking decision on which on which hypothesis would deserve a full feasibility study.
This is in line with a research method operating in terms of progressive improvement of
analysis and continual sophistication of decision support systems.

Acknowledgement
II
Special thanks to my supervisor Prof. Gideon Oron for sharing his unique capabilities of
foreseen, clearly and in advance, scientific risks and opportunities, for his kind guidance
and his precious friendship. Special tanks to Dr. Leonid Gillerman for congruent
precise, effective, and always kind suggestions. Thanks to the entire academic body of
the Zuckerberg Institute for Water Research (ZIWR), that has been always a source of
inspiration. Special thanks to the administrative, didactical and scientific management,
in particular to Mss. Dorit Levin, Dr. Drora Kaplan, and Prof. Eilon Adar for being in
turn engine and soul of all of us. Thanks to my colleagues with whom I shared precious
time, sincere friendship and surprising knowledge. And always thanks to my parents,
my mother Lucia and my father Rosario for having been willing to accept my absence
from home with loving faith. Thanks to my sister Manuela for her practical advices and
thanks to the reader that will be so kind to read this work.

Tables of contents
1 INTRODUCTION 1
1.1 THE ARID REALM AND THE SICILIAN WATER MANAGEMENT 1
1.2 WATER BALANCE ASSESSMENT 3
III
1.3 RELEVANCE AND LIMITATIONS OF THE WATER BALANCE
APPROACH 4
1.4 TECHNICAL SOLUTIONS FOR WATER SHORTAGES: INTER-BASIN
TRANSPORTATION OF WATER 5
1.5 PUMPED STORAGE HYDROELECTRICITY 6
1.6 OPERATIONAL RESEARCH 6
1.7 LINEAR PROGRAMMING 7
2 BACKGROUND INFORMATION FOR THE WATER ISSUE IN SICILY 7
2.1 THE STUDY AREA 8
2.2 CLIMATIC CONDITIONS 9
2.3 RAINFALL TREND IN SICILY: SPATIAL DISTRIBUTION 10
2.4 GROUNDWATER RESOURCES IN SICILY: SPATIAL DISTRIBUTIO 12
2.4.1 Volcanic aquifer of Etna 12
2.4.2 Miocenic calcareous aquifer in the area of Ragusa 12
2.4.3 Volcanic aquifer in the area of Lentini 12
2.4.4 Plio-quaternary sandy-calcarenitic aquifer 13
2.4.5 Alluvial aquifer 13
2.5 GROUNDWATER RESOURCES IN SICILY: QUALITY ASPECTS 14
2.5.1 Potential vulnerability of the water strata to contamination 16
2.6 MAIN ECONOMICS (AGRICULTURE, INDUSTRY, POPULATION) 17
3 METHODOLOGY 18
3.1 THE TRANSPORTATION MODEL 18
3.2 USES AND FUNCTION OF THE TRANSPORTATION MODEL 21
3.3 THE TRANSSHIPMENT MODEL 21
3.4 PARAMETERS OF THE MODEL 23
3.4.1 Units of Water Supply 23
3.4.2 Surplus and Deficit of Water at Basin Level 26
3.5 THE UNIT TRANSPORTATION COST 27
3.5.1 Positive Cij 27
3.5.2 Negative Cij 29

3.6 THE DECISION VARIABLE 30
3.7 PRELIMINARY WORK FOR NETWORK LAY-OUT 30
3.8 THE TRANSPORTATION NETWORK 31
IV
3.9 FROM THE TRANSPORTATION MODEL TO THE TRANSSHIPMENT
NETWORK 32
3.9.1 The Transshipment Networks: Two Different Schemes, Four Variants 34
3.10 THE SOLVER 35
4 RESULTS 36
4.1 WATER BALANCE AT BASIN LEVEL 36
4.1.1 Acate and Basins between Gela and Acate 36
4.1.2 Basin: Ippari 37
4.1.3 Basin: Irmino 38
4.1.4 Basins between Scicli and Capo Passero 39
4.1.5 Basins between Capo Passero and Tellaro 40
4.1.6 Basin:Tellaro 40
4.1.7 Basin: Cassibile 41
4.1.8 Basin: Anapo 42
4.1.9 Basins between Anapo and Lentini 42
4.1.10 Basin: S. Leonardo 43
4.1.11 Basins number: 19079, 19081, 19083, 19087, 19088, 19090 44
4.2 TOTAL WATER BALANCE 44
4.3 THE TRANSPORTATION PROBLEM 46
4.4 OPTIMAL SOLUTION OF THE TRANSPORTATION PROBLEM 47
4.5 THE COSTS OF TRANSSHIPMENT 49
4.6 TRANSSHIPMENT OPTIMAL SOLUTIONS 50
5 CONCLUSIONS 52
6 REFERENCES 55

Figures and tables
V
Figure 1 - Conceptual framework for a Water Resource Systems analysis (after
UNESCO 2005) 8
Figure 2 – The study area 9
Figure 3 – Rainfall distribution (1931-60) (after Piccione, 2008) 11
Figure 4 – Rainfall distribution (1961-90), (after Piccione, 2008) 11
Figure 6 - Qualitative features of groundwater resources (after Brucculeri, 2002) 15
Figure 7- Transportation network with m sources and n destinations 19
Figure 8 – An explicative example of a transhipment problem 22
Figure 9 – Geographical map of the study area: elevation, hydrographical basins, and
nodes locations 31
Figure 10 – Network representation and arc length 32
Figure 11 – Overlapping of a 14 arcs transhipment network on the transportation
solution 33
Figure 12 – Lay-out of the transhipment network according to the geomorphology of
the study area 34
Figure 13 – Two networks, four variants 35
Figure 14 – Water supply, demand and balance at basin level 46
Figure 15 – Transportation network: optimal solution 48
Figure 16 – Transhipment optimal solution 13 arcs 51
Figure 17 – Transhipment optimal solution 14 arcs 51
Table 1 - Sicilian Import / Export balance in the 2007 (after OEMCI, 2008) 17
Table 2- Tableau form of a transhipment problem 22
Table 3- Litres of water consumption per inhabitant per day in demographic classless
(CDEBTAS, 2007) 25
Table 4– Water Balance Assessment 37
Table 5 - Water Balance Assessment 38
Table 6 – Water balance assessment: Irmino 38
Table 7 - Water Balance Assessment basins between SCICLI and CAPO PASSERO
39
Table 8– Water Balance Assessment basins between Capopassero and Tellaro 40
Table 9– Water Balance Assessment basin Tellaro 41
Table 10– Water Balance Assessment basin Cassibile 41
Table 11 – Water Balance Assessment basin Anapo 42
Table 12 – Water Balance Assessment basins between Anapo and Lentini 43
Table 13 – Water Balance Assessment basin Irmino 44
Table 14 - Water balance at basin level 45
Table 15 - Arc length, and elevation at supply and demand nodes. 47
Table 16 - Transportation network: cost (€/m3) 47
Table 17 - Optimal solution 48
Table 18 – Transhipment costs 49
Table 19 – Value of the optimal solution for the transhipment problem (13 arcs)
50
Table 20 – Value of the optimal solution for the transhipment problem (14 arcs)
50

Abbreviations
VI
AIS Administrative and Institutional System
CB Consorzio di Bonifica (Consortium for water distribution)
Csa Mediterranean Climate
Csb Mediterranean Climate
FAO Food and Agricultural Organization
GDP Gross Domestic Products
LP Linear programming
NRS Natural Resources System
OR Operational Research
PSH Pumped Storage Hydroelectricity
SES Socio-Economic System
UNEP United Nation Environmental Program
UNESCO United Nation Educational Scientific and Cultural Organiazation
WB Water Budget
WBA Water Budget Approach
WBS Water Budget Sheet
ή Pump efficiency
∆Z Difference in elevation
Ad Agricultural demand
C Smoothness of the internal pipe
Cij Unit transportation cost
D Internal diameter of pipe
Dw Recycled water
F Infiltration
g Acceleration
H Reassure head
h Height in meters
HP Hors power
I Industrial demand
J Gradient of the head loss
k Coefficient of efficiency
L Length
m Total number of supply sites
n Total number of demand sites
p Population
P Power in kilo watts
Q Water consumption per day per inhabitant
qm Cubic meters
R Runoff, rivers, lakes, reservoirs potential
r Flow rate
u Estimated urban demand
U Urban demand
Z Value of the objective function
∆h Pressure friction losses

1
1 Introduction
The Sicilian water balance shows a substantial equilibrium between the total water
demand and total consumption on a yearly basis. Nevertheless, a closer analysis, at
basin level, reveals local situations of dramatic shortages both in terms of spatial and
temporal distribution of water resources.
The problem to be solved, and the objective to be reached, concerns the selection of the
most economical water distribution scheme that would meet water supply and demand
of a specific study area in South-East Sicily. In other words, given an unbalanced
situation where basins are presenting either surplus or deficit of water, mathematical
tools were applied to select among different theoretical distribution schemes on the
basis of their operational costs. The model seeks the selection of the distribution scheme
that generates the lowest operational cost.
Beside the main purpose of the work, a number of intermediate objectives were defined
as follows: a) characterization of the geophysical main features of the study area; b)
drafting of a water balance assessment of the study area; c) drafting of a map of water
sources and destination (georeferencing of water demand and supply); d) drafting of
possible water distribution network schemes; e) selection of the most economical
network scheme and estimation of the total operational cost and the unit cost per cubic
meter of water transported in one year.
In practice, point (e) corresponds to the general objective of the study.
1.1 The Arid Realm and the Sicilian Water Management
The arid realm is a vast area covering one-third of the earth's land surface and includes
approximately 40 percent of the world's population (Agnew and Anderson, 1992;
Wilson, 2004). Arid regions are characterized by great environmental and economic
contrasts and contain some of the world's most important mineral resources (Heathcote,
1983: Mather, 1984: Helweg, 1985). However, they are also water scarce areas that
limit human settlement and industrial activities (Bruins and Lithwick, 1998). UNESCO
has listed 'lack of water resources' and 'hostility' as two of the main obstacles to
development in these areas (Roberts, 1993). With growing demand and limited
availability of water resources, there is a mounting global need to manage more
efficiently available water resources in these areas, particularly in cases where all or
nearly all water supplies are exploited (Van Vleck et al., 1987; Molden 1997).

2
Sicily does not strictly belong to the arid realm but it has a number of features in
common with arid and semiarid regions. It is here acknowledged that solutions for the
Sicilian water problems can be found in the experience developed in arid and semiarid
regions because, likewise in those regions, the Sicilian water welfare depends on: a) the
physical availability of water resources connected to the use of appropriate
technologies; and b) the existence of an integrated regional management system that can
serve the goal of efficient water allocation on the basis of maximal productivity and
public welfare. In the framework of this work, it is considered to be convenient to
compare Sicily to arid and semiarid zones for the following two reasons:
a) Sicily is affected by local phenomena of water shortages related to physical water
scarcity. These are the reasons of discontinuous water distribution in several
municipalities (Agrigento and Caltanissetta provinces) and low pressure distribution in
the provinces of Trapani, Siracusa and Ragusa. In the last two decades water shortages
have reached alarming proportions so that on the 31 st of May 1999 with Regional
Ordinance number 2983, it was declared the "regional state of emergency for water and
waste water management". After ten years Sicily is still in a state of emergency.
b) Water management plays a central role in the Sicilian water welfare. In facts, only a
portion of the above mentioned water shortage can be directly attributed to water
scarcity, while, historically, inadequate water management has been the drive for
several ill services. At this respects Hess, the chair of Criminology of the University of
Utrecht, referring to Sicilian history up until the 1950's, clearly stated "springs in Sicily
are private property, their exploitation, yielding large profits, is traditionally associated
with mafioso affairs: that is, they are economic monopoly guaranteed by mafioso
power" (Hess, 1999). Nowadays the situation has different connotation but it remains
disputable and further research would be desirable.
The quantitative correlations between Sicilian water management practices and water
shortages are out of the scope of this study. The focus of this work is on the
improvement of the system of transportation of water (via aqueducts) here intended as
one of the many possible technical options available in the field of water management.

3
1.2 Water Balance Assessment
One of the first research questions of this study focused on the perception of water
scarcity and its measurement. Experts have developed a system called Water Resource
Management to measure existing water resources and allocate them to different sectors,
taking into account the water quality demands of each sector (Lundqvist et al. 1985).
Allocation is a particularly complex issue, addressed by a number of researchers.
According to Khouri (1992), allocation decisions are usually guided by economic and
social considerations, while Lithwick et al. (1998) and Allan (1998) maintain that these
decisions often reflect solely political considerations. Svendsen (2005) notes that
allocation decisions must take into account the disparate geographical locations of the
various consumers. Zaslavsky (2002) demonstrate that allocation decisions stem
directly from the number of available water resources.
There is a broad consensus among scholars within the water management field (e.g.
Mather, 1984; Waldman and Shevah, 1985: Lundqvist et al, 1985) that the policy
decisions regarding water allocation are frequently poor, and fail to take into
consideration some important factors affecting present water use patterns. This is
particularly dramatic in regions where water resources are not abundant and/or not
easily available.
Lomborg (2001) claims that water scarcity, especially in the arid regions of the world, is
attributed first and foremost to inappropriate management. Similar claims have been
made by Roberts (1993) with regard to water resource management in arid zones in
China and America Southwest. For example, according to Pigram and Musgrave
(1998), the overall deterioration of water resources in the Murray Darling River Basin
in Australia is the results of neglect and inability to adapt, as traditional bureaucratic
development decisions, that were made during periods of relatively abundant water
supply, have remained in place for a protracted period of time.
Similar opinions are held by different researchers who focus on water scarcity in the
Middle East. Kliot (1994) attribute poor water management to the negative water
balance in the Middle East. Nachmani (1995) specifically points to existing patterns of
allocation in the Middle Eaast that fail to take into account its scarcity value. Zaslavsky,
a former Israeli Water Commissioner affirmed: "there are local and temporary shortages

4
because it's not the highest priority of the countries involved; that's all" (Lithwick, 1998,
pg 27).
In the framework of this study water is allocated with the single objective to meet local
demands, no consideration has been given to water marginal productivity.
1.3 Relevance and Limitations of the Water Balance
Approach
No singular method of water management is far superior to the rest, but the consensus
concerning inadequate management in the arid realm underlines the importance of
providing decision makers in arid and semi arid countries with a better understanding of
current patterns. Many methods have been developed over the years to assess water use
patterns based on the availability of water resources. One such method, the Water
Budget Analysis, follows from the Water Balance Approach (Molden, 1997). The
disaggregated Water Balance Inventory has long been used as a key tool for calculating
the ratio between water demand patterns and the availability of water sources in a given
domain (Mather, 1984). The Water Budget Inventory under various different names, is
essentially a quantitative summary of all of the inputs and outputs from and to a water
system (Helweg, 1985).
The central notion of the water budget concept is based on the argument that
understanding current water resources and the associated demand and use pattern is
essential for successful water management. Ideally, a water budget analysis can act as a
stepping stone for innovative and practical recommendations that can be applied to
specific water systems. An assessment of available water through a water budget
analysis is vital in trying to understand the potential effect of different policy options. It
may also aid in the development of a more appropriate allocation system that will better
meet desired objectives (Barker et al 2003).
However, the Water Budget method to date has been given only perfunctory attention
on the state level, usually in the context of ensuring adequate national supplies. More
recently, the Water Budget method has also been applied to certain subsystems,
including river basins, some inter-state basins and few international basins (Roberts,
1993).

