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

Node 4: Q46 + Q47 = Q14 + Q24 + Q34
Node 5: - Q35 + Q56 = -B5
Node 6: - Q36 - Q46 - Q56 + Q67 = -B6
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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);