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Optimal planning of water supply system for long-term sustainability
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Available online at www.sciencedirect.com
ScienceDirect Journal of Hydro-environment Research xx (2014) 1e11 www.elsevier.com/locate/jher
Research paper
Optimal planning of water supply system for long-term sustainability Jaehyun Ahn a, Doosun Kang b,* b
a Dept. of Civil & Architectural Engineering, Seokyeong Univ., 16-1 Jungneung-dong, Sungbuk-gu, Seoul 136-704, Republic of Korea Department of Civil Engineering, Kyung Hee Univ., 1732 Deogyeong-daero, Giheung-gu, Yoingin-si, Gyeonggi-do 446-701, Republic of Korea
Received 26 August 2013; revised 4 August 2014; accepted 5 August 2014
Abstract Developing a long-term system plan for sustainable water supply is a challenging task due to system complexity and future uncertainties in water demands and source availability. Here a coupled optimization model is proposed for water supply system design and long-term operations by deciding system component sizes and water flow allocations simultaneously. The objective is to minimize overall system costs (i.e., sum of capital and operation costs) while meeting water demands and operational constraints. The economic costs include initial component construction costs and operation expenditure over pre-defined operation years. The proposed model integrates a genetic algorithm with a linear programming model to optimize water infrastructure investments and annual water transfers satisfying flow constraints. The coupled model was applied to a simplified water supply network composed of multiple water sources and users. For the application network, various qualities of water from different sources could be supplied to different users. Plausible future scenarios with time varying water demands were simulated representing potential future conditions. Application results show that the proposed coupled model is beneficial in decision making process to design structural components in near future and prepare long-term policies for water shortage and water right issues in upcoming years. The model can be tailored to a specific system and various regulations and conditions can be incorporated within the model without adding complexity to the optimization framework. © 2014 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.
Keywords: Long-term water supply planning; Coupled optimization model; Scenario planning; Uncertainties
1. Introduction 1.1. Water supply system planning A long-term water supply planning is a challenging task with time-varying water demands and uncertainties associated with available water sources. Rapid urbanization and climate related changes stress water availability in the future. To that end, reclaimed effluent and desalinated water are getting spotlight as crucial water resources for sustaining long-term water supply. In addition, areal imbalance in water
* Corresponding author. Tel.: þ82 312015275. E-mail addresses: [email protected] (J. Ahn), [email protected] (D. Kang).
availability enforces water-trading across boundaries. As the new water sources (i.e., treated wastewater and desalinated water) become part of water supply system, and large-scale water transfer could become alternative water management strategies, optimal decisions should be made for locating and sizing water supply infrastructures in order to convey water from sources to end users in economic and sustainable way. The decisions are complicated requiring sophisticated decision support tool. This tool should be able to decide the optimal component sizes (e.g., pipe size, treatment plant capacity, and pumping facilities' scale) and water allocation decisions while supplying adequate amount of water to end users. Several studies have been devoted on optimization of water supply system planning. Early works include Ocanas and Mays (1981a) in which non-linear programming under steady and dynamic conditions were applied to solve a water
http://dx.doi.org/10.1016/j.jher.2014.08.001 1570-6443/© 2014 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.
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reuse planning optimization. In their follow-up paper, the problem was formulated in a dynamic planning model with single and multiple periods and solved by successive linear programming (Ocanas and Mays, 1981b). Their studies were valuable by considering water quality and operation cost within the objective function. They, however, simplified the conveyance system hydraulics without detailed representation of energy loss and its capacity. Recently, Chung and Lansey (2009) applied an evolutionary search algorithm for optimization of large-scale water supply system to decide the component capacities in two step time frame. Their study, however, did not consider annual water allocation decisions and future uncertainties were not part of optimization framework. Recent studies attempted to consider the uncertainties in water supply planning and suggested stochastic programming models for water supply optimization. Several stochastic optimization approaches have been applied to water supply system design and operation. Most works have adopted twostage or multi-stage linear or nonlinear stochastic programming. Some representative studies are summarized herein: Watkins et al. (2000) developed a multi-stage stochastic programming model for the management of the Highland Lakes by the Lower Colorado River Authority (LCRA) in Central Texas. Pallottino et al. (2005) developed a decision support tool linked to a linear programming model for optimal water resources management under uncertainty. The uncertainty is modeled by a scenario tree in a multistage environment to find a robust decision policy. Chung et al. (2009) suggested a robust optimization model for municipal water supply system optimization, which is supposed to be applied to a general water supply system. Ray et al. (2012) proposed a multistage stochastic linear programming model to optimize the water system planning and management under uncertainties of demographic and climate change. The main focus of these studies was to find optimal component scale or policy to hedge against various future conditions. However, decision for flow allocations over the planning period was prohibitive due to computational limit of the stochastic programming approaches. Also the stochastic programming approaches were highly complex to be implemented in real-life system planning. In this study, a coupled optimization model is proposed for a sustainable long-term planning and management of water supply system to minimize overall capital/operation costs while meeting demand requirements and satisfying operational constraints. Decision variables include the component sizes of transmission pipe network, pumping stations, and treatment facilities. Annual flow allocations of the individual conveyance system is also determined over the simulation period to estimate the operation and management cost. The resulting problem is highly nonlinear and can contain a number of decision variables. A genetic algorithm (GA) has been implemented to determine component sizes and a linear programming (LP) is coupled with the GA to determine annual flow allocation minimizing water transferring cost over simulation period. The coupled optimization approach is not new here and several studies have been devoted for