5
In the initial process of any water inventory, various problems may arise, such as data
deficiency (partial or complete lack of data) and inaccuracy due to different
measurement methods used (not comparable data) and unreliable sources from which
data is obtained. This can present a faulty or inaccurate picture of the investigation
inventory.
Nonetheless, a Water Budget Analysis is considered a necessary step and adequate
method of quantifying the tolerable supply levels in arid regions, while taking into
account local constraints. Thus in this study, a Water Budget Analysis is held to provide
a first approximation of water allocation and consumption. As ineffective this method
may be in directly assessing current water supply and use patterns, it must be noted that
without adequate records of quantities of water in a given domain, problems cannot be
accurately determined and solutions cannot be found.
1.4 Technical Solutions for Water Shortages: Inter-basin
Transportation of water
In order to overcome perceived shortages, a number of schemes have been developed
through the years (Lithwich et al. 1998). While the bulk of water management-related
constrains seems to be shared by most arid regions, water demand and usage patterns
differ according to several variables, such as population growth, economic
development, cultural and foreign policy objectives (Le Marquand, 1977). Given these
factors, the success of methods implemented in one country may not obtain elsewhere
(Agnew and Anderson, 1992). Dingman, (1994) wrote: "No specific formula for a long
range water resources plan for a country or for hydrologic units has ever been defined"
(Agnew and Anderson, 1992, pg 270). Among the most prevalent of methods are, as
Mather (1994) points out, storage via captured runoff, the manipulation of pricing
system, the introduction of water savings techniques and conveyances facilities, etc.
In the framework of this work it is studied the inter-basin transportation of water, here
intended as a technical remediation to water shortages. This solution is considered to be
significant because there are no inter-basin aqueducts in the study area so that it is here
investigated what would be the operational cost of an aqueduct scheme that would meet
water demand with existing water supply.
Transportation of water is the movement of water over large distances. Methods of
transportation fall into two categories: a) aqueducts, which include pipelines, canals,

6
and tunnels; b) container shipment, which includes transport by tank truck, tank car, and
tank ship. In these study only pipelines solutions will be studied.
1.5 Pumped Storage Hydroelectricity
The transportation schemes here addressed includes the possibility to create electrical
energy out of the elevation difference between sources and destinations of water. In
other words, it is here assumed, that water transportation consumes energy when a
negative elevation (destination higher than source) has to be overcome and genertes
energy otherwise.
Pumped storage hydroelectricity (PSH) and its many practical variations, is a type of
hydroelectric power generation that can be integrated to water distribution systems
(Oron et al 1988). The classical PSH method consists in the storage of energy in the
form of water, pumped from a lower elevation reservoir to a higher elevation, and the
production of hydroelectricity releasing water from the higher to lowest elevation. The
first use of pumped storage was in the 1890s in Italy and Switzerland. In the 1930s
reversible hydroelectric turbines became available. These turbines could operate as both
turbine-generators and in reverse as electric pumps. Although the losses of the pumping
process makes the plant a net consumer of energy overall, the system generates
revenues by operating the turbines during periods of peak demand, when electricity
prices are maximal, and running the pumps during periods of off-peak demand when
electricity prices are minimal.
Pure pumped-storage plants just shift the water between reservoirs but combined pump-
storage plants also generate their own electricity like conventional hydroelectric plants
through natural stream-flow. A hybrid form of pumped storage hydroelectricity
generation will be taken into consideration as a feature of network design.
1.6 Operational Research
Operational research was adopted to build and optimize a transportation model.
“Operational research is concerned with scientifically deciding how to best design and
operate a man-machine system, usually under conditions requiring allocation of scarce
resources” (Ravindran, 1984). In other words, operational research (OR) seeks the
determination of the best (optimum) course of action of a decision problem under the
restriction of limited resources. The term operational research quite often is associated

7
almost exclusively with the use of mathematical techniques to model an analyze
decision problems.
A decision model is merely a vehicle for “summarizing” a problem in a manner that
allows systematic identification and evaluation of all decisions the alternative that is
judged to be the “best” among all available options.
The decision making process in OR consists of constructing a decision model and then
solving it to determine the optimal decision (Taha, 1987). The model is defined as an
objective function and restrictions expressed in terms of the variables (alternatives) to
the problem.
1.7 Linear Programming
The term linear programming defines a particular class of programming problems that
meet the following conditions:
1. The decision variable involved in the problem are nonnegative (i.e.
positive or zero)
2. The criterion for selecting the “best” values of the decision variables can
be described by a linear function of these variables, that is, a
mathematical function involving only the first powers of these variables
with no cross products. The criterion function is normally referred as the
objective function.
Operating rules governing the process (e.g. scarcity of the resources) can be expressed
as a set of linear equations or linear inequalities. This set is here referred as constrains
set.
It mast be also noticed that the solution procedure are inherently iterative in nature, and
hence even for moderate size problems, one has to resort to computers for solutions.
2 Background information for the water issue in
Sicily
In order to depict the Sicilian water resource system data and figures were collected in
three major domains: a) available natural and infrastructural resources, that determine
water supply; b) social and economic activities, that determine water demand); c)
administrative framework, that regulates the relation between demand and supply.
This conceptual framework is in line with the guidelines given by UNESCO (2005)
where a water resource system, can be fully described through the analysis of the above
mentioned three domains. Figure 1 describes the interrelations between the NRS (the

8
natural resources system), the SES (the socio-economic system), and the AIS (the
administrative and institutional system).
In the following sections information will be grouped according to this theoretical
framework.
Figure 1 - Conceptual framework for a Water Resource Systems analysis (after UNESCO 2005)
2.1 The study area
The study area includes 16 hydrolographical basins covering the provinces of Siracusa
and Ragusa, South-East Sicily, 4,300 km 2 (out of 25,000 km 2 of total regional area)
inhabited by about 850,000 permanent resident (out of 4,968,900 of total regional
population). The area is not equipped with inter-basins water carrier networks. Figure
n.2 shows the study area and its hydrographic basins.

Figure 2 – The study area
9
2.2 Climatic conditions
According to the Köppen climate classification, one of the most widely used climate
classification systems (Peel et al, 2007), Sicily belongs to the Group C:
Temperate 1 /mesothermal 2 climates, sub-groups Csa, Csb: Mediterranean climate.
Central areas of the island belong to the Group B: Dry, arid and semiarid 3 climates. The
city of Enna, for instance, is a classic example of Group B sub-climatic group Bsh.
Among others, one of the characteristics of this group is that precipitations are less than
potential evapotranspiration (Beck et al. 2006).
During summer, Sicily, being part of the Mediterranean basin, is dominated by
subtropical high pressure cells, with dry sinking air capping a surface marine layer of
varying humidity but making rainfall impossible or unlikely. During winter the polar jet
stream and associated periodic storms reach into the lower latitudes of the
Mediterranean zones, bringing rain, with snow at higher elevations. As a result, Sicily
receives almost all of their yearly rainfall during the winter season, and during the
1
TemperThe changes in these regions between summer and winter are generally mild, rather than extreme
hot or cold (FAO, 2008)
2
It has a moderate amount of heat, with winters not cold enough to sustain snow cover. Summers are
warm within oceanic climate regimes, and hot within continental climate regimes (FAO, 2008).
3
A Semi-arid climate or steppe climate generally describes climatic regions that receive low annual
rainfall (250-500 mm), (FAO, 2008).

10
summer it may have from to 2 to 5 months without having any significant precipitation
(Beck et al. 2006).
Temperatures during winter only occasionally reach freezing and snow only rarely
occurs at sea level. In the winter, the temperatures range from mild to very warm,
depending on distance from the sea and elevation. Even in the warmest locations,
however, temperatures usually don't reach the highest readings found in adjacent desert
regions due to cooling effect of water bodies, although strong winds (Scirocco 4 ) from
North African desert regions can sometimes boost summer temperatures. Inland
locations sheltered from or distant from sea breezes can experience severe heat during
the summer (Beck et al. 2006).
2.3 Rainfall trend in Sicily: Spatial Distribution
Historical series were analyzed using spatial analysis techniques in a GIS environment
(Piccione et al., 2008). The application was conducted using monthly data, recorded or
reconstructed from 247 rain gauge stations during the period 1931–1990.
Average annual rainfall indexes have been calculated according to the Medalus
methodology (European Commission, 1999) in two different periods (1931-1960 and
1961-1990). Figures 3 shows in dark green the spatial distribution of year precipitations
larger than 650 mm in the period 1931-1960 and figure 4 shows the same patterns in the
period 1961-90. The percentage of regional surface areas with precipitations larger than
650 mm per year decreased from 60% to 34%. Moreover, it can be seen that a great
number of stations with a statistically significant negative trend are located in the
western and south-western part of the island (Piccione et al., 2008) corresponding to the
study area.
4 Sirocco, scirocco, jugo or, rarely, siroc is a Mediterranean wind that comes from the Sahara and reaches
hurricane speeds in North Africa and Southern Europe. It is known in North Africa by the arabic word
qibli (i.e. "coming from the qibla".)

11
Figure 3 – Rainfall distribution (1931-60) (after Piccione, 2008)
Figure 4 – Rainfall distribution (1961-90), (after Piccione, 2008)

12
2.4 Groundwater resources in Sicily: Spatial Distribution
The following two sections (§2.4 and §2.5) describe the main hydrological features of
the Sicilian aquifers. Information here gathered is based on the reports provided in
"Piano delle Acque in Sicilia" (CDEBTAS, 2007) and Brucculeri et al. (2002).
The hydro-geological features of Sicilian aquifers (figure 6) are mostly characterized by
pelitcs sediments with low permeability, consequently large areas are characterized by
local and superficial aquifers of low extension and low potentiality for productive
exploitation. These characteristics do not allow the existence of the underground
aquifers, but only of local and relatively superficial aquifers, with limited extension and
potentiality. The carbonatic hydro-geological structures, on the contrary, have good
potentialitis for productive exploitation. Figure 5
The permeable complexes, both for porosity and fissuration, are relevant from a
hydrogeological point of view. These corresponds to the most important aquifers in
terms of water productivity. Fig. 6 shows the spatial distribution of different aquifers.
The aquifers comprised in the study area of this work can be ranked (by water
productivity) as follows (Brucculeri et al. 2002).

Figure 6 - Qualitative features of groundwater resources (after Brucculeri, 2002)
13
2.4.1 Volcanic aquifer of Etna
About 1227,6 km 2 it shows an elevated permeability and it is wide and developed along
three hydrological basins where abundant precipitations, mostly snowy, occur (900-
1220 mm per year). It represents the richest aquifer of the island.

14
2.4.2 Miocenic calcareous aquifer in the area of Ragusa
It is divided in: a) limestones in the area of Syracuse, approximately 630,8 km 2 wide; b)
limestones in the area of Ragusa, approximately 467,7 km 2 wide. They show an
elevated permeability and they are situated in zones with precipitations between 800
and 1100 mm per year. They contain an almost continuous stratum (in the porous layers
and/or in the fractured ones) drained by a karst net developed all along the fault lines.
The aquifer’s thickness can vary between 100 and 300 m.
2.4.3 Volcanic aquifer in the area of Lentini
It develops along the basin of Lentini and it also involves contiguous basins on a
surface of 440 km 2 ; it shows moderate permeability. The area of recharge is compressed
among the quotas 200 - 600 m and the precipitations are 550 - 800mm per year. The
average thickness of the aquifer is approximately of 200 m; towards north the thickness
of the vulcanites can sometimes go over 500 m. Permeability is limited to some parts of
the vulcanites (lapilli, breccias, fissured lavas, intercalated calcareous layers). The
aquifer is partially drained by the hydrografical net; the aquifer’s exploitation is now
performed through numerous wells dislocated in the zone of Francofonte, Palagonia,
Lentini. As a result, this aquifer appears in phase of overexploitation.
2.4.4 Plio-quaternary sandy-calcarenitic aquifer
It essentially develops in the following areas: - area of Victoria-Caltagirone: outcrop of
about 110 km 2 ; - area of Piazza Armerina-Mazzarino: outcrop of about 840 km 2 ; -
coastal plain from Trapani to Sciacca: outcrop of about 800 km 2 ; - Agro of Palermo,
from Castellamare del Golfo to Termini Imerese: outcrop of about 430 km 2 .
The most important basin, for extension and resources, is that of Victoria. It must be
quoted, for memory, even the small outcrop of Licata-Gela, Agira, and Regalbuto,
Augusta, and Syracuse and Avola.
From the point of view of the morphology, the zones of the calcarenitis constitute some
plains and some plateaus relatively of low quota (inferior to 160 m) divided into plates
by the hydrographical net. Formation is moderately permeable. Its thickness varies from
50-100 m in the basin of Victoria from 10 to 50 in the area of Palermo. It does not
overcome 100 m in the coast plain from Trapani and Sciacca, instead it can reach 200-
250 m in Piazza Armerina and Leonforte. Rainfalls in these zones are on average low
(from 500 mm to 700 mm per year) but some calcarenitic plates receive also a side
supply by the limestones’ aquifers (areas of Syracuse, Victoria, Trapani, Palermo,
Termini Imerese).

15
The aquifer is generally modestly deep and continuous; this explains the very numerous
works of extraction that affect it, particularly in the zones of Vittoria, Palermo, Termini
Imerese and Mazara del Vallo.
It also occurs a certain drainage of the aquifer from the rivers and an outflow towards
the sea in the coastal zones. However, the quantity of available water appears still
reduced and further extractions do not seem to be possible.
2.4.5 Alluvial aquifer
Alluvial water strata follow the course of the principal valleys. Floods are not
significant in terms of aquifer recharge in the area of Trapani, along the Belice, along
the Gela River because of their slimy nature and the consequent reduced permeability.
Moreover, the waters’ salinity limits particularly the possibilities of use of the Platani
alluvial stratum and the southern Hymera. On the contrary the alluvium of the northern
slope of the island; the alluvium of the Simeto and the Plain of Catania; the alluvium of
the river in the areas of Messina; the ancient alluvium of the Acate; the ancient alluvium
of the Plain of Milazzo, provide low salinity water.
2.5 Groundwater resources in Sicily: Quality Aspects
The heterogeneity of the underground water resources distribution and the variability of
rainfalls coupled with recurrent dry years imply that Sicilian water resources may be
insufficient to meet demand in several areas of the region and in several periods of the
year. This has led to overexploitations of a number of sub-surface water resources,
especially in the costal areas, where sea water intrusions are already in place (INEA,
2000).
For these areas it is pointed out: a) general lowering of the piezometrics, to up to 10 m
varying according to the zones; b) mineralised waters with values of conductibility
progressively increasing; c) in certain zones (Plain of Colli, Cruillas, Bagheria and
coastal area) elevated concentrations of chlorides, d) symptoms of sea water intrusion;
concentrations of nitrates increasing in some wells; c) symptoms of a certain
interference with fertilizers and pesticides or sewers unloading.
According to Brucculeri et al. (2002) the qualitative situation of the aquifers inscribed
in the study area can be summarized as follows:

16
- In the plain of Catania and in the area of Syracuse the presence of large irrigated
areas for the production of agricultural products determines the intensive and
uncontrolled exploitation of the underground aquifers (fig. 6 points 36 and 35).
- In the territories of Augusta and of Syracuse there is a great concentration of
industries, mostly of them belonging to the petrochemical type that were
established and progressively developed since the early 1950 (fig. 6 point 35).
- In the basin of the Simeto, the lack of residential areas in the zone of the
aquifers’ slide, the location of those existing to the edges and particularly, the
location of the sewerages unloading of these areas, implies that it is not possible
any contamination of the waters’ flowing within the paleo-valleys of the Simeto.
Neither, it should be expected any influence for the modest waste-materials
coming from the few existing residences in the area. Nevertheless, it should be
taken into consideration a possible contamination because of chemical fertilizers
or fungicides used for agricultural purposes. The nature of the crops and even
more the remarkable thickness of the lava blanket that separates the level of
stratum from the ground make contamination a remote possibility (fig. 6 points
36).
- In the area of Ragusa there is single stratum in the calcarenitis, which is
intensely exploited. The data about the quotas of the static levels show strong
lowering of the water-bearing surface and the advancement of the front of sea
intrusion. This lets suppose that the stratum is in a precarious equilibrium. As
regards the stratum in the limestones, an interesting datum is constituted by the
waters’ salinity of the same stratum. Under the profile of the chemical
composition, the waters withdrawn by some sources of the principal calcareous
aquifer have showed a chemism of calcium - chloride and calcium - alkali type.
Also the waters withdrawn by wells dug in the superficial aquifer can have
different chemism (water of calciumchloride composition and calcium-alkaline
water). (fig. 6 point 34).

