Abstract
The development of an optimization model for planning regional wastewater systems is centered on reducing the overall costs of wastewater treatment plants (WWTP) locations and sewer layout while taking treatment capacity uncertainty into account. The goal of the model is to reduce overall costs while taking uncertainty into account, with a given degree of reliability, ensuring that the amount of flow to be treated does not exceed the treatment capacity. The model is formulated using a chance-constrained method which have been used for addressing optimization problems with a range of uncertainties. The model is developed in the General Algebraic Modeling System (GAMS) program using Mixed-Integer Linear Programming (MILP), and it is then applied to a simple example utilizing various reliability percentages ranging from 60 to 95%. A simple example demonstrates that employing 60–75% reliability has the same total costs and layout for the system. The system’s layout and overall costs would be higher although, as the reliability value exceeds 80%.
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Abbreviations
- I:
-
Set of wastewater sources nodes on Iso-nodal line i.
- J:
-
Set of the possible location of collection nodes on Iso-nodal line j.
- K:
-
Set of possible location WWTP nodes on Iso-nodal line k.
- \({\text{QR}}_{{\text{i}}}\) :
-
Amount of wastewater produced at sources node on Iso-nodal line i.
- \({\text{QS}}_{{{\text{i}},{\text{j}}}}\) :
-
Flow carried from sources nodes on Iso-nodal line i to collection nodes on Iso-nodal line j.
- \({\text{QC}}_{{{\text{j}},{\text{k}}}}\) :
-
Flow carried from intermediate nodes on Iso-nodal line j to WWTP nodes on Iso-nodal line k.
- \({\text{QT}}_{{\text{k}}}\) :
-
Amount of treated wastewater at WWTP node on Iso-nodal line k.
- \({\text{x}}_{{{\text{i}},{\text{j}}}}\) :
-
Binary variable that will take value 1 if there is existence of a particular pathway that linking nodes on Iso-nodal line i to nodes on Iso-nodal line j and 0 otherwise.
- \({\text{y}}_{{{\text{j}},{\text{k}}}}\) :
-
Binary variable that will take value 1 if there is existence of a particular pathway that linking nodes on Iso-nodal line j to nodes on Iso-nodal line k and 0 otherwise.
- \({\text{Qmin}}_{{{\text{i}},{\text{j}}}}\) and \({\text{Qmin}}_{{{\text{j}},{\text{k}}}}\):
-
Minimum amount of wastewater from source nodes on Iso-nodal line i through collection nodes on Iso-nodal line j to WWTP nodes on Iso-nodal line k.
- \({\text{Qmax}}_{{{\text{i}},{\text{j}}}}\) and \({\text{Qmax}}_{{{\text{j}},{\text{k}}}}\):
-
Maximum amount of wastewater from source nodes on Iso-nodal line i through collection nodes on Iso-nodal line j to WWTP nodes on Iso-nodal line k.
- \({\upmu }_{{{\text{MaxQ}}_{{{\text{wwtp}}}} }}\) :
-
The mean of maximum wastewater plant capacity \(\left( {{\text{MaxQ}}_{{{\text{wwtp}}}} } \right)\).
- \({\upsigma }_{{{\text{MaxQ}}_{{{\text{wwtp}}}} }}\) :
-
The standard deviation of maximum wastewater plant capacity \(\left( {{\text{MaxQ}}_{{{\text{wwtp}}}} } \right)\).
- \({\text{Z}}_{{{\text{B}}_{{{\text{i}},{\upalpha }_{{\text{i}}} }} }}\) :
-
The quantal function for the normal distribution, or the cumulative distribution function, interpolated from the normal distribution tables for specific values of \({\alpha i}\).
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Alfaisal, F.M. (2023). Model for Optimal Regional Wastewater Systems Planning with Uncertain Wastewater Treatment Capacity. In: Sherif, M., Singh, V.P., Sefelnasr, A., Abrar, M. (eds) Water Resources Management and Sustainability. Water Science and Technology Library, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-031-24506-0_25
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