hydrosystems design and operation problems. Some representative studies in this field are summarized herein: Hsiao and Chang (2002) introduced a procedure integrating GA with dynamic programming (DP) to determine the optimal solutions for a groundwater management problem. They claimed the combined model overcame the limitation of conventional optimization algorithms by simultaneously considering fixed cost and time-varying pumping rates. Lansey et al. (2007) applied the two-stage GA-LP model to determine optimal satellite booster location in water distribution network in order to maintain disinfectant residuals and avoid high dosages near sources. They reported that the framework could avoid long water quality simulation thus reduce the computational burden significantly and provide better solutions. Krapivka and Ostfeld (2009) applied a coupled optimization model for least-cost design of simple water distribution network with one demand loading condition. They showed promising results in optimization efficiency but limited to one loading gravitational simple network. As reported in the previous studies, coupled optimization model is beneficial by integrating two approaches into one framework and overcoming the limitations of each. This study integrates GA with LP and determines the structural component sizes and operational decisions simultaneously. This approach is beneficial than the stochastic programming in terms of computational efficiency and simplicity in real-life implementation and anticipated to find better solutions than the individual optimization approaches. 1.2. Problem statement In a long-term planning of water supply system, providing required water for each end user with minimum cost is a goal of water providers. To that end, climate-related changes are critical issues and spatiotemporal demand variations should also be considered when planning the system. Deciding component sizes and allocating water for each demand sector for entire operation period is complex task, thus required assistance by optimization tools. The proposed coupled decision model combines a heuristic search algorithm (GA) and a linear programming (LP) model to simultaneously determine the component sizes and time-varying water allocation decisions. That is, a GA determines the component sizes in an outer-loop and the decisions from GA are provided to the inner-model (LP) in which flow allocations along the links are determined based on the GA-proposed component sizes and unit costs to minimize the operation cost over the scheduled operation period. Note the unit costs in LP are determined based on the component sizes suggested by the GA. In this way, GA and LP are coupled to find the most economic decisions overall. Operational decisions and costs from LP are sent back to GA and total costs (¼capital cost þ operation cost) and constraints are evaluated in GA. Potentially new solutions for system component sizes are regenerated from GA and transmitted to LP to determine new flow allocations. This process is repeated until the GA termination criteria are met or optimal decisions are found. To determine optimal flow allocations in LP, transmission pipe system hydraulics (which is
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linearized) is directly embedded in the model to better estimate the operation cost. The operational constraint is to meet the system demand at all consumer locations with appropriate end node pressure requirements. All supply sources are limited by flow capacity and allowable minimum flow is to be maintained over the simulation period. A water supply system typically includes multiple sources and demand sectors and its purpose is to deliver adequate amount of water with minimal economic costs. The decision should be made subject to uncertainties induced by future growth rates and demand locations, water resources availability, and changing institutional regulations and public sentiments. The design of the component size, layout, and operation is usually based on predictions of future population and climate conditions. Decisions based on a deterministic model without consideration of future uncertainties may result in system failure. Here the system failure is defined as not meeting a required demand or paying additional cost (generally, costly than scheduled) to supply the unexpected demand. This study considers multiple plausible futures and final optimal decisions are determined based on the acceptance as common elements obtained from the multiple future scenarios. Thus, the model can assist decision makers to plan a long-term sustainable water supply to cope with the future changes in water demands. The important features of this study as compared to the previous studies mentioned above are: (1) GA-LP combination to solve not only structural decisions but also long-term annual allocations (2) Adopting and applying a scenario-based planning approach for long-term water system design/planning (3) Applying a deterministic optimization algorithm in an intuitive way to solve the complex stochastic problem 2. Model formulation
agricultural and domestic outdoor uses is not required to be treated. Wastewater returned from domestic and industrial users must be treated at wastewater treatment plants (WWTP). After treatment, the reclaimed water could be reused for agricultural irrigation, domestic outdoor uses, or discharged to the aquifer for groundwater replenishment or released to the river. 2.2. A GA-LP coupled optimization model Fig. 1 illustrates the GA-LP coupled model components and their interactions. The outer-model is a component investment decision model, in which GA determines water infrastructure sizes. The decisions are passed to the second component (inner-model), in which optimal water allocation decisions are made using a LP model. The purpose of this component is to determine the least-cost distribution of water along the links over the simulation period. Water will be transported from sources to end users given infrastructure availability decided by GA and associated unit operation/ management cost. Communities and other major water users will be represented as sink nodes and water sources are denoted as supply nodes. The conveyance system comprises the links in the network flow LP model. The decisions are the flow rates in each link with constraints of the water volume at each source and demand point over a planning time period. The decisions obtained from the GA and LP models are fed into the post-processor to calculate economic cost and the constraints applied. The process continues with the communication of the objective values to the major investment model (GA) in order to update the infrastructure decisions and consequently the flow allocations for the links. The procedure is repeated until the GA convergence criteria are met. In the proposed model, the capacities of the water transmission structures such as pipes, pumps, and treatment plants are described as structural variables determined in GA. Flow
2.1. Water supply network Water supply network can be schematically represented by nodes and links. Potential flow paths connected with transmission links are shown between sources and users while sources and users are denoted as nodes. Water uses generally include agricultural, domestic and industrial demands. Available water supply sources include groundwater aquifer and surface water supply from reservoir and river. In addition, locally produced reclaimed water that is mainly supplied for agricultural irrigation and domestic outdoor uses is receiving a spotlight as a valuable alternative source at water shortage areas. If these local supplies fail to meet demands in the service area, water importation from outer sources should be pursued, which is in general more costly than local supplies. Due to rapid urbanization in some areas with limited supplies, the inter-basin water transfer becomes a growing trend. Regarding water/wastewater treatment within the basin, any flow provided to domestic and industrial users from surface water sources (e.g., river and reservoir) must be treated at water treatment plants (WTP), while surface water provided to
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Fig. 1. A GA-LP coupled optimization model.