17
2.5.1 Potential vulnerability 5 of the water strata to
contamination
According to Brucculeri et al. (2002) potential vulnerability of the water strata can be
defined as follows. The carbonatic massifs inscribed in the study area (Siracusa and
Ragusa, fig. 6 points 34 and 35) have particular aspects of fragility especially where
karst fields are combined under areas of agricultural activity and stock-raising. These
carbonatic massifs, with very high vulnerability feed spring groups of remarkable
importance. The areas at the foot of the carbonatic massifs where generally the great
springs appear on the surface are exposed to contamination risks as well. Besides, the
areas affected by a number of anthropogenic activities (especially quarry areas), that
provoked the removal of the original soil coverage, seem to be more vulnerable than the
mountainous slopes, sometimes also characterized by moderate vulnerability.
The volcanic aquifers (fig. 6 point 36) for their intrinsic characteristics (litho- structural
characteristics, discontinuity, modalities of underground water circulation) show a high
degree of vulnerability on which it has also a meaningful incidence the stratum depth;
therefore, in correspondence of the downhill zones and the lowland, the important
underground water resources, largely exploited for drinkable purposes, are also
subjected to high risk, if considering the dangerousness determined by the
environmental conditions (residential and productive installations that can provoke
phenomena of pollution in absence of any protection measure).
5 . "Sensitivity"and/or "Vulnerability" are relative terms used to describe how well an aquifer is protected
from infiltrating contamination. A highly sensitive aquifer would have little or no defense, whereas an
aquifer with low sensitivity would be very well protected. A shallow, unconsolidated sand-and-gravel
aquifer is highly sensitive to contamination. The physical characteristics of the aquifer permit rapid
infiltration of recharge. Conversely, a deep, confined, layered basalt aquifer has a very low sensitivity.
Infiltrating recharge could take years to reach the aquifer, allowing time for contaminants to abate or
degrade. The sensitivity of an aquifer can vary greatly, depending on geologic conditions. Fractured or
faulted terrain tends to conduct recharge much more quickly than unfractured rock because fractures act
as conduits for fluid flow. Hence, faulted or fractured bedrock aquifers tend to be highly sensitive.
Limestone terrain that has undergone dissolution (dissolving) by groundwater often forms karst
topography, which is characterized by sinkholes, caves, and rapid underground drainage. With its many
conduits connecting the surface and subsurface, karst terrain makes for a highly sensitive aquifer. Highly
impermeable strata, such as silt and clay, provide a physical barrier above an aquifer. Aquifers that are
overlain by thick sequences of silt and clay or unfractured bedrock tend to be less sensitive to surface
activities (Geophysics Study Committee, 1984).

18
2.6 Main Economics (Agriculture, Industry, Population)
On the basis of the last census ISTAT (2006) the total amount of resident citizen in
Sicily (390 municipalities) is 4,968,991 (0,3% increase 2000-2001). The provinces of
Syracuse and Ragusa have respectively 400,764 and 311,760 inhabitants.
Regional economic indicators are lower than the national average (ISTAT, 2006). The
main aspects of the Sicilian economy can be summarized as follow:
• The regional GDP is in line with the average of the southern Italian
regions, but is below the Italian average;
• The regional demand of products and services is mainly oriented on
commodity and goods for mass consumption;
• The investment rate is lower than the national average;
• The production of services is mainly based on public services not for sale
3(public offices);
• Export represent 6% of GDP
According to official statistic published by the Osservatorio Economico Ministero per il
Commercio Internazionale (2008) In the year 2007 the Sicilian import/export balance
was as follow:
Table 1 - Sicilian Import / Export balance in the 2007 (after OEMCI, 2008)
Export Million Euro Percentage Import Million Euro Percentage
Refined Oil 4.592 66.2 Crude Oil 9.978 74.7
Basic chemical
products
455 6.6 Refined oil 1.301 9.7
Pipes 270 3.9 Metals 234 1.7
Agriculture 219 3.2 Basic chemical
products
219 1.6
According to the European Statistic on Income and Leaving Conditions EU-SILC, in
2005, the mean total-income (after tax) per family in Sicily was 20.952 Euro per year
which is about 1750 Euro per month per family. Nevertheless it must be noted that,
50% of the families are below the level of 16.658 Euro/year (1400 Euro/month), and the
Gini coefficient 6 of inequality is equal to 0.346, which is far above the average national
level.
6 The Gini coefficient is a measure of statistical dispersion most prominently used as a measure of
inequality of income distribution or inequality of wealth distribution. It is defined as a ratio with values
between 0 and 1: A low Gini coefficient indicates more equal income or wealth distribution, while a high
Gini coefficient indicates more unequal distribution. 0 corresponds to perfect equality (everyone having
exactly the same income) and 1 corresponds to perfect inequality (where one person has all the income,
while everyone else has zero income). Worldwide, Gini coefficients range from approximately 0.232 in
Denmark to 0.707 in Namibia.

3 Methodology
19
Two different models were built to solve the transportation and the transshipment
schemes addressed in this work. The transportation model is a stepping stone for the
construction of the transshipment model.
3.1 The Transportation Model
Two systems of equations were built to model a water transportation scheme in the
study area. This model seeks the determination of a transportation plan of a single
commodity: water. This chapter focuses on the algebraic statement of the problem. The
formulation of the standard form and the specific algorithm used for the solution are
technical problem embedded in the programming of the solver. Further details are
provided in the user's manual of the Lingo softwere.
The objective of the transportation model is to determine which routes of transportation
should be used among the many available option and how much water should be
transported in them such that the total transportation cost is minimized.
The basic assumption of the model is that the transportation cost is always directly
proportional to the number of units transported. The unit transportation cost, will be
proportional to the energy required for the transportation of every unit of water, it
depends on a number of technical factors (elevation, pipe friction, length, etc).
The data of the model are:
1. Supply and demand of water at each source and destination;
2. Transportation cost for each unit of water transported (the unit
transportation cost is different for every arc);
3. Network lay-out.
Figure 7 shows the transportation model as a network with i sources and j destinations.

Units of
supply
20
Figure 7- Transportation network with m sources and n destinations
For the formulation of this model the classical scheme proposed by Revindran et al.
(1984) was adopted. Each and every source and each and every destination are
represented by "nodes" and transportations roots by “arcs”. The amount of supply at
source i is Ai and the amount of demand at destination j is Bj.
The LP model representing the transportation problem is given by a number of
equations grouped in: a) one objective function and b) a set of constraints equations.
The objective function which stipulates that the sum of each cost associated to each
transportation arc must be minimal is given as follows:
where:
Qij
Cij
A1
A2
Ai
m
n
∑∑
min( Z)
= Q for i=1,2,…m; j=1,2,…n (1)
i=
1 j=
1
ijC
ij
is the amount of water transported from source i to destination j (m 3 /yr); It is the
decision variable, the incognita of the model;
is the unit transportation cost between source i and destination j (Euro/m 3 /yr);
m is the total number of supply sites;
n the total number of demand sites;
1
2
i
Am m
Sources Destinations
C11 ; Q11
Cmn ; Qmn
Z is the value of the objective function. The minimum value is calculated trough
an iterative procedure that stops when the value of Z at iteration x is larger the
value of Z at iteration x-1. The "simplex" algorithm and its variations can be
used for the solution of the transportation model as here formulated.
1
2
j
n
B1
B2
Bj
Bn
Units of
demand

21
The objective function is subjected to a set of constrains that vary according to the
specific problem. In any transportation problem they can be expressed as in equation
(2), (3) and (4).
For each supply site, equation (2) stipulates that the sum of the shipments from a
specific source to all connected destinations cannot exceed the supply available at that
specific supply site. In other words the sum of Qij transported from each source i must
be smaller or equal then Ai.
n
∑
j=
1
Q
ij
≤ A
i
i =1, 2, … m (2)
For each destination site, equation (3) stipulates that the sum of all the shipments to
each destination must satisfy the demand at every destination, meaning that the amount
Qij transported on to each destination j must be larger or equal to Bj.
m
∑
i=
1
Q ≥ B , j = 1, 2, … n (3)
ij
j
Finally, equation (4) stipulates that the decision variable cannot be negative, meaning
that any transportation of "negative" amounts of good is not allowed. This avoids
solutions that although would be correct from a mathematical point of view would make
no sense in practical terms.
Q ≥ 0,
for i = 1,2,…m; j = 1,2,…n (4)
ij
When the total sum of supply is not equal (so that larger or smaller) than the total sum
of demand the problem is unbalanced, meaning that not all demand will be met or not
all available supply will be shipped. A transportation model can always be balanced
using slack variables which represent fake sources and fake destination of water where
the relative transportation cost is extremely high so that the algorithm will automatically
discard them. Software applications automatically balance the problem using one of the
many algorithms developed for this purpose.
In the framework of this study, the transportation model is basically a balanced linear
problem that can be solved by the regular simplex method. The application of the
simplex algorithm is only one of the possible techniques to solve the model.
3.2 Uses and Function of the Transportation Model
The transportation model is used to obtain a first approximation of how much water
should be transported and in which directions. This is functional to the construction of a

22
more sophisticated model that allows a better description of real life situation: the
transshipment model.
Though, the transportation model is not realistic for the following reasons:
1. the network is designed with no consideration for the geomorphologic
aspect of the study area. Therefore, the arcs of connection that were
sketched in the model may be completely unfeasible in a real life
situation;
2. each source is directly connected to each and every destination with a
dedicated arc.
3. destinations are not connected between each other.
These may be the reasons of very probable unwanted redundancies of arcs resulting in
the calculation of unpractical solutions. Therefore the transportation model does not
provide realistic solutions for this study in terms of any practical field application. The
transportation model is used as a stepping stone for the transshipment model
3.3 The Transshipment Model
The standard transportation model assumes that the direct route between a source and a
destination is the only possible connection between supply and demand of water.
An alternative procedure to the use of regular transportation model is the so called
transshipment model. This model has the additional feature of considering the
transportation from sources to destination to be allowed to pass through intermediate
nodes before ultimately reaching their designated destination.
An example will be used to describe the mathematical method applied for the solution
of the problem. Figure 8 represents a lay-out of a transshipment scheme where the
supply amount at the two sources, node 1 and 2, are A1 and A2. The water demand at
destination 5, 6, and 7 are B5, B6, and B7. Water is transported to destination nodes 5,
6, and 7 through intermediate nodes 3 and 4.; and water can be transported from a
destination to another destination, for instance from node 5 to node 6. In terms of
connection nodes 1 and 2 are characterized by outgoing arcs only, whereas node 7 is
characterized by incoming arcs only. All the remaining nodes have both incoming and
outgoing arcs. In the nodes 3 and 4 water is not consumed so that all the input is equal

23
to the output. This is not the case for nodes 5 and 6 where a certain amount of water is
consumed and a remaining part can be transshipped to neighboring nodes.
Figure 8 – An explicative example of a transhipment problem
Let Qij be the amount shipped from node i to node j, than the LP model is given in a
tableau format as shown in table 2. This is used to show how to translate a
transshipment network lay-out into a system of equations. This format is actually used
as an input matrix in all the solvers based on the simplex algorithm.
Table 2- Tableau form of a transhipment problem
Arcs of water transportation: tableau of coefficients
Nodes
+A1
Units of
Supply
+A2
Sources Destinations
Q13 Q14 Q23 Q24 Q34 Q35 Q36 Q46 Q47 Q56 Q67
Amount
1 1 1 0 0 0 0 0 0 0 0 0 A1
2 0 0 1 1 0 0 0 0 0 0 0 A2
3 -1 0 -1 0 1 1 1 0 0 0 0 0
4 0 -1 0 -1 -1 0 0 1 1 0 0 0
5 0 0 0 0 0 -1 0 0 0 1 0 -B5
6 0 0 0 0 0 0 -1 -1 0 -1 1 -B6
7 0 0 0 0 0 0 0 0 -1 0 -1 -B7
The tableau format in table 2 can be expressed into the algebraic format via a system of
equations representing the entire set of constraints plus the objective function:
Node 1: Q13 + Q14 = A1
Node 2: Q23 + Q24 = A2
Node 7: -Q47 - Q67 = -B7
1
2
C1 3 ; Q1 3
For the remaining nodes (3, 4, 5, and 6) each equation is written in the following way:
Node 3: Q34 + Q35 + Q36 = Q13 + Q23
3
4
5
6
7
-B5
-B6
-B7
Units of
Demand

Node 4: Q46 + Q47 = Q14 + Q24 + Q34
Node 5: - Q35 + Q56 = -B5
Node 6: - Q36 - Q46 - Q56 + Q67 = -B6
24
Each constraint in the formulation above is associated with a node. The constraints
equations simply represent the conservation of flow in and out of the node. Namely, for
each intermediate node the followings equations apply: the sum of input flow is equal to
the sum of output flow, which states that the water balance at each intermediate node is
null because no water is produced and neither consumed there.
The objective function is expressed by equation (1), likewise the case of the
transportation model. The system of equations, including the objective function and
system of constraints, can be solved using different algorithms. The application of the
simplex algorithm is one of the possible techniques to solve the model. The study of
these different techniques is beyond the scope of this work. Lindo System Inc. software
was used to solve the system.
3.4 Parameters of the Model
This paragraph presents the entire set of parameters entering the model. It must be
immediately highlighted that every node represents an entire hydrographical basin.
Each node (i.e. each basin) has specific supply and demand of water, nevertheless only
the difference between supply and demand (the actual surplus or deficit of water) is
used in the model.
3.4.1 Units of Water Supply
Units of water supply ai represents the averaged amount of water in cubic meters per
year available at node i. Water sources are: springs and wells, reservoirs, lakes, treated
water (such as water from desalination plants). Node i represent an entire hydrographic
basin. For each basin the entire water supply is located in a single location: node i; it is
equal to the sum of the following:
ai = (Fi+ Di+ Ri) (5)
where:
Fi = Infiltration - aquifer recharge at node i, (m 3 /yr);
Di = Recycled water - water produced by desalination plants and wastewater
treatment at node i, (m 3 /yr);

Ri = Runoff, rivers, lakes, reservoirs potential at node i, (m 3 /yr).
25
The sum of these figures was considered as representative of the yearly amount of water
resource at the basin level. Nevertheless, these figures do not represent the amount of
water that can be safely used at basin level. According to Sophocleous (2000), the
sustainable yield of an aquifer must be considerably less than recharge if adequate
amounts of water are to be available to sustain both the quantity and quality of streams,
springs, wetlands, and ground-water-dependent ecosystems.
A reasonably conservative estimate of sustainable yield would take a suitable fraction of
deep percolation. As a rule of thumb, deep percolation is about 2% of precipitation
(Sophocleous, 2000). Sustainable yield may also be expressed as a percentage of
recharge. Experience suggests that average suitable percentages may be around 40%
(Sophocleous, 2000). A holistic approach to groundwater sustainability considers the
hydrological, ecological, socioeconomic, technological, cultural, institutional and legal
aspects of groundwater utilization, seeking to establish a reasonable compromise
between conflicting interests.
In the framework of this study the sustainable yield of an aquifer has been fixed around
50% of the aquifer recharge rate per year. Regarding the surface water, the sustainable
yield was extracted from official sources.
3.4.1.1 Total Water Demand
Units of water demand bi represents the averaged amount of water per year required at
node i. Water demand is grouped into: urban, industrial and agricultural demand. Node i
represents an entire hydrographic basin. For each basin the entire water demand is
locate in a single location: node i; it is equal to the sum of the following:
bi= (Ui+ Ii + Adi) (6)
where:
(Ui) = Urban demand at basin i (m 3 /yr);
(Ii) = Industrial demand at basin i (m 3 /yr);
(Adi) = Agricultural demand at basin i (m 3 /yr);
In the framework of this study it is assumed that the total current demand of water
resources at each basin is equal to the mean total documented consumption.

26
It means that demand at basin i is considered to be equal to consumption at basin i. The
water demand elasticity in relation to prices and quantities is a complex subject that
transcend the scope of this work. This is further discussed in Carraro (2007).
When no data on effective consumption is available, estimations were done according
to the different methodologies further documented in the following sections.
As a general principle whenever the recorded demand (officially documented) diverges
from the estimated one, the largest value among them is taken into account. This is
considered to be a safety measure meant to prevent any demand underestimation.
3.4.1.2 Urban Demand (Uj) per node j
Urban demand (Uj) was derived in two different ways: a) public available data or b)
estimations. Whenever recorded data (from public available sources) diverges from
estimated data, the largest figure among them was selected and used in the model.
Figures of urban water demand have been calculated, according to the following
assumptions derived from "Piano delle Acque in Sicilia" (CDEBTAS, 2007): a) every
municipality with less than 5,000 inhabitants consumes 260 liters per inhabitant per
day; b) this value is augmented progressively according to the dimension of the city,
considering that in bigger cities there is an higher consumption of water per inhabitant.
Table 3 shows the classes of consumption adopted.
Table 3- Litres of water consumption per inhabitant per day in demographic classless (CDEBTAS,
2007)
Demographic class Total stock per day (liters)
100,000 340
The total consumption of water is then calculated by multiplying the number of
inhabitants of every municipality r by the respective total approximated consumption
per day, times 365 days. The number of municipalities r in basin i goes from 1 to s.
u p ∗ q ∗365
r = 1,2,..,s; [m 3 /yr] (7)
r = r r
ur =Estimated urban demand at municipality r, (m 3 /yr);
pr= Population at municipality r;
qr= Consumption per day per inhabitant at municipality r, (m 3 /d);
The sum of the estimated consumption at each municipality r in basin i is the total
estimated urban consumption for the entire basin i.

U
j
=
s
∑
r = 1
u
r
27
for r = 1,2,..,s; [m 3 /yr] (8)
3.4.1.3 Irrigation Demand (Adj) per node j
Irrigation is here considered as the only use of water for agricultural purposes, so that
other uses of water, related to agriculture activities, were not considered.
The only public available data on water used for irrigation is represented by the volume
of water annually supplied to farmers through consortiums of irrigation (Consorzi di
bonifica, CB). Consortiums of irrigations are public pipelines networks dedicated to
agricultural uses.
INEA (2001) provides an estimation of the volume of water, not recorded in public
records, extracted from private wells for agricultural purposes. This complements the
information available on the volumes distributes through public network. Information
were estracted from "Stato dell'Irrigazione in Sicilia, studio sull’uso irriguo della risorsa
idrica, sulle produzioni agricole irrigate e la loro redditività" (QCS 1994-1999).
3.4.1.4 Industrial Demand (Ii) per node i
Data on industrial demand at nodes i (representative of an entire basin) have been
collected from the "Piano di Tutela delle Acque in Sicilia” published by the
Commissario Delegato per l'Emergenza Bonifiche e la tutela delle Acque in Sicilia
(CDEBTAS, 2007).
3.5 The Unit Transportation Cost
The unit transportation cost Cij represents the cost of transportation of a single unit of
water in a specific arc, meaning from a source i to destination j along an arc i-j. This
cost is introduced as a positive value in the objective function, eq. (1). If the movement
of water dos not generate a cost but an income (through the generation of electricity) Cij
is negative.
This is the case of the models that take into consideration the possibility of producing
hydroelectricity during the transportation of water from an higher to a lower elevation.
Positive and negative values of Cij are presented in the two following sections

28
3.5.1 Positive Cij
Given a pipeline network of a specific diameter and with a specific friction index, the
cost of transportation depends on pumping costs which are strictly related to electricity
costs. The amount of energy required to move every unit of water depends on the
specific arc of transportation in which the water is moving. The energy applied depends
on: 1) the distance between source i and destination j; 2) the difference in elevation
between source i and destination; 3) the diameter and the type of the pipe utilized, other
factors were neglected. Maintenances costs were not included in the computation.
Let us consider total required head (minor losses due to bends, valves, etc, are
neglected), ∆ H,
to be given by:
where
∆H
= ∆Z
+ ∆h
f
∆ Z = difference in elevation between a source and a destination (m);
∆hf= pressure friction losses (m)
The energy requirements at the pump used to convey the water to demand site are
given (Jensen, 1983) by:
HP=
Where:
Q∆H
2. 7η
H = pressure head, (m)
HP = the power of the pump in horsepower (1HP=0.746 kW)
Q = flow rate (m 3 /h)
η = pump efficiency ( %)
The energy loss ∆hf (m) in pipes depends on several factors, water flow, pipe’s length,
pipe's materials and shape.
The gradient of the energy loss in a pipe is usually expressed in ‰ (part per thousand)
J(‰), as:
J f
= 1000*
∆ h / L
The gradient of the head loss J(‰), due to friction is assessed by Hazen-Williams
equation (Jensen, 1983) :
1.
852
J = 1.
131*
10 ( Q/
C)
D
12 −4.
87
J = gradient of the head loss (‰);
Q = flow rate (m 3 /h);
D = internal diameter of a pipe (mm);
(11)
(12)
(13)
(14)

29
C = smoothness of the internal pipe (Hazen-Williams coefficient);
The head loss ∆hf (m), can therefore be written as:
9 1.
852 -4.
87
∆ h ( 1.
131*
10 (Q/C) D )L
` (15)
f =
In evaluating this general form of the equation for pressure loss in pipes, the model
optimization uses the following assumptions:
a) 166.9 million cubic meters of water must be transported every year into inter-basins
pipes; b) let's assume that this volume will be transported into 10 different pipes, for a
relative volume of 16.69 million cubic meters of water per year per pipe; c) the flow
rate per pipe is a typical value, Q = 4227 m 3 /h. This derives from a flow of 16.69
Million m 3 /yr transferred in 3948 hours (329 days per 12 hr/day) per year; d) Pipes have
a constant diameter, D = 750 mm; e) Hazen-Williams coefficient, C = 90 for a still
featured pipe; f) the pump efficiency η = 65%.
Given these assumptions equation (5) reduces as:
∆
hf
−2
= ( 1.
4063*
10 ) L
From equation 1 and 6, equation 2 can be converted into power P (kWh) as:
−2
4227(
∆z
+ ( 1.
4063*
10 ) L ) * 0.
746*
3948
P(
kWh)
=
=
2.7*
65
−2
= ( 2.
997^8)
* ( ∆z
+ ( 1.
4063*
10 ) L )
With regards to the assumed flow rate Q = 4227 m 3 /hr and pumping time of 3948 hrs
the power, P (kWh), can be converted into cost per m 3 /yr C ij ($/m 3 /yr), given the
electricity cost, λ (€/kWh/yr), where λ ∈ [ 0.
1 → 0.
3]
as:
C ij
(17)
−2
3 4227(
∆z
+ ( 1.
4063*
10 ) L ) * ( 0.
746*
3948)
* λ 1
( Euros/
m / yr)
=
*
=
2.7*
65
(166.9*
10^9)
-3
−2
= 1.796*
10 ( ∆Z
+ ( 1.
4063*
10 ) L ) λ
The parameter Cij is cost of water transfer (€/m 3 /yr) from source basin i to demand site
j per year. It depends on the distance L(m) and the height at which water has to be
raised ∆Z(m).
3.5.2 Negative Cij
When water is transported from high to a low elevation, the transshipment model takes
into consideration the possibility of generating hydroelectricity using that difference in
(16)

30
elevation. Hydroelectricity production was calculated for the arcs departing nodes from
B91 and B93 by the following equation (Horsley, 2002):
P = h*r*g*k (18)
Where:
P is power in kilowatts (kWh/m 3 );
h is height in meters (m);
r is flow rate in cubic meters per second (m 3 /s);
g is acceleration due to gravity of 9.8 m/s 2 ;
k is a coefficient of efficiency ranging from 0 to 1.
Efficiency is higher with larger turbines. Annual electric energy production depends on
the available water supply. In the framework of this study an approximation of
electricity production was calculated as follows (Horseley, 2002):
h = 100 (m);
r = 1/3600 (m 3 /s);
g = 9.8 (m/s 2 );
k = 0.73
P = 100 * 9.8 * 1/3600 * 0.73 = 0.2 (kWh/m 3 ).
3.6 The Decision Variable
Qij is the decision variable, which represent the flow rate to be transported from a given
source to a given destination every year.
3.7 Preliminary Work for Network Lay-out
A total of five different theoretical networking schemes were constructed: one
transportation scheme and four transshipment schemes. The transshipment schemes are
based on the results obtained from the solution of the transportation problem. The
geographical lay-outs were translated into mathematical equations as it is illustrated in
the previous paragraphs.
Some preliminary work was conducted for the lay-out of the networks.
The study area was divided into hydrological basis according to the official mapping
provided by ARRA Sicilia (Agenzia Regionale per i Rifiuti e le Acque).

31
The resulting polygons of every partition may be convex or non-convex, and they may
or may not have holes. In this case the polygons are not presenting any hole so that the
labeling placement algorithm that locate a label at a centroid of a poligon was applied
(for convex polygons without holes) in order to locate the barycentre of the basin. This
is used as a demand node or supply node for the entire basin.
The automatic labeling function in ArcView worked correctly for all the polygons
included in the study. Supply and demand nodes were located in the centroide of the
polygon, these points represent the location of either the surplus or deficit of water at
each hydrological basin. Figure 11 represents the partition of the study areas in different
hydrographical basins, the location of nodes and the digitized topographical elevation.
Nodes were then interconnected in various ways in order to create different networks.
Figure 9 – Geographical map of the study area: elevation, hydrographical basins, and nodes
locations
3.8 The Transportation Network
According to the classical formulation of the model (Ravindran et al. 1984) the
theoretical transportation network (see figure 6) was superimposed on a digital map of
the study area using Esri ArcGIS software. The network connects each source to every
destination (according to the classical formulation of the LP transportation model).

32
So that, for a network composed by 4 sources and 5 destinations there are 20 possible
arcs of transportation (see figure 12). ArcGis was used to measure the relevant
characteristic of the network: a) location of the nodes; b) length of the arcs; c) elevation
of every supply and demand node.
Figure 10 – Network representation and arc length
3.9 From the Transportation Model to the Transshipment
Network
The transshipments network was built on the basis of the solution obtained from the
transportation model. Figure 11 shows the transshipment network overlapped on the
solution of the transportation problem. Light blue arrows show the directions and the
amounts of water transported from sources to destinations.
The layout of the transshipment network was made on the basis of the following
considerations:
a) The number of supply nodes were reduced from 4 to 2. Supply n.91 and n.86
were grouped in a single node and nodes n.86 and n.78 were excluded because
they provide a negligible supply;
b) The number of demand nodes was reduced from 5 to 4. Demand nodes n.84 and
n.85 were grouped in a single node;

33
c) The location of supply nodes were georeferences according to the real location
of aquifers and wells; the bulk of the water available in the study area comes
from basins n.19093 and n.19091, very rich in natural springs and sub surface
water with a surplus of water resources of 84.5 and 61.8 millions cubic meters
per year respectively.
Figure 11 – Overlapping of a 14 arcs transhipment network on the transportation solution
d) The location of demand nodes were georeferenced according to the real location
of industrial, urban and agricultural areas; demand nodes where moved from the
geographical center of the basin to the center of the demand-areas. The major
deficit of water are located in: i) three important agricultural areas the basins
n.19080 and n.19082 and the complex n.19084-19085 with deficits of 19.3, 12.7
and 64.4 millions cubic meters per year and ii) a major industrial basin with
deficit of more than 50 million cubic meters per year;
e) Two intermediate nodes were arbitrary located in two different zones of
the study area. The exact location of feasible areas for that porpuse is out
of the scope of this work. The areas here identified are regarded feasible
for pumped storage hydroelectricity for they comply with the following:

34
a) high elevation on the sea level; b) high-land with steep mountain side;
c) central location in the study area.
When the nodes of supply and demand were defined, the arcs of the transshipment were
adjusted according to the following considerations (from the observation of the
transportation's solution):
a) Patterns in the direction of the water can be divided in two main directives: i)
from basin n.19093 to the south west and north-east zones, including major
industrial sites in Gela and Augusta and ii) from basin n.19091 to south east
zones including large green houses agricultural sites in the basins 19082-19085;
b) Destination C92 and C82 can be supplied both from source A91 and A93;
According to the above mentioned observation, combined with the geomorphology of
the study area, the transshipment network was drafted (figure 12).
Figure 12 – Lay-out of the transhipment network according to the geomorphology of the study area
3.9.1 The Transshipment Networks: Two Different
Schemes, Four Variants
Two transshipment networks were built: one made of 13 arcs and one made of 14 arcs.

35
In the network made of 13 arcs the water must pass through the reservoirs (B91 and
B93) in order to arrive at nodes C80, C82 and C84-85.
In the network made of 14 arcs water from supply node A91 can flow either directly to
destinations (C84-85, C82), or pass through the reservoir (B91), the transshipment
through the reservoir is not forced by the model.
Moreover, ceteris paribus, arcs connecting C82, C84 and C85,86 were oriented in turn
toward East or West
The networks studied are siilustareted in figure 13:
• 13 arcs West oriented
• 13 arcs East oriented
• 14 arcs West oriented
• 14 arcs East oriented
Figure 13 – Two networks, four variants
3.10 The Solver
The model was solved using a known general-purpose optimization package LINGO
(Schrage, 2002; Hyper Lindo, 2001). This package developed by LINDO Systems,
which is a leading supplier of software tools for building and solving optimization

36
models. It uses the algorithms: simplex and branch and bound to solve linear, integer or
mixed-integer problems. LINGO package is a complete tool developed for solving
linear, nonlinear and integer optimization.
Putting together the data section, the sets section, the objective function, and the
constraints, the completed model scripts for transportation and transshipment model are
described in appendixes A and B.
4 Results
This chapter illustrates the results of the study. Results were grouped in: a) data
collection; b) results of the model (data analysis).
The paragraph "Water balance at basin level", as well as its sub-paragraphs, illustrates
the result of data collection activities and shows the basic figures used in the model.
Data focus on the water supply and demand at basin level on a yearly scale. Other
information, such geomorphology of the study area and allocation of resources, are
embedded in the digital maps of the study area.
Data collection resulted in the following outcomes: a net surplus of water was registered
in 4 basins, thereafter defined water supply sites; net deficit of water was registered in 5
basins, thereafter defined water demand sites. The reaming six basins are in a
substantial balance, in a way that the entire basin demand is met by local resources so
that neither water export nor import is possible or needed.
4.1 Water Balance at Basin Level
In the following subparagraphs main figures and data will be presented in tables and
briefly commented. Information was collected from Piano delle Acque, (CDEBTAS,
2007).
4.1.1 Acate and Basins between Gela and Acate
The hydrographic basin of Acate is 776 km 2 . The basin belongs to three different
administration provinces Catania, Ragusa and Caltanissetta. It includes the Acate river
54 Km long that begins in Casa Vascello and end-up in the Mediterranean sea southeast
of Gela. It also includes the Dirillo lake (called Ragoleto as well) which has been
constructed in 1962. The dike is enclosing a basin of 118km 2 and it has an effective
volume of 20 million m 3 . The reservoir is used for agricultural and industrial purposes.
During the period 1921-2000 the basin received an average amount of rain between 450

37
and 600 mm per year. Springs and wells provide about 130 l/s of water for a total of 4.1
million m 3 per year. The total water demand for urban consumption is 9.4 million m 3
which is met by importing from other basins.
75% of the basin area is cultivated, only 30% of that is irrigated (176km 2 ), out of that
only 12 km 2 are irrigate by public networks and pipelines (Consorzio of irrigatio 4, 7
and 8). The remaining part is irrigated by private wells.
Industrial activities are very much developed in the petrochemical sector. The industrial
area extracts 0.536 Millions m 3 per year from private wells and consumes 8.65 million
m 3 per year from Dirillo reservoir. The average infiltration at basin level is estimated to
be 195.3 mm per year, which corresponds to 106 Million km 3 . Table 4 reports relevant
figures.
Table 4– Water Balance Assessment
Basin: ACATE and basins between GELA and ACATE,
Code: 19078
Area: 775.66 km 2
Water demand
Source
[Mm 3 /yr] Extraction Reservoirs Desalination Reuse Estimated
from sub
surface
value *
Total
Urban 4.1 - - - (9.4) 9.4
Destination
Agricultural 50.7 2.7 - - na 53.4
Industrial 0.5 8.65 1.9 - na 12.0
Total 55.3 11.4 1.9 - (9.1) 74.9
Water Sources Potential [Mm 3 /yr]
Sub surface water 53
Desalination and Water Reuse 11.4
Reservoirs 12
Total 76.4
Balance** +1.5
* Estimated figure, it was used only when it was larger than the officially recorded figure.
** When positive it refers to a basin in surplus of water, when negative it refers to a basin in deficit of
water
4.1.2 Basin: Ippari
The hydrographic basin Ippari is 259 km 2 wide. The basin belongs to the administration
provinces of Ragusa. It includes the Irmino river 30 Km long that begins in Cifali
Ganzeria and end-up in the Mediterranean sea in Punta Camerina During the period
1921-2000 the basin received an average amount of rain between 450 and 600 mm per
year. Springs and wells provide about 400 l/s of water for a total of 12.5 million m 3 per
year. The average total water demand for urban consumption is million 10.2m3.
81% of the basin area is cultivated, only 40% of that is irrigated (86km 2 ), out of that
only 9 km 2 are irrigate by public networks and pipelines (Consorzio 8). The remaining
part is irrigated by private wells for a total of 28.5 million m3 per year. Industrial