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allocations over the water supply network are operational variables determined in LP. The objective function consists the construction cost of all system components (pipes, pumps, and treatment facilities) and operation cost over the simulation time period including pumping, water/wastewater treatment, and water importing expenditures if needed. Details of the cost functions and applied constraints are described in the following sections.
3. Optimization formulation 3.1. Cost functions Here the economic cost functions of system components and operation are summarized. The cost functions employed in this study are mainly appropriate for planning level design. All costs are updated using the Engineering News-Record (ENR) construction cost index for 2011 and expressed in US dollars. The annual operation costs are converted to present worth value based on the defined planning time horizon and discount rate. Details of the cost functions can be found in the noted references and they are briefly summarized as below.
2.3. Scenario-based system planning Predictions of future conditions contain unavoidable uncertainties. The most significant uncertainty in water supply planning occurs in water demand predictions and available water supply estimates. In deterministic optimization process, it is commonly assumed that all parameters are known in advance at planning stage. However, future conditions can never be predicted with accuracy and uncertainties must be considered in decision making process, especially for a largescale and long-term infrastructure planning. One way to deal with uncertainties is to consider multiple scenarios that represent plausible futures and to determine system components based on the potential scenarios (Schwartz, 1991). By doing so, the system remains feasible and operates in a satisfactory condition for a range of future circumstances with possibly minimal adjustments. Here the scenario-based planning scheme has been incorporated to find optimal decisions hedging against future uncertainties. Deterministic models select decision variables with perfect knowledge of the future (in other words, it is a single-scenario planning), while (multiple) scenario-based planning approach considers a number of possible futures to reduce the risk of system failure and prohibitive system adjustment costs. Preparing for a range of possible futures provides flexibility and adds robustness to the system so it can respond to uncertain events at reasonable costs while satisfying service requirements. Large-scale and long-term planning should be carefully analyzed and decisions should account for uncertainties in future water uses change and source availability. By incorporating multiple scenarios in the planning stage, the system planners could have better chance to obtain robust decisions that are supposed to perform satisfactorily across a range of possible future conditions. Thus the decisions would be costeffective, reliable, and sustainable across a wide range of future realities.
3.1.1. Pipe construction cost Ductile iron pipe is assumed to be used for transmission lines. The general form of the pipe construction cost function developed by Clark et al. (2002) is: y ¼ fa þ bðxc Þ þ dðue Þ þ f ðxuÞg
ð1Þ
where y ¼ cost of a particular component (USD/ft, 1ft ¼ 0.3048m); x ¼ pipe diameter in inch (1inch ¼ 2.54 cm); u ¼ indicator variable; and a, b, c, d, e, and f are parameter values estimated using regression methods. Pipe construction costs are the sum of the base installation cost, trenching and excavation cost, embedment, backfill, and compaction cost. Parameters for each component are listed in Table 1. 3.1.2. Pump construction cost The general equation for pump construction cost is function of the rated pump discharge and head and is taken from Walski et al. (1987): PumpCC ¼ 500 Q0:7 H 0:4
ð2Þ
where Q ¼ rated discharge in GPM (gallons per minute, 1 gallon ¼ 3.78 L); H ¼ rated head in feet (1ft ¼ 0.3048 m). 3.1.3. Water treatment plant construction cost Water treatment plant (WTP) construction cost is given below (Davis and USBR, 2009) as a function of plant capacity. In this study, the WTP treatment type is assumed to be conventional treatment; if needed, more cost functions for other types of treatment can be found from the reference (Davis and USBR, 2009).
Table 1 Parameters for pipe installation cost. Description
Type
Pipe material Trenching and excavation
Ductile iron pipe Concrete cylinder pipe Sandy gravel soil with 1:1 side slope
Embedment Backfill and compaction
Ordinary embedment Sandy gravel soil with 1:1 side slope
Parameter values a
b
c
d
e
f
44.0 11.7 24.0 2.9 1.6 0.094
0.33 0.51 0.32 0.0018 0.0062 0.062
1.72 1.38 0.67 1.90 1.83 0.73
2.87 0.0 16.7 0.13 0.20 0.18
0.74 0.0 0.38 1.77 1.00 2.03
0.0 0.0 0.0 0.0 0.07 0.02
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WTPCC ¼ e14:444þ
0:5372 2
1:314667 Q0:881 WTP
ð3Þ
where QWTP is the capacity of the plant in MGD (million gallons per day, 1 million gallon ¼ 3785.4 m3). 3.1.4. Wastewater treatment plant construction cost Wastewater treatment plant (WWTP) construction cost is a function of the plant capacity and the treatment type (Davis and USBR, 2009). Here a sequencing batch reactor is assumed as the treatment type and more information of the WWTP construction costs for other treatment types could be found from the reference. WWTPCC ¼ ð1 þ fs Þ 12; 892; 000 Q0:6289 WWTP
ð4Þ
where QWWTP is the capacity of the plant in MGD (million gallons per day) and fs is a factor accounting for on-site solids handling (here, fs ¼ 0.0). 3.1.5. Operation unit cost The pump operation cost includes energy consumption for lifting water to demand nodes using a flat rate of $0.20/kWh. The annual required pumping energy (P ¼ Ku*Q*H/h in kW, where Ku ¼ unit conversion factor, h ¼ pump efficiency) is first estimated using the pumping flow rate (Q, operational decision) and head gained (H ); then annual pumping cost is computed by multiplying the flat rate. Unit cost of potable water treatment was assumed to be $0.30/m3. Two different unit costs were assumed for the wastewater treatment; $0.40/ m3 was assigned for river effluent treatment and slightly higher unit cost of $0.50/m3 was assigned for water reuse treatment that could be supplied to domestic non-potable uses and agricultural irrigation. Imported water from external sources was priced at unit cost of $0.75/m3. Potential conveyance structures for water importation were not explicitly considered as economic cost but included implicitly in the unit cost applied. Note the water importation cost would be system specific depending on the conveyance distance and market conditions. Here the unit cost of importing water was Table 2 Input parameters and system data for application study. Parameter