38
activities (related to mining and plastic materials) require bout 4 million m 3 per year.
The average infiltration at basin level is estimated to be 168.3 mm per year, which
corresponds to 44 Million m 3 .
Basin, Km 2 : IPPARI
Code: 19080
Area: 259.06 km 2
Water demand
[Mm 3 /yr] Extraction
from sub
surface
Urban 12.5
Destination
Table 5 - Water Balance Assessment
Reservoirs
Source
Desalination Reuse Estimated
value *
Total
- - - (10.1) 12.5
Agricultural 28.5 - - - na 28.5
Industrial 4.1 - - - na 4.1
Total 45.2 - - - (10.1) 45.2
Water Sources Potential [Mm 3 /yr]
Sub surface water 22
Desalination and Water Reuse -
Reservoirs 2
Total 24
Balance** -21.2
* Estimated figure, it was used only when it was larger than the officially recorded figure.
** When positive it refers to a basin in surplus of water, when negative it refers to a basin in deficit of
water
4.1.3 Basin: Irmino
The hydrographic basin Irmino is 254 km 2 wide. The basin belongs to the
administration provinces of Ragusa. It includes the Irmino river and the artificial
reservoir of St. Rosalia. During the period 1921-2000 the basin received an average
amount of rain between 700 and 800 mm per year. Springs and wells provide about
665l/s of water for a total of 21 million m 3 per year. The average total water demand for
urban consumption is million 6.9m3 which is meet by import from other basins.
71% of the basin area is cultivated, only 16% of that is irrigated (33km 2 ), out of that
only 23 km 2 are irrigate by public networks and pipelines (Consorzio 8). The remaining
part is irrigated by private wells for a total of 18.2 million m 3 per year.
No relevant industrial activity is active in the basin. The average infiltration at basin
level is estimated to be 231 mm per year, which corresponds to 20.3 Million m 2 . Table
6 reports relevant figures.
Basin: IRMINO
code: 19082
Area: 254.55 km 2
Water demand
[Mm 3 /yr] Extraction
from sub
surface
D
es
ti
na
Table 6 – Water balance assessment: Irmino
Reservoirs
Source
Desalination Reuse Estimated
value *
Total
Urban 6.9 - - - (6.9) 6.9

39
Agricultural 13.4 4.4 - - Na 17.8
Industrial - 7.6 - - Na 7.6
Total 20.3 12 - - (6.9) 32.3
Water Sources Potential [Mm 3 /yr]
Sub surface water 9.6
Desalination and Water Reuse -
Reservoirs 11.0
Total 19.6
Balance** -12.7
* Estimated figure, it was used only when it was larger than the officially recorded figure.
** When positive it refers to a basin in surplus of water, when negative it refers to a basin in deficit of
water
4.1.4 Basins between Scicli and Capo Passero
The hydrographic basin Irmino is 363 km 2 wide. The basin belongs to the
administration provinces of Ragusa and Siracusa. During the period 1921-2000 the
basin received an average amount of rain between 450-600 mm per year. Springs and
wells provide about 170 l/s of water for a total of 5.3 million m 3 per year. The average
total water demand for urban consumption is million 11m3 which is meet by import
from other basins.
68% of the basin area is cultivated, only 37% of that is irrigated (114km 2 ), out of that
only 19 km2 are irrigate by public networks and pipelines (Consorzio 8 and 10). The
remaining part is irrigated by private wells for a total of 58 million m3 per year.
Million m3 are consumed for industrial activities. The average infiltration at basin
level is estimated to be 85 mm per year, which corresponds to 29.2 Million m2. Table 7
reports relevant figures.
Table 7 - Water Balance Assessment basins between SCICLI and CAPO PASSERO
Basin: Basins between SCICLI and CAPO PASSERO
Code: 19084
Arae: 363.27 km 2
Water demand [Mm Source
3 /yr]
Extraction Reservoirs Desalination Reuse Estimated
from sub
surface
value *
Total
Urban 5.4 - - - 11 11
Destination
Agricultural 58 - - - Na 58
Industrial 2.3 - - - Na 2.3
Total 65.3 - - - 11 71.3
Water Sources Potential [Mm 3 /yr]
Sub surface water 14.6
Desalination and Water Reuse -
Reservoirs -
Total 14.6
Balance** -56.7
* Estimated figure, it was used only when it was larger than the officially recorded figure.
** When positive it refers to a basin in surplus of water, when negative it refers to a basin in deficit of
water

40
4.1.5 Basins between Capo Passero and Tellaro
The hydrographic basin between Capo Passero and Tellaro is 100.1 km 2 . The basin
belongs to the administration provinces of Ragusa and Siracusa. During the period
1921-2000 the basin received an average amount of rain between 450-600 mm per year.
The total water demand for urban consumption is million 5.3m 3 .
60% of the basin area is cultivated, for a total of 58 million m3 per year for irrigation.
0.5 Million m 3 are consumed for industrial activities. The average infiltration at basin
level is estimated to be 104.6 mm per year, which corresponds to 10.5 Million m 2 .
Table 8 reports relevant figures.
Table 8– Water Balance Assessment basins between Capopassero and Tellaro
Basin: Basins between Capopassero and Tellaro
Code: 19085
Area: 213.27 km 2
Water demand
Source
[Mm 3 /yr] Extraction Reservoirs Desalination Reuse Estimated
from sub
surface
value *
Total
Urban 3.3 - - - (3.3) 3.3
Destination
Agricultural 27 - - - - 27
Industrial 0.5 - - - - 0.5
Total 30.8 - - - (3.3) 30.8
Water Sources Potential [Mm 3 /yr]
Sub surface water 5.2
Desalination and Water Reuse -
Reservoirs -
Total 5.2
Balance** -25.6
* Estimated figure, it was used only when it was larger than the officially recorded figure.
** When positive it refers to a basin in surplus of water, when negative it refers to a basin in deficit of
water
4.1.6 Basin:Tellaro
The hydrographic basin Tellaro in 388 km 2 wide. The basin belongs to the
administration provinces of Siracusa. It includes the Tellaro river, 45 km long. During
the period 1921-2000 the basin received an average amount of rain between 450 and
600 mm per year. Springs and wells provide about 302l/s of water for a total of 9.5
million m 3 per year. The average total water demand for urban consumption is million
2.2m 3 .
5.1 km 2 of the basin area are irrigated, only 5% is irrigated by a public consortium. The
remaining part is irrigated by private wells for a total of 14.8 million m 3 per year.
No relevant industrial activity is active in the basin, the total demand per year is about
0.7 Million m 3 . The average infiltration at basin level is estimated to be 212 mm per
year, which corresponds to 82.5 Million m 2 . Table 9 reports relevant figures.

Basin: TELLARO
Code: 19086
Area: 388,93 Km 2
41
Table 9– Water Balance Assessment basin Tellaro
Water demand
Source
[Mm 3 /yr] Extraction Reservoirs Desalination Reuse Estimated
from sub
surface
value *
Total
Urban 9.5 - - - (2.2) 9.5
Destination
Agricultural 18.8 - - - Na 14.8
Industrial 0.7 - - - Na 0.7
Total 25 - - - (2.2) 25
Water Sources Potential [Mm 3 /yr]
Sub surface water 42.5
Desalination and Water Reuse -
Reservoirs -
Total 42.5
Balance** +17.5
* Estimated figure, it was used only when it was larger than the officially recorded figure.
** When positive it refers to a basin in surplus of water, when negative it refers to a basin in deficit of
water
4.1.7 Basin: Cassibile
The hydrographic basin of Cassibile is 92.9 km 2 . The basin belongs to the
administration provinces Siracusa. During the period 1921-2000 the basin received an
average amount of rain between 600 and 700 mm per year. Springs and wells provide
about 4.1 million 0.725 m 3 per year. The total water demand for urban consumption is
practically nil.
Total agricultural consumption is less than one million m 3 per year, entirely meet by
private wells. No industrial consumption. The average infiltration at basin level is
estimated to be 53.6 mm per year, which corresponds to 4.98 Million m 3 . Table 10
reports relevant figures.
Basin: CASSIBILE
Code: 19089
92.96 km 2
Water demand [Mm 3 /yr]
Destination
Table 10– Water Balance Assessment basin Cassibile
Extraction
from sub
surface
Reservoirs
Source
Desalination Reuse Estimated
value *
Urban 0.7 - - - Na 0.7
Agricultural 1 - - - Na 1.00
Industrial - - - - Na -
Total 1.7 - - - Na 1.7
Water Sources Potential [Mm 3 /yr]
Sub surface water Total
Desalination and Water Reuse 2.5
Reservoirs -
Total -
Balance** 0.8
Total

* Estimated figure, it was used only when it was larger than the officially recorded figure.
** When positive it refers to a basin in surplus of water, when negative it refers to a basin in deficit of
water
4.1.8 Basin: Anapo
42
The hydrographic basin of Anapo is 448 km 2 wide. The basin belongs eneterely to the
administration provinces Siracusa. It includes Anapo and Ciane rivers. The reservoir is
used for agricultural and industrial purposes. During the period 1921-2000 the basin
received an average amount of rain between 700 and 800 mm per year. Springs and
wells provide about 505 l/s of water for a total of 18 million m 3 per year. The average
total water demand for urban consumption is 6.5 million m 3 .
75% of the basin area is cultivated, for a total demand of 15 million m 3 per year.
Sources includes water works at Ciane and Anapo rivers.
Industrial activities demand about 1.9 million m 3 per year . The average infiltration at
basin level is estimated to be 221.7 mm per year, which corresponds to 99.4 Million m 3
per year. Average annual run-off is about 251mm which correspond to 112 Million m 3 .
Table 11 reports relevant figures.
Basin: ANAPO
Code: 19091
Area: 448.21 km 2
Table 11 – Water Balance Assessment basin Anapo
Water demand
Source
[Mm 3 /yr] Extraction Reservoirs Desalination Reuse Estimated
from sub
surface
value *
Total
Urban 4.2 - - - Na 4.2
Destination
Agricultural 15 - - - Na 15
Industrial 1.9 - - - Na 1.9
Total 21.18 - - - Na 21.1
Water Sources Potential [Mm 3 /yr]
Sub surface water 49.7
Desalination and Water Reuse -
Reservoirs 56.0
Total 105.7
Balance** +84.7
* Estimated figure, it was used only when it was larger than the officially recorded figure.
** When positive it refers to a basin in surplus of water, when negative it refers to a basin in deficit of
water
4.1.9 Basins between Anapo and Lentini
The hydrographic basin between Anapo and Lentini are 352 km 2 wide. The basin
belongs entirely to the administrative province of Siracusa. It includes the Marcellino
and the Gancio. It also includes 4 different reservoirs: Monte Cavallaro and Ponte
Diddio in the area of Priolo, which are exclusively used by the local hydroelectrical

43
plant: and the Fiumara Grande and Mulinello which are exclusively used for the Agip
Oil plant . During the period 1921-2000 the basin received an average amount of rain
between 600 and 700 mm per year. Springs and wells provide about 850l/s of water for
a total of 27 million m 3 per year. The average total water demand for urban
consumption is 21 million m 3 .
Only 32% of cultivated are is actually irrigated (80km2). Private sources meet almost
the entire agricultural demand for a total of 24 Million m 3 .
Industrial activities are developed in the petrochemical fields. The industrial area
demands 55.11 m3 per year, 20 million of that from reservoirs the remaining part from
private wells. The average infiltration at basin level is estimated to be 160.4 mm per
year, which corresponds to 56.6 Million m 3 . Table 12 reports relevant figures.
Table 12 – Water Balance Assessment basins between Anapo and Lentini
Basin: between Anapo and Lentini
Code: 19092
Area: 125.43 km 2
Water demand
Source
[Mm 3 /yr] Extraction Reservoirs Desalination Reuse Estimated
from sub
surface
value *
Total
Urban 26 - - - Na 26
Destination
Agricultural 18 6 - - Na 24
Industrial 55 - - - Na 55
Total 99 6 - - Na 105
Water Sources Potential [Mm 3 /yr]
Sub surface water 28.3
Desalination and Water Reuse -
Reservoirs 26
Total 54.3
Balance** -50.3
* Estimated figure, it was used only when it was larger than the officially recorded figure.
** When positive it refers to a basin in surplus of water, when negative it refers to a basin in deficit of
water
4.1.10 Basin: S. Leonardo
The hydrographic basin of S.leonardo is 558.9 km 2 . The basin belongs to two different
administration provinces Catania, Siracusa. It includes the S.Leonardo river, it also
includes the Lago di Lentini reservoir. The reservoir collect several fluvial water
resources and has a potential volume of 127 Million m3. It has been completed in 1988
to provide water resources for agricultural and industrial uses. The reservoir is not fully
operative and by the 11.11.2001 it can provides no more than 70 Million m3 per year,
30 for industrial uses and 40 for agricultural use. In the years 1995-2000 only 4.7
Million m3 where used for agricultural uses. During the period 1921-2000 the basin
received an average amount of rain between 600 and 700 mm per year. Springs and

44
wells provide about 16.9 million m 3 per year. The total water demand for urban
consumption is 8.8 million m 3 . Water demand for agricultural uses is about 61 Million
m3, this is met private and public sources.
Industrial demand is about 2.4 Million m 3 . The average infiltration at basin level is
estimated to be 219 mm per year, which corresponds to 123 Million m 3 per year. Table
13 reports relevant figures.
Table 13 – Water Balance Assessment basin Irmino
Basin: S.LEONARDO (LENTINI)
Code 19093
Area: 558.93 km 2
Water demand
Source
[Mm 3 /yr] Extraction Reservoirs Desalination Reuse Estimated
from sub
surface
value *
Total
Urban 16.9 8.8 16.9
Destination
Agricultural 49 12.4 61.4
Industrial 2.4 61.8 64.2
Total 68.3 74.2 142.5
Water Sources Potential [Mm 3 /yr]
Sub surface water 58.9
Desalination and Water Reuse -
Reservoirs 21.8
Total 80.7
Balance** -61.8
* Estimated figure, it was used only when it was larger than the officially recorded figure.
** When positive it refers to a basin in surplus of water, when negative it refers to a basin in deficit of
water
4.1.11 Basins number: 19079, 19081, 19083, 19087, 19088,
19090
For basins 19079, 19081, 19083, 19087, 19088, and 19090 are defined as "neutral
basins" because one or more of the following conditions applies: a) the basin is in
quantitative equilibrium in terms of demand and supply of water so that no water
transfers in/out of the basin is either required or possible; b) the basin is not relevant
because it is scarcely populated and there is not any major extraction and consumption;
c) the basin is densely populated but agricultural and/or industrial activities are
relatively insignificant; d) data are not available.
For one or more of these reasons these basins were not included in the model, and no
further details are reported. Nevertheless, several figures do show their location and
map legends refer to them as neutral basins.
4.2 Total Water Balance
When the entire study area is considered as a whole, the total water resources
consumption per year is slightly larger than 488 millions cubic meters per year. The

45
total balance (table 14) of the study area is minus 1.6 Million m 3 /yr, representing a
negligible deficit of water on a yearly base. On the base of data provided in Piano delle
acque (CDEBTAS, 2007) it is not possible to elaborate any statistical analysis of water
consumption trends and their standard deviation.
Table 14 - Water balance at basin level
Basin Code Supply
Million m 3 /yr
Demand Million m 3 /yr Balance
Million m 3 /yr
19078 76.4 -74.9 1.5
19079 - - -
19080 24 -45.2 -21.2
19081 - - -
19082 19.6 -32.3 -12.7
19083 - - -
19084 14.6 -71.3 -56.7
19085 5.2 -30.8 -25.6
19086 42.5 -25 17.5
19087 2.5 -1.69 0.8
19088 - - -
19089 - - -
19090 - - -
19091 105.7 -21.2 84.5
19092 54.3 -105 -50.7
19093 142.5 -80.7 61.8
Total 487.3 -488.09 -1.6
Figure 16 represents the geographical distribution of water demand, supply and water
balance. Only basins 93, 91, 86, 78 present a yearly surplus of water, basins 80, 82, 84,
85, 92 present deficits, and the remaining are neutral.

46
4.3 The transportation problem
The transportation network implies the direct connection between each and every
source to each and every destination. Figure 14 shows a digitized map of the study area
and the length of each arc (reported in meters) the model consist of twenty arcs of
connections. ∆z represents the difference in elevation between source and destination.
Table 13 reports arcs' length, elevation and relative ∆z between nodes.
Figure 14 – Water supply, demand and balance at basin level

47
Table 15 - Arc length, and elevation at supply and demand nodes.
Arc Length (m) Elevation at
source (m)
Elevation at
destination
(m)
Difference
in elevation,
∆z (m)
-
78-80 17714.53 336.8 255.8 80.9
78-82 23340.31 336.8 478.5 141.7
78-84 48696.75 336.8 138 198.8 -
78-85 59591.39 336.88 35.8 300.9 -
78-92 51389.52 336.8 185.1 151.6 -
86-80 32518.33 301.39 255.8 45.5 -
86-82 21187.35 301.3 478.5 177.1
86-84 17822.8 301.3 138 163.3 -
86-85 21565.42 301.3 35.8 265.5 -
86-92 31979.52 301.3 185.1 116.2 -
91-80 43676.04 360.7 255.8 104.8 -
91-82 32966.53 360.7 478.5 117.8
91-84 36004.3 360.7 138 222.7 -
91-85 35858.21 360.7 35.8 324.9 -
91-92 13226.91 360.7 185.1 175.6 -
93-80 44208.54 270.7 255.8 14.9 -
93-82 38600 270.7 478.5 207.7
93-84 53140.5 270.7 138 132.7 -
93-85 56482.5 270.7 35.8 234.9 -
93-92 20720.24 270.7 185.1 85.6 -
Transportation's costs were calculated using a simple Matlab code based on equation
(17). Table 16 illustrates the costs of transportation of water in every arc (Euros per
cubic meter per year).
Table 16 - Transportation network: cost (€/m3)
Transportation
Demand sites
cost €/m 3 /yr 80 82 84 85 92
78 0.030212 0.0844 0.08729 0.096469 0.102568
86 0.07396 0.08532 0.015687 0.006784 0.059902
91 0.091491 0.104421 0.05094 0.032216 0.00187
93 0.108982 0.134796 0.110385 0.100471 0.03696
Supply
sites
4.4 Optimal Solution of the Transportation Problem
Table 17 illustrates the optimal solution of the transportation problem. The solution
represents the yearly volume of water that should be transported in each arc in order to
obtain the minimum operating cost per year (electricity cost for pumping is set at 0.10
Euro per kW/h). The optimum is obtained for a total operational cost of 8.126 millions
Euros per year. Figure 18 illustrates the spatial distribution of the optimal solution,
where blue shadows are proportional to the amount of water to be transported.
This combination guarantees the most efficient solution where, available supply meets
entirely the demand and the whole system reaches the economical optimum (minimal
operational cost).

48
Figure 15 – Transportation network: optimal solution
Table 17 shows arcs that are actually involved in the optimal solution and the relative
water transported in millions cubic meters per year.
Table 17 - Optimal solution
Objective value: 8,126,728 Euros per year
Infeasibilities: 0.000000
From To Volume (Million m 3 /yr)
(A78, B80) 1.500000
(A78, B82) 0.000000
(A78, B84) 0.000000
(A78, B85) 0.000000
(A78, B92) 0.000000
(A86, B80) 0.000000
(A86, B82) 0.000000
(A86, B84) 17.50000
(A86, B85) 0.000000
(A86, B92) 0.000000
(A91, B80) 0.000000
(A91, B82) 0.000000
(A91, B84) 39.20000
(A91, B85) 25.60000
(A91, B92) 21.30000
(A93, B80) 19.70000
(A93, B82) 12.70000
(A93, B84) 0.000000
(A93, B85) 0.000000
(A93, B92) 29.40000

49
4.5 The Costs of Transshipment
The transshipment costs were calculated using a simple Matlab code based on equation
(18). Table 18 shows the transshipment costs. The procedure is similar to the one used
for the transportation model with a singular exception: the shipment of water departing
from the intermediate node B93 and B91 is actually generating rather than consuming
energy.
The profit generated from every cubic meter of water transported in arcs B93-C84, B93-
C82 and the profit from B91-C82 and B91-C80 is given by the following: 0.2 kWh/m 3
(the energy produced per cubic meter of water) times, 0.10 or 0.15 €/kWh (the
electricity selling-prices). The profit, in Euros, per cubic meter of water transported is
then: 0.02; 0.03.
Table 18 – Transhipment costs
Arc Length Elevation Elevation ∆z Cost in €/m
[m] Source Destination [dz]
3
A91-B91 14872.13 51 540 489 0.125387
A91-B93 27354.35 51 535 484 0.156016
A91-C84,85 33536.7 51 40 -11 0.082729
A91-C92 18036.87 51 11 -40 0.038372
A93-B91 29419.1 27 540 513 0.166439
A93-B93 23593.44 27 535 508 0.150827
A93-C92 19019.47 27 11 -16 0.045164
B91-B93 17337.1 540 535 -5 0.042891
B91-C82 38200.55 540 22 -518 0.02; 0.03
B91-C84,C85 33771.61 535 22 -513 0.02; 0.03
B93-C80 44898.19 535 67 -468 0.02; 0.03
B93-C82 46395.39 535 46 -489 0.02; 0.03
C82-C80 22624.21 60 67 7 0.0584
C84,C85-C82 34697.74 22 22 0 0.087637
C80-C82 22624.21 67 67 -7 0.055885
C82-C84 34697.74 22 22 0 0.087637

50
4.6 Transshipment Optimal Solutions
The value of the optimal solution for the transshipment problem in a network of 13 arcs
can be summarized in table n 19 and in figure 19. The numerical solutions for all
network variations are provided in annex C:
Table 19 – Value of the optimal solution for the transhipment problem (13 arcs)
Optimal solution in EUROS Arcs C84-C82-C80 Network
13 Arcs: East and West oriented
Orientation
Electricity buying price: 0.1 €/kWh West East
Electricity selling
0.10 €/kWh 12,887,000 12,887,000
price 0.15 €/kWh 11,923,000 11,923,000
The value of the optimal solution for the transshipment problem in a network of 14 arcs
can be summarized in table 20 and in figure 20. The numerical solutions for all
network variations are provided in annex D:
Table 20 – Value of the optimal solution for the transhipment problem (14 arcs)
Optimal solution in EUROS Arcs C84-C82-C80 Network
14 Arcs: East and West oriented
Orientation
Electricity buying price: 0.1 €/kWh West East
Electricity selling
0.10 €/kWh 11,427,000 11,427,000
price 0.15 €/kWh 11,107,000 11,107,000
It is immediate evident that the orientation of arcs C84-C82-C80 does not make any
difference for the optimal solution, so that in practice there are only two solutions (one
for the 13 arcs network, and one for the 14 arcs network). The differences in the final
values of the objective function (in Euros) depend only on the different sets of
electricity prices adopted. Obviously, the higher the selling prices of electricity the
lower the total operational cost.
The minimal operational cost is obtained in a network of 14 arcs. Considering the total
amount of water transported in those arcs is 147.1 million m3/yr the unit cost of
transportation of a single cubic meter of water is 0.075 €/m 3 per year.

51
Figure 16 – Transhipment optimal solution 13 arcs
Figure 17 – Transhipment optimal solution 14 arcs

52
5 Conclusions
Given an unbalanced allocation of water resources in the provinces of Siracusa and
Ragusa (South East Sicily) this work seeks the optimization of water distribution via
inter-basin aqueducts. The study area is not provided with any inter-basin scheme so
that several theoretical hypotheses were compared by means of operational research and
linear programming techniques.
According to concordant studies on meteorological conditions in Sicily, generalized
negative trends are in place both in terms of spatial and temporal distribution of
precipitations. It was observed that a large number of meteorological stations show
negative trends in terms of total precipitation per year. Moreover, overexploitation of
surface and sub-surface water resources are leading to serious cases of sea water
intrusion in vast areas of the costal aquifers, so that aspects of non-reversibility of
salinization phenomena are a growing concern for local communities. Therefore, the
water balance of the study area has a fragile equilibrium between supply and demand of
water, which cyclically results in water shortages.
It is also acknowledged that water shortages may pose serious limits to socio-
economical development, also increasing conflicts among different users (industrial,
urban and agricultural users). No strategy for social development can ignore vital
requirements for water; regional policies must address the need of water resources in
the interests of society as a whole in order to safeguard an equitable and long term use
of communal resources. For this reasons, technical measures are studied here to
improve local water security.
According to the literature reviewed, several investigations were conducted to assess the
state of the costal aquifers but no study focusing on inter-basins water transportation
systems has been found. This study compares different inter-basins transportation
schemes in order to minimize the total cost of inter-basin transportation of water. The
work was conducted in several steps.
As first step, an assessment of water resources availability was made on a basin level on
the basis of official information provided in "Piano di Tutela delle Acque in Sicilia”
published by the "Commissario Delegato per l'Emergenza Bonifiche e la tutela delle
Acque in Sicilia" (CDEBTAS, 2007). Thus, the water balance sheet shows a substantial

53
general equilibrium between the total water demand and total consumption when the
entire study area is taken into consideration as a whole. Nonetheless, a closer analysis,
at basin level, reveals local situations of dramatic shortages both in terms of spatial and
temporal distribution of water resources. Some basins are overexploited while others are
neither using nor exporting available water resources.
Given this situation, as a second step, a number of theoretical aqueducts schemes were
studied and adjusted to the study area. Inter-basins aqueducts are not in place in the
study area, so that transportation of water is here considered to be as a feasible
alternative to production of additional water. No alternative options of water production
(desalination, waste water treatment, etc) were analyzed in this study.
Once theoretical networks were integrated in the map of the study area, a third step was
taken. Linear programming was used to solve two different models: a transportation
model and a transshipment model. In practice, the transportation model was a
preliminary study used to build a transshipment model more coherent with filed
situation. The transshipment model is more realistic because it takes into consideration
geographical features that are not considered in the transportation model.
The transshipment model was used to determine which aqueduct network would serve
better the purpose of water distribution at a minimum operational cost. Results show
that operational costs are minimal when: basin 19091 provides water to the South-East
area (nodes C84-85 and C82) and basin 19093 provides water to the North-East and
South-West areas (nodes C93 and C80). The minimal value of the objective function is
11.107 Million Euros per year, for a unit transportation cost of 0.075 Euro per cubic
meter per year. These figures refer to operational costs only.
It is interesting to notice that for supply node C84-85 it is more convenient, when
possible, to skip the reservoir B91. It is also important to notice, that the arc that goes
from node C85-84 to C82 is not used in the optimal solution. Most probably this result
may change when infrastructural cost would be included in the model. It is reasonable
to assume that infrastructural costs of a single pipeline from C85-C84 to C82 would be
much cheaper, than an entire pumped storage hydroelectricity system passing from
reservoir B91. Therefore, when operational costs would be considered, the solution here
suggested may change and the PSH option at B91 may be no longer convenient.

54
This implies that PSH is not feasible for the lay-out here studied. Nevertheless, the
general idea of using any possible delta-elevation for hydroelectric production coupled
with water distribution remains intact. Further investigations are needed in order to
assess the feasibility, and best fitting, of this technology in the study area.
This study is not meant to inform any investment decision, but the methodology here
adopted can be used to narrow down the domain of possible investment options. This
solution can provide a decision support instrument for selecting which detailed
feasibility study to be conducted.
The methodology here presented can be applied to any different case study. It also
applies to larger regional areas because of its relative simplicity and because, remaining
invariant the precision of the data used, the larger the area studied the more realistic the
results obtained.
In this study a single management option, namely "inter-basins transportation of water"
was studied. For further investigation, this option can be then compared to other water
management options in the framework of a comprehensive regional water management
policy. Therefore, the benchmarking among different technical solutions: desalination,
waste water treatment, water saving measures etc, should be a further step to be taken in
order to evaluate the best possible technology or, better, the best combination of
technologies that would guarantee water security in the study area.

55
6 References
Agnew C. and AndersonE. (1992) Water Resources in The Arid Realm, Routledge
London
Agnew. C and Anderson E., (1992) “Water Resources in the Arid realm”, Routledge,
London
Allan. J, A “ Middle east water: local and global issues” In: Litwihwick , H., Shames T.,
and Wilensky, D. (1998) “ Evaluating water balance in Israel” , (1998) Negev
Center for Regional development, Ben Gurion University of the Negev.
Anthony Horsley, and Andrew J. Wrobel (2001) "Efficiency rents of pumped-storage
plants and their uses for operation and investment decisions", Journal of Economic
Dynamics and Control Volume 27, Issue 1, November 2002, Pages 109-142
Aronica G. Aronica, M. Cannarozzo and L.V. Noto, (2002) "Investigating the changes
in extreme rainfall series recorded in an urbanised area", Water Science and
Technology 45 (2002) (2), pp. 49–54.
Aronica et al., G. Aronica, M. Cannarozzo and L.V. Noto, (2002) Investigating the
changes in extreme rainfall series recorded in an urbanised area, Water Science and
Technology 45 (2), pp. 49–54.
Aureli A., Adorni G., Chiavetta A. F., Fazio F., (1987): Condizioni di vulnerabilità di
acquiferi in zone a forte insediamento industriale di tipo petrolchimico. Mem. Soc.
Geol. It. 37, 37-52, 1987
Aureli A., Adorni G., Chiavetta A. F., Fazio F., Tazzina S., Messineo G., (1987): Carta
idrogeologica di una regione ove sono presenti acquiferi sovrasfruttati. Mem. Soc.
Geol. It. 37, 27-34,
Ballatore G.P., Fierotti G. (1967) "Carta dei suoli della Sicilia". Ist. Agron. Gen.,
Università di Palermo
Barbagallo S., Indelicato S., Rossi G., (1990) "Individuazione di bacini di rilievo
regionale: proposte per la Sicilia. Atti del convegno nazionale: I piani di Bacino per
la difesa del suolo, la gestione delle acque e la tutela dell’ambiente, Taormina, 23-
24 novembre 1990.
Barker, R. Dawe D. and Innocencio A . (2003), “Economic of water productivity in
managing water for agricolture” In: Kijne J. W., Barker R., and Molden D., (2003)
“Water productivity in Agricolture: limits and Opportunities for Improvements”
CAB International

56
Bartolomei c., Celico P., Pecoraio A., (1983) "Schema idrogeologico della Sicilia nord-
occidentale. Boll. Soc. Geol. It. 102, 329-354, 1983.
Basso F., Bove E., Dumontet S., Ferrara A., Pisante M., Quaranta G., Taberner M.
(2000). Evaluating environmental sensitivity at the basin scale through the use of
geographic information systems and remotely sensed data: an example covering the
Agri basin (Southern Italy). Catena 40, p. 19-35.
Beck C, Rudolf B., Kottek M., Grieser J., Ruben F., (June 2006) "World Map of the
Koppen-Geiger climate classification" Meteorologische Zeitschrift, Vol. 15, No. 3,
259-263 Gebreder Borntraeger 2006
Beck, C., J. Grieser, M. Kottek, F. Rubel, and B. Rudolf, (2006): "Characterizing
Global Climate Change by means of Köppen Climate Classification.
Klimastatusbericht, 2005, 139-149.
Bonaccorso A, Cancelliere A., Rossi G. (2005), Detecting trends of extreme rainfall
series in Sicily, Advances in Geosciences 2 (2005), pp. 7–11.
Brucculeri R., Liguori V., (2002) "Groundwater management resources in Sicily"
Universita' di Palermo, Dipartimento Ingegneria Strutturale e Geotecnica, Facolta'
di Ingegneria Viale delle Scienze, PA, Italia
Bruins H.J. (1997) “Natural drought and human-made drought in Israel: proactive
planning and interactive management”. In: Genstion de las Sequias. Valencia:
Iberdrola Instituto Tecnologico , Ministerio del Medio Ambiente, Generalitat de
Valencia, pp 65-88
Budyko M.I., (1958) "The Heat Balance of the Earth's Surface" U.S. Department of
Commerce, Washington D.C (1958) 259 pp., translated by N.A. Stepanova.
Cannarozzo M. (1985) "Analisi statistica delle precipitazioni registrate in Sicilia
finalizzata allo studio dei cambiamenti climatici", Sviluppo Agricolo 3/4 (1985), pp.
53–64.
Cannarozzo M., L.V. Notoa, F. Violaa, (2006) Spatial distribution of rainfall trends in
Sicily (1921–2000), March 2006. Available online 1 November 2006.
Carraro C., Marciori C., Sgobbi A., (2007) “Negotiating on Water. Insights from Non-
cooperative Bargaining Theory” Environment and Development Economics , Vol.
12, pp. 1–21. Also FEEM Nota di Lavoro 65.05 and World Bank Working Paper
3641
Cassa per il Mezzogiorno, (1976) "Piano acque Sicilia - Studio delle acque sotterranee
della Sicilia". CMP Roma, 1976.