Value
Unit
Simulation period Discount rate Darcy-Weisbach friction factor, f Energy tariff Pump efficiency Water treatment unit cost Wastewater treatment unit cost For river effluent For non-potable reuse Water importation unit cost Initial population of municipal 1 at year 1 Initial population of municipal 2 at year 1 Population growth rate Per-capita water use Agricultural consumptive water use Required downstream river flow
20 5 0.02 0.20 75 0.30
year % e USD/kWh % USD/m3
0.40 0.50 0.75 100,000 150,000 2.0 400 1.2 1.0
USD/m3 USD/m3 USD/m3 e e % Liter/capita/day m3/sec m3/sec
5
assumed to be higher than local service costs; thus water importation will occur only if the local supplies are limited. The annual operation costs are converted to present worth value based on the defined planning time horizon and discount rate. The parameters used in the annual cost calculations are summarized in Table 2. 3.2. Objectives and constraints The model aims to minimize the overall system costs while meeting operation constraints. The total cost is the sum of the costs for system construction and operation over the simulation period; thus the objective function is expressed as: Minimize F ¼ CCðXconst;
t¼1 Þ þ
T X
OC Xoprt; t
ð5aÞ
t¼1
Subject to G Xconst;
t¼1 ;
Xoprt;
t
>0
ð5bÞ
where CC and OC are the system construction (capital) and operation costs, respectively. Xconst, t¼1 denotes structural decisions at initial time (t ¼ 1) and Xoprt, t denotes annual operation decisions at time t. G represents constraints for the flow requirements for all users and pressure requirements on that supply and mass balance at each location. The formulated optimization problem is a mixed integer nonlinear problem and is solved using the proposed GA-LP coupled model. GAs are stochastic search techniques based on the evolutionary mechanisms inspired by biological evolution processes, such as elitism, crossover, and mutation (Goldberg, 1989). Regarding GA processes, the best 10% of the current population are preserved as elite children to survive to the next generation. Here, varieties of crossover and mutation functions were tested as a preliminary test. The single-point crossover operator is adopted with a crossover fraction of 0.60. A Gaussian mutation operator is used for the mutation operation for the remaining individuals to introduce diversity in the population. The random nature of GAs implies that the global optimum is not guaranteed to be found, but with sufficient function realizations, near-optima are expected to be found. Several system operation constraints are posed here: (1) satisfy water demand for each end user; (2) satisfy conservation of mass at nodes; (3) meet flow requirement at defined source points; (4) restrict the amount of reclaimed water use for specified users; (5) satisfy required minimum allowable water pressure at demand nodes if needed; (6) do not exceed the capacity of the water and wastewater treatment plants; and (7) maintain minimum river flow rate at downstream location. 4. Applications 4.1. Study network The proposed GA-LP coupled optimization model was applied to a simplified water supply network. The system was simplified by lumping demand sectors and removing local distribution lines; thus only the large transmission lines were
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Fig. 2. Schematic of study network (note the numbers beside the links and nodes are pipe length (km) and elevation (m) respectively); the links are denoted from X1 to X11.
considered. However, overall system topography and component layout were remained realistic. A schematic of the study network is depicted in Fig. 2. The water system is composed of surface, and imported water sources, residential and agricultural irrigation users, and water and wastewater treatment plants. External water source can be imported at a cost per unit volume that includes the cost of conveyance system. It is assumed that the highly treated reclaimed water can be supplied to domestic users for non-potable uses, and agricultural irrigation, and to meet the downstream community's needs or environmental flows. However, the maximum limit of reclaimed water uses has been set for domestic users. That is, up to 20% of municipal demands and 30% of agricultural uses can be supplied by the reclaimed water. The objective function of the problem is to minimize the cost of construction and operation of system components as well as the cost of treating, conveying, or importing water to meet water demand. Design decisions are pipe diameters, pump design flows and heads, water and wastewater treatment plant capacities. Flow allocations for each link over the simulation period are operational decisions. Total 20-year simulation is conducted. The years are not hydrologically linked and there is no storage carryover between years, because only yields of river water supplies with no storage facilities are modeled. The infrastructure construction occurs in a first stage (i.e., current time step, t ¼ 1) in anticipation of water resources needs for subsequent years. The application network has 11 links with lengths given in Fig. 2. Eight of which are pipe connections (X1 ~ X8) along
which pump station could be built depending on energy requirement. Three potential importation paths (X9 ~ X11) from external sources are included. There are 2 treatment facilities (1 WTP and 1 WWTP) in the system. Thus, total number of structural design variables are 26 (¼8 pipe diameters þ 16 decisions for pump (¼design flow (Q) and head (H ) for each of 8 potential pumps) þ 2 treatment plant capacities). Flow allocations through 11 links are defined as operational decisions determined by mass balance constraints and unit cost of water transportation for each link. The simulation periods are 20 years thus total 220 operation decisions (¼11 links 20 years) should be determined. In total, the problem consists of 246 decision variables. Note the input parameters for the problem and system data are summarized in Table 2. 4.2. Results 4.2.1. Optimal decisions for base condition (Scenario 1) The model is programmed and simulated using MATLAB (MathWorks R2012a). The problem was run on an Intel Core i5 3.2 GHz with 4 GB of RAM and was solved in 30.8 min after twenty thousand function evaluations. Fig. 3 depicts the optimal component designs for the base condition (Scenario1, S1) in which the population growth rate, per-capita water use, and agricultural consumptive demand are assumed to be remained constant throughout the 20-yr simulation period as listed in Table 2. Based on the optimization results, link X5 is
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Fig. 3. Optimal decisions of system components for the base condition scenario.