57
Commissario Delegato per l'Emergenza Bonifiche e la Tutela delle Acque in Sicilia
CDEBTAS (2007) "Piano di tutela delle Acque in Sicialia", Regione Sicilia,
Sogedis SPA.
CSEI (1982) "Censimento dei corpi idrici" – Regione Siciliana. Ass.to Territorio e
Ambiente – Catania, 1982.
Cusimano G., Liguori V., (1980) "Idrogeologia della Piana di Palermo. 4° Convegno
Internazionale sulle acque sotterranee", Acireale CT, 17-21 febbraio 1980.
Cusimano G., Liguori V., (1988) "Idrodinamica e potenzialità delle risorse idriche
sotterranee del sistema idrogeologico dei Monti Trabia, Termini Imprese (Sicilia)".
Acque sotterranee, Anno V,III trimestre, 1988.
Dingman R. J. (1984) “ development of a water resources plan for the Sulatanate of
Oman”, Public Authority for Water resources, Oman.
Encyclopedia Britannica (2000), Water Transportation, Volume V02, Page 248 of 1911.
European Commission (1999) "The MEDALUS project Mediterranean desertification
and land use" Project report. Kosmas C., Kirkby M., Geeson N. (eds.), EUR 18882,
V.
FAO (2008) Thorthwaite C.W.,"Climatic classification in forestry". Available at:
http://www.fao.org/docrep/x5375e/x5375e02.htm
Gao X. Giorgi F., (2008) "Increased aridity in the Mediterranean region under
greenhouse gas forcing estimated from high resolution simulations with a regional
climate model", Global and Planetary Change 62 195–209
Geophysics Study Committee, Geophysics Research Forum, Commission on Physical
Sciences, Mathematics, and Resources, National Research Council (1984)
"Groundwater contamination" Washington, D.C., National Academy Press
Heatcote R. (1983) “Arid lands: their use and abuse” Longman, London
Helweg, J. O., (1985) "Water Resources: Planning and Management", Texas University
& Water Studies center / King Faisal University
Hess H. (1999) "Mafia & Mafiosi: Origin, Power and Myth", NYU Press, 232p.
Horsley A., Andrew J. (2002) "Efficiency rents of pumped-storage plants and their uses
for operation and investment decisions", Journal of Economic Dynamics and
Control, Volume 27, Issue 1, November 2002, Pages 109-142
INEA, (2001) "Stato dell’irrigazione in Sicilia, Programma Operativo Multiregionale,
“Ampliamento e adeguamento della disponibilità dei sistemi di adduzione e
distribuzione delle risorse idriche nelle regioni" Obiettivo 1. QCS 1994/99.
ISTAT, (2006) "Annuario statistico regioale, Sicilia", Istituto Italiano di Statitistica.

58
Jensen M.E., (1983) "design and operation of farm irrigation systems" The American
Society for Agricultural Engineers
Khouri N., (1992) “Wastewater reuse implementation in selected countries of the
Middle-East and North Africa” In Schiller E J (1192) “ Suatinable water resource
management in arid countries: middle-East and North Africa, Canadian Journal of
development studies.
Kliot N., (1994) “ Water resources and conflicts in the Middle_East, Routledge
LeMarquauad D., (1994) “ Politics of international river basin cooperation and
management” In Kliont N. (1997) “Water resources and conflicts in the Middle –
East” Routledge.
Liguori V., Cusimano G., (1988) "Idrodinamica e potenzialità delle risorse idriche
sotterranee del sistema idrogeologico dei Monti Trabia, Termini Imprese (Sicilia)".
Acque sotterranee, Anno V, 3 trimestre.
Lithwick H., Shames T., and Wilensky D., (1998) “ Evaluating water balance in Israel”
Negev center for regional Development , Ben Gurion University of the Negev.
Lomborg B., (2001) The Skeptical Environmentalist, Measuring the Real State of the
World” , Cambridge University Press. U.K.
Lundqvist J., Lohm U. and Falkenmaark M., (1995) “ Strategies for River Basin
management: Environemntal International inegration of land and water in a river
basin” Geojeournal Library, A Reidel Pubblishing Company.
Mather J. R., (1984) “Water resources: Distribution use and management” Department
of Geography, University of Delware.
Molden D., (1997) “ Accounting for water use and productivity, SWIN paper No. 1
IWMI, Colombo, Sri Lanka.
Moore T., (1994). Storing megawatthours with SMES. Electric Power Research
Institute Journal 19 5, pp. 24–33.
Nachmani A., (1995) “ Water jitters in the Middle East” Studies in conflict and
terrorism Vol. 17 No. 1, Rand, California.
OEMCI (2008) "L'area del Mediterraneo: prospettive di internazionalizzazione per le
imprese italiane", Quaderno n.2 - marzo 2006
Oron G., Ranowitz G., Mehrez A. (1988) "A non lineat optimization model of water
allocation for hydroelectric energy production and irrigation" Management Science,
Volume 34, number 8, August 1988

59
Peel M. C., Finlayson B. L., and McMahon T. A., (2007) "Updated world map of the
Koppen-Geiger climate classification" Hydro. Earth Syst. Sci. Discuss., 4, 439–473,
2007
Perry C. J. (1999) The IWMI water resources paradigm – definitions and implications"
Agricultural Water Management Volume 40, Issue 1, 1 March 1999, Pages 45-50
Piccione V., Campisi S., Malacrinò V., Veneziano V., (2008) "Rischio desertificazione
nella Regione Sicilia (protocollo Medalus) Mappe ragionate della sensibilità e
incidenza territoriale a scala comunale del processo in divenire", Quad. Bot. Amb.
Appl., 19 1-200
Pigram J. J., and Musgrave W. F., (1987) “ Sharing the wates of the Murray Darling
Basin: Cooperative federalism under test in Australia” In : just R., and Nethaniau S.
(1998) “ conflict and cooperation in trasboundary water resources” Kluwer
Academic Publisher.
Ravindran A., D.T. Phillips J.J. Solberg, (1984) Operational Research principle and
practice, John Wiley & Sons, New York, 1984, pp. 13-34
Rober B. R., (1993) “Water management in desert environment a comparative analysis“
Springer Verlag Berlin Heidelberg.
Schrage L., "Optimization Modeling with LINDO", 5th. ed. Belmont, CA: Duxbury
Press,
Sciortino M., Colonna N., Ferrara V., Grauso S., Iannetta M., Svalduz A., (2000), "La
lotta alla desertificazione in Italia e nel bacino del Mediterraneo" Energia, Ambiente
e Innovazione 2 p. 29-40.
Sophocleous M., (2000) "From safe yield to sustainable development of water
resources—the Kansas experience" Journal of Hydrology Volume 235, Issues 1-2,
22 August 2000, Pages 27-43
Svendsen M., (2005) “ Irrigation and river basin management : Options for governance
and institutions” CABI publishing, Cambridge USA.
Taha H.A., (1987), "Operations research: an introduction"; Macmillan Publishing Co.,
Inc. Indianapolis, IN, USA
Trewartha and Horn, G.T. Trewartha and L.H. Horn, (1980) "An Introduction to
Climate" (5th Ed), McGraw Hill, New York, USA
UNEP, (1992). "World Atlas of Desertification". Edward Arnold, London, UK.
UNESCO (2005) "Water Resource System Planning and Management" ISBN 92-3-
103998-9

Union of the Electricity Industry EURELECTRICR (2005) "Review of European
60
Electricity Prices", KEMA Consulting GmbH, Bonn, Germany
Van Vleck G. K. Deukmejian G and Kennedy D J (1987) “ California Water: looking to
the future” Bullettin 160-87 November 1987
Waldman M., Shevan Y., (1985) “Research and development ad an integral element in
water resources management in Israel “ In Diskin M (1985) “ Scientific Basis for
water resources management “ IAHS Pubblication No. 153.
Wilson J., (2004) “ Time series analysis of global cereal trade, reserves and cereal food
aid for the period 1961-2001, with an enphais on dry lands nations” Mscv Thesis
Desert Studies Department, Ben Gurion University of the Negev.
Wirl E., (1987) Optimal Electricity Production from Hydro Power Plants with Storage,
ZOR - Zeitschrift fiir Operations Research, Volume 32, page 121-136
Zaslavsky D., (1997) “ Solar energy without a collector for electricity and water in the
21 st century, Lecture to the Australian Academy of sciences, May Mimeo In:
Lithwick Shames T., and Wilensky D., (1998) “ Evaluating water balances in Israel”
Negev Center for Regional development , Ben Gurion University of the Negev.

ANNEX A
Transportation script
MODEL:
! A 4 Sources, 5 Destinations
Transportation Problem;
SETS:
SOURCE / A78, A86, A91, A93/ : CAPACITY;
DESTINATION / B80, B82, B84, B85, B92/ : DEMAND;
ROUTES( SOURCE, DESTINATION) : COST, VOLUME;
ENDSETS
61
! The objective;
[OBJ] min = @SUM( ROUTES: COST * VOLUME);
! The demand constraints;
@FOR( DESTINATION( J): [DEM]
@SUM( SOURCE( I): VOLUME( I, J)) >=
DEMAND( J));
! The supply constraints;
@FOR( SOURCE( I): [SUP]
@SUM( DESTINATION( J): VOLUME( I, J))

ANNEX B
Transshipment Script
End
Model:
! Transhipmente 14 arcs
SETS:
Basins/A91 A93 B91 B93 C84 C82 C80 C92/:;
Arcs(Basins,Basins) / A91,B91 A91,B93 A91,C92 A91,C84
A93,B93 A93,B91 A93,C92
B91,B93 B91,C84 B91,C82
B93,C82 B93,C80
C80,C82
C82,C84/: C,X1;
ENDSETS
DATA:
! Here are the costs that correspond to the above arcs;
C = 0.125387 0.156016 0.038372 0.082729
0.150827 0.166439 0.045164
0.042891 -0.02 -0.02
-0.02 -0.02
0.0558
0.087637
;
ENDDATA
!Sum over Arcs the cost*Number of cars i.e. THE OBJECTIVE FUNCTION;
62
min = @sum(Arcs(i,j): C(i,j)*X1 (i,j));
!Subject to the following constraints
1) Path must leave Node 1 and 2 (CAPACITY CONSTRAINTS);
@sum(Arcs(i,j) | i #EQ# 1: X1(i,j))=84900;
@sum(Arcs(i,j) | i #EQ# 2: X1(i,j))=62200;
! 2) Path must enter Node 7 (DEMAND CONSTRAINTS);
@sum(Arcs(i,j) | j #EQ# 7: X1(i,j))=19300;
@sum(Arcs(i,j) | j #EQ# 8: X1(i,j))=50700;
! 2) Path must pass through intermediate nodes (Demand constraints);
@for(Basins(j) | j #GT# 2 #AND# j #LT# 5:
@sum(Arcs(i,k) | k #EQ# j: X1(i,k))- @sum(Arcs(k,i) | k #EQ# j:
X1(k,i))=0);
@for(Basins(j) | j #EQ# 5:
@sum(Arcs(i,k) | k #EQ# j: X1(i,k))- @sum(Arcs(k,i) | k #EQ# j:
X1(k,i))=64400);
@for(Basins(j) | j #EQ# 6:
@sum(Arcs(i,k) | k #EQ# j: X1(i,k))- @sum(Arcs(k,i) | k #EQ# j:
X1(k,i))=12700)

ANNEX C
Global optimal solution found. TRANSPORTATION
Objective value: 8.126728
Infeasibilities: 0.1776357E-13
Total solver iterations: 11
63
Variable Value Reduced Cost
CAPACITY( A78) 1.500000 0.000000
CAPACITY( A86) 17.50000 0.000000
CAPACITY( A91) 86.10000 0.000000
CAPACITY( A93) 61.80000 0.000000
DEMAND( B80) 21.20000 0.000000
DEMAND( B82) 12.70000 0.000000
DEMAND( B84) 56.70000 0.000000
DEMAND( B85) 25.60000 0.000000
DEMAND( B92) 50.70000 0.000000
COST( A78, B80) 0.3021200E-01 0.000000
COST( A78, B82) 0.8440000E-01 0.000000
COST( A78, B84) 0.8729000E-01 0.000000
COST( A78, B85) 0.9646900E-01 0.000000
COST( A78, B92) 0.1025680 0.000000
COST( A86, B80) 0.7396000E-01 0.000000
COST( A86, B82) 0.8532000E-01 0.000000
COST( A86, B84) 0.1568700E-01 0.000000
COST( A86, B85) 0.6784000E-02 0.000000
COST( A86, B92) 0.5990200E-01 0.000000
COST( A91, B80) 0.9149100E-01 0.000000
COST( A91, B82) 0.1044210 0.000000
COST( A91, B84) 0.5094000E-01 0.000000
COST( A91, B85) 0.3221600E-01 0.000000
COST( A91, B92) 0.1870000E-02 0.000000
COST( A93, B80) 0.1089820 0.000000
COST( A93, B82) 0.1347960 0.000000
COST( A93, B84) 0.1103850 0.000000
COST( A93, B85) 0.1004710 0.000000
COST( A93, B92) 0.3696000E-01 0.000000
VOLUME( A78, B80) 1.500000 0.000000
VOLUME( A78, B82) 0.000000 0.2837400E-01
VOLUME( A78, B84) 0.000000 0.8003000E-01
VOLUME( A78, B85) 0.000000 0.1079330
VOLUME( A78, B92) 0.000000 0.1443780
VOLUME( A86, B80) 0.000000 0.3532100E-01
VOLUME( A86, B82) 0.000000 0.2086700E-01
VOLUME( A86, B84) 17.50000 0.000000
VOLUME( A86, B85) 0.000000 0.9821000E-02
VOLUME( A86, B92) 0.000000 0.9328500E-01
VOLUME( A91, B80) 0.000000 0.1759900E-01
VOLUME( A91, B82) 0.000000 0.4715000E-02
VOLUME( A91, B84) 39.20000 0.000000
VOLUME( A91, B85) 25.60000 0.000000
VOLUME( A91, B92) 21.30000 0.000000
VOLUME( A93, B80) 19.70000 0.000000
VOLUME( A93, B82) 12.70000 0.000000
VOLUME( A93, B84) 0.000000 0.2435500E-01
VOLUME( A93, B85) 0.000000 0.3316500E-01
VOLUME( A93, B92) 29.40000 0.000000
Row Slack or Surplus Dual Price
OBJ 8.126728 -1.000000
DEM( B80) 0.000000 -0.1089820
DEM( B82) 0.000000 -0.1347960
DEM( B84) 0.000000 -0.8603000E-01
DEM( B85) 0.000000 -0.6730600E-01
DEM( B92) 0.000000 -0.3696000E-01
SUP( A78) 0.000000 0.7877000E-01
SUP( A86) 0.000000 0.7034300E-01
SUP( A91) 0.000000 0.3509000E-01
SUP( A93) 0.000000 0.000000

ANNEX D
64
Global optimal solution found. Tranship_west_13arcs_0.02Eqm
Objective value: 12887.14
Infeasibilities: 0.000000
Total solver iterations: 6
Variable Value Reduced Cost
C( A91, B91) 0.1253870 0.000000
C( A91, B93) 0.1560160 0.000000
C( A91, C92) 0.3837200E-01 0.000000
C( A93, B93) 0.1508270 0.000000
C( A93, B91) 0.1664390 0.000000
C( A93, C92) 0.4516400E-01 0.000000
C( B91, B93) 0.4289100E-01 0.000000
C( B91, C84) -0.2000000E-01 0.000000
C( B91, C82) -0.2000000E-01 0.000000
C( B93, C82) -0.2000000E-01 0.000000
C( B93, C80) -0.2000000E-01 0.000000
C( C84, C82) 0.8763700E-01 0.000000
C( C82, C80) 0.5840000E-01 0.000000
X1( A91, B91) 77100.00 0.000000
X1( A91, B93) 0.000000 0.1198100E-01
X1( A91, C92) 7800.000 0.000000
X1( A93, B93) 19300.00 0.000000
X1( A93, B91) 0.000000 0.3426000E-01
X1( A93, C92) 42900.00 0.000000
X1( B91, B93) 0.000000 0.2424300E-01
X1( B91, C84) 64400.00 0.000000
X1( B91, C82) 12700.00 0.000000
X1( B93, C82) 0.000000 0.1864800E-01
X1( B93, C80) 19300.00 0.000000
X1( C84, C82) 0.000000 0.8763700E-01
X1( C82, C80) 0.000000 0.3975200E-01
Row Slack or Surplus Dual Price
1 12887.14 -1.000000
2 0.000000 -0.1440350
3 0.000000 -0.1508270
4 0.000000 0.2000000E-01
5 0.000000 0.1056630
6 0.000000 0.1864800E-01
7 0.000000 0.000000
8 0.000000 0.3864800E-01
9 0.000000 0.3864800E-01

65
Global optimal solution found. Tranship_west_13arcs_0.03Eqm
Objective value: 11923.14
Infeasibilities: 0.000000
Total solver iterations: 6
Variable Value Reduced Cost
C( A91, B91) 0.1253870 0.000000
C( A91, B93) 0.1560160 0.000000
C( A91, C92) 0.3837200E-01 0.000000
C( A93, B93) 0.1508270 0.000000
C( A93, B91) 0.1664390 0.000000
C( A93, C92) 0.4516400E-01 0.000000
C( B91, B93) 0.4289100E-01 0.000000
C( B91, C84) -0.3000000E-01 0.000000
C( B91, C82) -0.3000000E-01 0.000000
C( B93, C82) -0.3000000E-01 0.000000
C( B93, C80) -0.3000000E-01 0.000000
C( C84, C82) 0.8763700E-01 0.000000
C( C82, C80) 0.5840000E-01 0.000000
X1( A91, B91) 77100.00 0.000000
X1( A91, B93) 0.000000 0.1198100E-01
X1( A91, C92) 7800.000 0.000000
X1( A93, B93) 19300.00 0.000000
X1( A93, B91) 0.000000 0.3426000E-01
X1( A93, C92) 42900.00 0.000000
X1( B91, B93) 0.000000 0.2424300E-01
X1( B91, C84) 64400.00 0.000000
X1( B91, C82) 12700.00 0.000000
X1( B93, C82) 0.000000 0.1864800E-01
X1( B93, C80) 19300.00 0.000000
X1( C84, C82) 0.000000 0.8763700E-01
X1( C82, C80) 0.000000 0.3975200E-01
Row Slack or Surplus Dual Price
1 11923.14 -1.000000
2 0.000000 -0.1440350
3 0.000000 -0.1508270
4 0.000000 0.3000000E-01
5 0.000000 0.1056630
6 0.000000 0.1864800E-01
7 0.000000 0.000000
8 0.000000 0.4864800E-01
9 0.000000 0.4864800E-01

66
Global optimal solution found. Tranship_East_13arcs_0.03Eqm
Objective value: 11923.14
Infeasibilities: 0.000000
Total solver iterations: 7
Variable Value Reduced Cost
C( A91, B91) 0.1253870 0.000000
C( A91, B93) 0.1560160 0.000000
C( A91, C92) 0.3837200E-01 0.000000
C( A93, B93) 0.1508270 0.000000
C( A93, B91) 0.1664390 0.000000
C( A93, C92) 0.4516400E-01 0.000000
C( B91, B93) 0.4289100E-01 0.000000
C( B91, C84) -0.3000000E-01 0.000000
C( B91, C82) -0.3000000E-01 0.000000
C( B93, C82) -0.3000000E-01 0.000000
C( B93, C80) -0.3000000E-01 0.000000
C( C80, C82) 0.5580000E-01 0.000000
C( C82, C84) 0.8763700E-01 0.000000
X1( A91, B91) 77100.00 0.000000
X1( A91, B93) 0.000000 0.1198100E-01
X1( A91, C92) 7800.000 0.000000
X1( A93, B93) 19300.00 0.000000
X1( A93, B91) 0.000000 0.3426000E-01
X1( A93, C92) 42900.00 0.000000
X1( B91, B93) 0.000000 0.2424300E-01
X1( B91, C84) 64400.00 0.000000
X1( B91, C82) 12700.00 0.000000
X1( B93, C82) 0.000000 0.1864800E-01
X1( B93, C80) 19300.00 0.000000
X1( C80, C82) 0.000000 0.1044480
X1( C82, C84) 0.000000 0.8763700E-01
Row Slack or Surplus Dual Price
1 11923.14 -1.000000
2 0.000000 -0.1440350
3 0.000000 -0.1508270
4 0.000000 0.3000000E-01
5 0.000000 0.1056630
6 0.000000 0.1864800E-01
7 0.000000 0.000000
8 0.000000 0.4864800E-01
9 0.000000 0.4864800E-01

67
Global optimal solution found. Tranship_East_13arcs_0.02Eqm
Objective value: 12887.14
Infeasibilities: 0.000000
Total solver iterations: 7
Variable Value Reduced Cost
C( A91, B91) 0.1253870 0.000000
C( A91, B93) 0.1560160 0.000000
C( A91, C92) 0.3837200E-01 0.000000
C( A93, B93) 0.1508270 0.000000
C( A93, B91) 0.1664390 0.000000
C( A93, C92) 0.4516400E-01 0.000000
C( B91, B93) 0.4289100E-01 0.000000
C( B91, C84) -0.2000000E-01 0.000000
C( B91, C82) -0.2000000E-01 0.000000
C( B93, C82) -0.2000000E-01 0.000000
C( B93, C80) -0.2000000E-01 0.000000
C( C80, C82) 0.5580000E-01 0.000000
C( C82, C84) 0.8763700E-01 0.000000
X1( A91, B91) 77100.00 0.000000
X1( A91, B93) 0.000000 0.1198100E-01
X1( A91, C92) 7800.000 0.000000
X1( A93, B93) 19300.00 0.000000
X1( A93, B91) 0.000000 0.3426000E-01
X1( A93, C92) 42900.00 0.000000
X1( B91, B93) 0.000000 0.2424300E-01
X1( B91, C84) 64400.00 0.000000
X1( B91, C82) 12700.00 0.000000
X1( B93, C82) 0.000000 0.1864800E-01
X1( B93, C80) 19300.00 0.000000
X1( C80, C82) 0.000000 0.9444800E-01
X1( C82, C84) 0.000000 0.8763700E-01
Row Slack or Surplus Dual Price
1 12887.14 -1.000000
2 0.000000 -0.1440350
3 0.000000 -0.1508270
4 0.000000 0.2000000E-01
5 0.000000 0.1056630
6 0.000000 0.1864800E-01
7 0.000000 0.000000
8 0.000000 0.3864800E-01
9 0.000000 0.3864800E-01

ANNEX E
Global optimal solution found. Tranship_west_14arcs_0.02Eqm
Objective value: 11427.96
Infeasibilities: 0.000000
Total solver iterations: 7
68
Variable Value Reduced Cost
C( A91, B91) 0.1253870 0.000000
C( A91, B93) 0.1560160 0.000000
C( A91, C92) 0.3837200E-01 0.000000
C( A91, C84) 0.8272900E-01 0.000000
C( A93, B93) 0.1508270 0.000000
C( A93, B91) 0.1664390 0.000000
C( A93, C92) 0.4516400E-01 0.000000
C( B91, B93) 0.4289100E-01 0.000000
C( B91, C84) -0.2000000E-01 0.000000
C( B91, C82) -0.2000000E-01 0.000000
C( B93, C82) -0.2000000E-01 0.000000
C( B93, C80) -0.2000000E-01 0.000000
C( C84, C82) 0.8763700E-01 0.000000
C( C82, C80) 0.5840000E-01 0.000000
X1( A91, B91) 12700.00 0.000000
X1( A91, B93) 0.000000 0.1198100E-01
X1( A91, C92) 7800.000 0.000000
X1( A91, C84) 64400.00 0.000000
X1( A93, B93) 19300.00 0.000000
X1( A93, B91) 0.000000 0.3426000E-01
X1( A93, C92) 42900.00 0.000000
X1( B91, B93) 0.000000 0.2424300E-01
X1( B91, C84) 0.000000 0.2265800E-01
X1( B91, C82) 12700.00 0.000000
X1( B93, C82) 0.000000 0.1864800E-01
X1( B93, C80) 19300.00 0.000000
X1( C84, C82) 0.000000 0.6497900E-01
X1( C82, C80) 0.000000 0.3975200E-01
Row Slack or Surplus Dual Price
1 11427.96 -1.000000
2 0.000000 -0.1053870
3 0.000000 -0.1121790
4 0.000000 -0.1864800E-01
5 0.000000 0.6701500E-01
6 0.000000 -0.2000000E-01
7 0.000000 -0.3864800E-01
8 0.000000 0.2265800E-01
9 0.000000 0.000000

69
Global optimal solution found. Tranship_west_14arcs_0.03Eqm
Objective value: 11107.96
Infeasibilities: 0.000000
Total solver iterations: 7
Variable Value Reduced Cost
C( A91, B91) 0.1253870 0.000000
C( A91, B93) 0.1560160 0.000000
C( A91, C92) 0.3837200E-01 0.000000
C( A91, C84) 0.8272900E-01 0.000000
C( A93, B93) 0.1508270 0.000000
C( A93, B91) 0.1664390 0.000000
C( A93, C92) 0.4516400E-01 0.000000
C( B91, B93) 0.4289100E-01 0.000000
C( B91, C84) -0.3000000E-01 0.000000
C( B91, C82) -0.3000000E-01 0.000000
C( B93, C82) -0.3000000E-01 0.000000
C( B93, C80) -0.3000000E-01 0.000000
C( C84, C82) 0.8763700E-01 0.000000
C( C82, C80) 0.5840000E-01 0.000000
X1( A91, B91) 12700.00 0.000000
X1( A91, B93) 0.000000 0.1198100E-01
X1( A91, C92) 7800.000 0.000000
X1( A91, C84) 64400.00 0.000000
X1( A93, B93) 19300.00 0.000000
X1( A93, B91) 0.000000 0.3426000E-01
X1( A93, C92) 42900.00 0.000000
X1( B91, B93) 0.000000 0.2424300E-01
X1( B91, C84) 0.000000 0.1265800E-01
X1( B91, C82) 12700.00 0.000000
X1( B93, C82) 0.000000 0.1864800E-01
X1( B93, C80) 19300.00 0.000000
X1( C84, C82) 0.000000 0.7497900E-01
X1( C82, C80) 0.000000 0.3975200E-01
Row Slack or Surplus Dual Price
1 11107.96 -1.000000
2 0.000000 -0.9538700E-01
3 0.000000 -0.1021790
4 0.000000 -0.1864800E-01
5 0.000000 0.5701500E-01
6 0.000000 -0.3000000E-01
7 0.000000 -0.4864800E-01
8 0.000000 0.1265800E-01
9 0.000000 0.000000

70
Global optimal solution found. Tranship_EAST_14arcs_0.02Eqm
Objective value: 11427.96
Infeasibilities: 0.000000
Total solver iterations: 7
Variable Value Reduced Cost
C( A91, B91) 0.1253870 0.000000
C( A91, B93) 0.1560160 0.000000
C( A91, C92) 0.3837200E-01 0.000000
C( A91, C84) 0.8272900E-01 0.000000
C( A93, B93) 0.1508270 0.000000
C( A93, B91) 0.1664390 0.000000
C( A93, C92) 0.4516400E-01 0.000000
C( B91, B93) 0.4289100E-01 0.000000
C( B91, C84) -0.2000000E-01 0.000000
C( B91, C82) -0.2000000E-01 0.000000
C( B93, C82) -0.2000000E-01 0.000000
C( B93, C80) -0.2000000E-01 0.000000
C( C80, C82) 0.5580000E-01 0.000000
C( C82, C84) 0.8763700E-01 0.000000
X1( A91, B91) 12700.00 0.000000
X1( A91, B93) 0.000000 0.1198100E-01
X1( A91, C92) 7800.000 0.000000
X1( A91, C84) 64400.00 0.000000
X1( A93, B93) 19300.00 0.000000
X1( A93, B91) 0.000000 0.3426000E-01
X1( A93, C92) 42900.00 0.000000
X1( B91, B93) 0.000000 0.2424300E-01
X1( B91, C84) 0.000000 0.2265800E-01
X1( B91, C82) 12700.00 0.000000
X1( B93, C82) 0.000000 0.1864800E-01
X1( B93, C80) 19300.00 0.000000
X1( C80, C82) 0.000000 0.5580000E-01
X1( C82, C84) 0.000000 0.1102950
Row Slack or Surplus Dual Price
1 11427.96 -1.000000
2 0.000000 -0.1053870
3 0.000000 -0.1121790
4 0.000000 -0.1864800E-01
5 0.000000 0.6701500E-01
6 0.000000 -0.2000000E-01
7 0.000000 -0.3864800E-01
8 0.000000 0.2265800E-01
9 0.000000 0.000000

71
Global optimal solution found. Tranship_EAST_14arcs_0.03Eqm
Objective value: 11107.96
Infeasibilities: 0.000000
Total solver iterations: 7
Variable Value Reduced Cost
C( A91, B91) 0.1253870 0.000000
C( A91, B93) 0.1560160 0.000000
C( A91, C92) 0.3837200E-01 0.000000
C( A91, C84) 0.8272900E-01 0.000000
C( A93, B93) 0.1508270 0.000000
C( A93, B91) 0.1664390 0.000000
C( A93, C92) 0.4516400E-01 0.000000
C( B91, B93) 0.4289100E-01 0.000000
C( B91, C84) -0.3000000E-01 0.000000
C( B91, C82) -0.3000000E-01 0.000000
C( B93, C82) -0.3000000E-01 0.000000
C( B93, C80) -0.3000000E-01 0.000000
C( C80, C82) 0.5580000E-01 0.000000
C( C82, C84) 0.8763700E-01 0.000000
X1( A91, B91) 12700.00 0.000000
X1( A91, B93) 0.000000 0.1198100E-01
X1( A91, C92) 7800.000 0.000000
X1( A91, C84) 64400.00 0.000000
X1( A93, B93) 19300.00 0.000000
X1( A93, B91) 0.000000 0.3426000E-01
X1( A93, C92) 42900.00 0.000000
X1( B91, B93) 0.000000 0.2424300E-01
X1( B91, C84) 0.000000 0.1265800E-01
X1( B91, C82) 12700.00 0.000000
X1( B93, C82) 0.000000 0.1864800E-01
X1( B93, C80) 19300.00 0.000000
X1( C80, C82) 0.000000 0.5580000E-01
X1( C82, C84) 0.000000 0.1002950
Row Slack or Surplus Dual Price
1 11107.96 -1.000000
2 0.000000 -0.9538700E-01
3 0.000000 -0.1021790
4 0.000000 -0.1864800E-01
5 0.000000 0.5701500E-01
6 0.000000 -0.3000000E-01
7 0.000000 -0.4864800E-01
8 0.000000 0.1265800E-01
9 0.000000 0.000000