not installed (through which the reclaimed water was supposed to be supplied to agricultural area), because treating/conveying effluent is more costly than acquiring surface water directly from the river. Hence, all the agricultural demand is satisfied by the raw water from the river for the entire simulation period. In addition, no pumping unit will be required for link X8 (transporting WWTP effluent to downstream river), since sufficient elevation difference is secured for gravity flow. Regarding water importation, Municipal Area1 is receiving outer source water from year 9 to the end of simulation period. Note the imported flow rate at year 20 is 0.19 cm, which is almost 30% of the total demand of Municipal Area 1. However, no water importation is required for Municipal Area 2 for entire period; thus, all demand is supplied from WTP for potable uses and WWTP for non-potable purposes. Total construction and operation cost for 20-year period with discount rate of 5% was $512 million as a present value. Detailed cost breakdowns for each system component are shown in Fig. 4. It is seen that the system construction costs (i.e., pipe, pump, WTP and WWTP construction costs) comprise 48.5% of total cost, while system operation costs (i.e., WTP/WWTP operation, pump operation, and water importation costs) are 51.5% of overall system cost. Among the operation costs, water and wastewater treatment facilities operation cost comprises the majority while pumping and water importation costs are relatively low. 4.2.2. Multiple scenarios and common elements Future water demand projections are inherently uncertain. As such, two more scenarios were simulated representing
potential future conditions, such as community growth projections represented by per capita water use and agricultural consumptive water demand. Scenario2 (S2) represents a severe future condition in which the per capita water use of municipal area is kept increasing over time to reach 450 lpcd at year 20 and agricultural consumptive use is assumed to be linearly increased by 10% at year 20. In contrast, Scenario3 (S3) simulates mild future condition for which the municipal water demand is decreased due to demand management and water conservation (350 lpcd at year 20) and agricultural demand is also linearly decreased by 10% at year 20. Therefore, the uncertain parameters are water demands for municipal and agricultural sectors reflected in the per capita water use and consumptive demand, respectively. Note the potential
Fig. 4. Optimal design costs for the base condition scenario.
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Table 3 Economic costs for individual scenarios. System construction cost ($M)
S1 (Base) S2 (Severe) S3 (Mild)
System operation cost ($M)
Pipe
Pump
WTP
WWTP
Pump
WTP/ WWTP
Water import
Total Cost ($M)
81.2
27.2
59.6
80.2
23.0
228.5
12.3
512.0
73.1
28.1
59.6
86.3
27.0
231.9
36.4
542.5
77.9
24.6
59.6
73.7
26.9
220.3
0.0
483.1
uncertainties in water availability caused by climate-related changes or uncertainties in imported water availability due to water market variations were not simulated in this study but can be incorporated if information is available without altering design framework. Overall system costs for the three scenarios are summarized in Table 3. For S2 (severe condition), water importation was initiated at year 6 for Municipal Area1 and continued till the end of the simulation period due to the increased water demand. For S3 (mild condition), however, no water importation was required and local demands during the simulation years were met by local supplies. Comparing system costs, S2 requires $542.5M, which is $30.5M higher than the base condition (S1, $512.0M) and the difference is mostly from the water importation cost. Total cost of S3 is $483.1 M ($28.9 M less than S1) and the reductions are from the system operation savings (e.g., no water importation). It is interesting to note that overall system construction costs (pipe, pump, WTP, and WWTP construction costs) of the three scenarios are similar; that is, $248.2M, $247.1M, and $235.9M for S1, S2, and S3, respectively. The main differences in total costs are observed from the system operation costs (WTP/WWTP and pump operation costs and water importation cost); that is, $263.7M, $295.4M, and $247.2M for S1, S2, and S3, respectively. The similarity in system construction costs of the different scenarios are confirmed in Table 4 that summarizes the optimal component sizes of the obtained three scenario designs. As seen, the optimal pipe diameters and WTP/WWTP
sizes for the three scenario designs are similar. These common construction decisions (listed in the bottom row of Table 4) from the multiple scenarios are the robust solutions that remain viable for a range of potential futures if implemented (Schwartz, 1991). These common elements narrow down the planners' decision ranges and, once implemented, ensure system's reliability against the future uncertainties. Identifying the common projects across the scenarios in planning stage helps to prioritize the capital investments and reduce potential regret and risk. The goal of scenario-based optimization is to identify sets of projects that will be viable for all potential futures and avoid over-investment and costly retrofitting. The proposed optimization model and the scenario-based planning approach will assist to make proper decisions in time-varying conditions. It should be noted that, however, there is no guarantee that the exactly common solutions would be found for all decisions across the scenarios considered. Some decisions could be common across the scenarios, some are partly common, and some decisions could be variable over the scenarios. In our simulations, it is seen that only some structural decisions are common across the scenarios and the obtained common elements would be robust over the futures considered. The point is that the process of identifying the common elements helps to narrow down the decision ranges and aids decision makers' on system planning process. This whole process is called “scenario planning” (Schwartz, 1991) and it aims for a sustainable system planning in a changing environment.
Table 4 Optimal designs for individual scenarios and common ranges. Scenarios y parameters S1 (Base) S2 (Severe) S3 (Mild) Range
Plants (m3/s)
Links X1
X2
X3
X4
X5
X6
X7
X8
WTP
WWTP
Diameter (mm) Pump (kW) Diameter (mm) Pump (kW) Diameter (mm) Pump (kW) Diameter (mm)
1200 196.0 1200 117.6 1200 117.6 1200
900 235.2 900 441.0 900 274.4 900
900 156.8 900 235.2 900 196.0 900
900 274.4 900 156.8 900 196.0 900
900 e 900 e 900 e 900
1.20
0.80
1.20
0.90
1.20
0.70
1.20
0.70 ~0.90
117.6 ~196.0
1200 441.0 900 548.8 1200 294.0 900 ~1200 294.0 ~441.0
e e e e e e No Link
Pump (kW)
1800 294.0 1500 411.6 1500 264.6 1500 ~1800 264.6 ~411.6
No Pump
156.8 ~235.2
156.8 ~274.4
No pump
235.2 ~441.0
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Fig. 5. Projected demands and water supplies for municipal areas.
4.2.3. Projected water demands/supplies and downstream river flows One of the advantages of the proposed model is to estimate annual flow allocations for each link; thus projected water demands and supplies over the simulation period can be obtained for interesting nodes. Fig. 5 shows projected water demands and supplies (broken down by supplying sources) of municipal areas for 20yr simulation period under scenarios 1 and 2 conditions. For Municipal Area 1, demands are met by three different water sources, such as potable, reclaimed, and imported water. Under base condition (S1) (Fig. 5a), water importation is initiated at year 9 and kept increasing. Overall, the majority of supplies is potable water from the river flow and portions of reclaimed and imported water increase in later years. Notably, under severe condition (S2) (Fig. 5b), the water importation starts at year 6 and the amount rapidly increases. At year 20, more than half of the demand is supplied by the imported water and portion of potable water from river decreases dramatically. The results indicate that under the rapid community growing conditions, Municipal Area 1 largely depends on imported water in the future. This is because more river flows are provided for Municipal Area 2 and agricultural demands. For Municipal Area 1, proactive demand management plans should be prepared and/or uses of reclaimed water should be encouraged by modifying the current regulations in order to reduce the dependence on the imported water. Note
that the reclaimed water can only be supplied up to 20% of municipal demands for outdoor uses following current regulations. Looking at the projected supplies for Municipal Area 2, no water importation is needed for the next 20 years (even under S2 condition). However, this area also needs efforts of demand management and stimulating reclaimed water usage to save river water source and reduce system-wide water importing expenditure. Although not presented here, under mild condition (S3), all municipal demands are supplied by local sources (river flow and reclaimed water) thus no importation is required. Fig. 6 shows projected flow rates of river at downstream for three scenarios. The minimum flow rate should be maintained for downstream community supplies and the required amount is set for 1.0 m3/s for the entire simulation period as hard constraint. As seen, the minimum flow is satisfied for entire period under three future scenarios. Under the mild condition (S3) (Fig. 6c), some surplus can flow for the next 20 years, while under severe scenario (S2) (Fig. 6b), there is no left-over flow after year 5. The downstream river flow is composed of the left-over upstream river flow (after supplying the upstream study area) and WWTP effluent produced from the upstream community. The composition of the river water would be critical for the downstream community since it is related to the water quality of the source. Under the severe (S2) scenario, the proportion of WWTP effluent is kept increasing and at year 20
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5. Conclusions
Fig. 6. Projected composition of downstream river flows.
about 45% of river water is composed of the effluent. This is because the amount of effluent increases with the demand growth in municipal area (44% of municipal demand returns to WWTP); but the reuse of reclaimed water is limited as maximum 20% of the demand. Since more river water is consumed in upstream area, the required downstream flow is increasingly supplemented by the WWTP effluent. If needed, the amount of effluent released to the downstream river should be regulated based upon the request of downstream users. In terms of the water quality and water right issues, comprehensive discussions involving a diverse group of stakeholders and system planners are required and the proposed model can aid to provide projected quantities under various future scenarios and assist the decision making process.
In a changing environment, water system planners face difficult challenges regarding significant investments of infrastructure construction and its operation for long-term sustainability. The investments are significant and poor decisions are costly in terms of economics and public confidence. Community growth rate is a key projection for construction and operation planning. In addition, the regional imbalance of community growth makes providing an adequate water supply more difficult. If a lower than expected growth occurs, constructed infrastructure will likely be oversized; while, if the implemented components are under-sized due to rapid growth, the system may be inadequate to deliver the desired level of service. In both cases, regret cost occurs and the public will lose trust in the service providers. Large-scale, long-term, and high-budget investments should be carefully determined and the sophisticated decision tools are needed to assist this highly consequential decision process. Since future conditions change, it becomes less likely to predict the future accurately. So the goal becomes to choose cost efficient robust solutions that allow flexibility as future conditions unfold. Therefore, the decision process should account for the uncertainties in the future, and the tools should be developed based on that need. The objective of this study is to develop a water infrastructure planning/management tool for long-term water sustainability with emphasis on needs for new infrastructure that is necessary to meet increasing demands. The proposed modeling tool will be able to evaluate various future scenarios and suggest potential optimal policy. As a decision supporting tool, an intelligent optimization model is proposed by coupling a genetic algorithm (GA) with linear programming (LP) model, in which one-time structural decisions and long-period operational decisions are determined simultaneously. The model was demonstrated using a simplified water supply network to find optimal policy of construction and operation decisions minimizing overall capital and operation costs. Decision variables are component sizes at the beginning year and the water allocations for each of the flow links for entire simulation time period. To account for the system uncertainties, various plausible future conditions were produced as multiple scenarios and common elements (¼decisions) over the scenarios were suggested preparing for the diverse future conditions. In addition, timevarying projected demands/supplies and river flows were predicted to investigate the potential issues of water shortage and water quality/right in coming years and suggest proactive actions for preparedness. The proposed model has several advantages for water system planning: (1) GA-LP coupled framework provides construction decisions and long-term operation schedules simultaneously; (2) it provides stakeholders and system planners with intuitive solutions; (3) the framework is intuitive and easy to implement in practice and does not require specialized optimization technique such as stochastic programming; (4) it provides view of multiple futures and solutions using scenario-based planning; (5) the common solutions found across scenarios would remain valid
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for a wide range of plausible futures; (6) it can aid in developing preparedness plans for future water shortage and water right issues involving diverse stakeholders; and (7) the model can be tailored to the specific system and various regulations and conditions can be incorporated within the model without adding complexity to the optimization framework. This study has several limitations that future research must address to improve the proposed approach; (1) uncertainties addressed here were limited to the demand projections; clearly the uncertainties in source availability will be crucial for future water planning thus must be addressed in the further study; (2) the optimization framework considers that the system design is completed in current stage (t ¼ 1) with assumption of future modifications to adapt to the evolving conditions. In practice, this process will likely be multi-staged as conditions change over time. In this case, multi-stage design and construction should be considered leading to a multi-staged optimization framework. The model proposed here is a first step for long-term planning of water supply system. It allows for the design in the relatively near future based on the best projections at the current time. The multistaged optimization approaches should be pursued since it is a fruitful area of research; (3) this study was initiated by the request of a city planner to develop a simulation model for city-wide capital improvement planning (CIP). The project is on-going and here some preliminary results were presented. Note that the researches are under way applying the proposed model to large scale water networks in order to include better representation of the system while minimizing network simplification; (4) the proposed model is mainly appropriate for the preliminary system planning under various future scenarios. Our approach would suggest better results than early LP models, but still detailed hydraulic simulations are needed to provide final solutions to be implemented; and finally (5) intensive scenario analyses should be conducted on a variety of system parameters, such as population growth patterns, water demand variations (per-capita use and spatial distribution), water source availability due to climate changes, and drought conditions.
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Acknowledgments This research was supported by Seokyeong University in 2011. References Chung, G., Lansey, K., 2009. Application of the shuffled frog leaping algorithm for the optimization of a general large-scale water Supply system. Water Resour. Manag. 23 (4), 797e823. Chung, G., Lansey, K., Bayraksan, G., 2009. Reliable water supply system design under uncertainty. Environ. Model. Softw. 24 (4), 449e462. Clark, R.M., Sivaganesan, M., Selvakumar, A., Sethi, V., 2002. Cost model for water supply distribution systems. J. Water Resour. Plan. Manag. 128 (5), 312e321. Davis, S., U.S. Bureau of Reclamation (USBR), 2009. Decision Support System for Selection of Satellite Vs. Regional Treatment for Reuse. Water Reuse Foundation, Alexandria, VA. Goldberg, D.E., 1989. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, New York. Hsiao, C., Chang, L., 2002. Dynamic optimal groundwater management with inclusion of fixed costs. J. Water Resour. Plan. Manag. 128 (1), 57e65. Krapivka, A., Ostfeld, A., 2009. Coupled genetic algorithm e linear programming scheme for least-cost pipe sizing of water distribution systems. J. Water Resour. Plan. Manag. 135 (4), 298e302. Lansey, K., Pasha, F., Pool, S., Elshorbagy, W., Uber, J., 2007. Locating satellite booster disinfectant stations. J. Water Resour. Plan. Manag. 133 (4), 372e376. Ocanas, G., Mays, L.W., 1981a. A model for water reuse planning. Water Resour. Res. 17 (1), 25e32. http://dx.doi.org/10.1029/WR017i001p00025. Ocanas, G., Mays, L.W., 1981b. Water reuse planning models: extensions and applications. Water Resour. Res. 17 (9), 1311e1327. http://dx.doi.org/ 10.1029/WR017i005p01311. Pallottino, S., Sechi, G.M., Zuddas, P., 2005. A DSS for water resources management under uncertainty by scenario analysis. J. Environ. Model. Softw. 20, 1031e1042. Ray, P.A., Kirshen, P.H., Watkins, D.W., 2012. Staged climate change adaptation planning for water supply in Amman, Jordan. J. Water Resour. Plan. Manag. 138 (5), 403e411. Schwartz, P., 1991. The Art of the Long View. Doubleday, New York. Walski, T.M., et al., 1987. Battle of the network models: Epilogue. J. Water Resour. Plan. Manag. 113 (2), 191e203. Watkins, D., McKinney, D., Lasdon, L., Nielsen, S., Martin, Q., 2000. A scenario-based stochastic programming model for water supplies from the highland lakes. Intl. Trans. Op. Res. 7, 211e230.
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Available online at www.sciencedirect.com
ScienceDirect Journal of Hydro-environment Research xx (2014) 1e11 www.elsevier.com/locate/jher
Research paper
Optimal planning of water supply system for long-term sustainability Jaehyun Ahn a, Doosun Kang b,* b
a Dept. of Civil & Architectural Engineering, Seokyeong Univ., 16-1 Jungneung-dong, Sungbuk-gu, Seoul 136-704, Republic of Korea Department of Civil Engineering, Kyung Hee Univ., 1732 Deogyeong-daero, Giheung-gu, Yoingin-si, Gyeonggi-do 446-701, Republic of Korea
Received 26 August 2013; revised 4 August 2014; accepted 5 August 2014
Abstract Developing a long-term system plan for sustainable water supply is a challenging task due to system complexity and future uncertainties in water demands and source availability. Here a coupled optimization model is proposed for water supply system design and long-term operations by deciding system component sizes and water flow allocations simultaneously. The objective is to minimize overall system costs (i.e., sum of capital and operation costs) while meeting water demands and operational constraints. The economic costs include initial component construction costs and operation expenditure over pre-defined operation years. The proposed model integrates a genetic algorithm with a linear programming model to optimize water infrastructure investments and annual water transfers satisfying flow constraints. The coupled model was applied to a simplified water supply network composed of multiple water sources and users. For the application network, various qualities of water from different sources could be supplied to different users. Plausible future scenarios with time varying water demands were simulated representing potential future conditions. Application results show that the proposed coupled model is beneficial in decision making process to design structural components in near future and prepare long-term policies for water shortage and water right issues in upcoming years. The model can be tailored to a specific system and various regulations and conditions can be incorporated within the model without adding complexity to the optimization framework. © 2014 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.
Keywords: Long-term water supply planning; Coupled optimization model; Scenario planning; Uncertainties
1. Introduction 1.1. Water supply system planning A long-term water supply planning is a challenging task with time-varying water demands and uncertainties associated with available water sources. Rapid urbanization and climate related changes stress water availability in the future. To that end, reclaimed effluent and desalinated water are getting spotlight as crucial water resources for sustaining long-term water supply. In addition, areal imbalance in water
* Corresponding author. Tel.: þ82 312015275. E-mail addresses: [email protected] (J. Ahn), [email protected] (D. Kang).
availability enforces water-trading across boundaries. As the new water sources (i.e., treated wastewater and desalinated water) become part of water supply system, and large-scale water transfer could become alternative water management strategies, optimal decisions should be made for locating and sizing water supply infrastructures in order to convey water from sources to end users in economic and sustainable way. The decisions are complicated requiring sophisticated decision support tool. This tool should be able to decide the optimal component sizes (e.g., pipe size, treatment plant capacity, and pumping facilities' scale) and water allocation decisions while supplying adequate amount of water to end users. Several studies have been devoted on optimization of water supply system planning. Early works include Ocanas and Mays (1981a) in which non-linear programming under steady and dynamic conditions were applied to solve a water
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reuse planning optimization. In their follow-up paper, the problem was formulated in a dynamic planning model with single and multiple periods and solved by successive linear programming (Ocanas and Mays, 1981b). Their studies were valuable by considering water quality and operation cost within the objective function. They, however, simplified the conveyance system hydraulics without detailed representation of energy loss and its capacity. Recently, Chung and Lansey (2009) applied an evolutionary search algorithm for optimization of large-scale water supply system to decide the component capacities in two step time frame. Their study, however, did not consider annual water allocation decisions and future uncertainties were not part of optimization framework. Recent studies attempted to consider the uncertainties in water supply planning and suggested stochastic programming models for water supply optimization. Several stochastic optimization approaches have been applied to water supply system design and operation. Most works have adopted twostage or multi-stage linear or nonlinear stochastic programming. Some representative studies are summarized herein: Watkins et al. (2000) developed a multi-stage stochastic programming model for the management of the Highland Lakes by the Lower Colorado River Authority (LCRA) in Central Texas. Pallottino et al. (2005) developed a decision support tool linked to a linear programming model for optimal water resources management under uncertainty. The uncertainty is modeled by a scenario tree in a multistage environment to find a robust decision policy. Chung et al. (2009) suggested a robust optimization model for municipal water supply system optimization, which is supposed to be applied to a general water supply system. Ray et al. (2012) proposed a multistage stochastic linear programming model to optimize the water system planning and management under uncertainties of demographic and climate change. The main focus of these studies was to find optimal component scale or policy to hedge against various future conditions. However, decision for flow allocations over the planning period was prohibitive due to computational limit of the stochastic programming approaches. Also the stochastic programming approaches were highly complex to be implemented in real-life system planning. In this study, a coupled optimization model is proposed for a sustainable long-term planning and management of water supply system to minimize overall capital/operation costs while meeting demand requirements and satisfying operational constraints. Decision variables include the component sizes of transmission pipe network, pumping stations, and treatment facilities. Annual flow allocations of the individual conveyance system is also determined over the simulation period to estimate the operation and management cost. The resulting problem is highly nonlinear and can contain a number of decision variables. A genetic algorithm (GA) has been implemented to determine component sizes and a linear programming (LP) is coupled with the GA to determine annual flow allocation minimizing water transferring cost over simulation period. The coupled optimization approach is not new here and several studies have been devoted for
hydrosystems design and operation problems. Some representative studies in this field are summarized herein: Hsiao and Chang (2002) introduced a procedure integrating GA with dynamic programming (DP) to determine the optimal solutions for a groundwater management problem. They claimed the combined model overcame the limitation of conventional optimization algorithms by simultaneously considering fixed cost and time-varying pumping rates. Lansey et al. (2007) applied the two-stage GA-LP model to determine optimal satellite booster location in water distribution network in order to maintain disinfectant residuals and avoid high dosages near sources. They reported that the framework could avoid long water quality simulation thus reduce the computational burden significantly and provide better solutions. Krapivka and Ostfeld (2009) applied a coupled optimization model for least-cost design of simple water distribution network with one demand loading condition. They showed promising results in optimization efficiency but limited to one loading gravitational simple network. As reported in the previous studies, coupled optimization model is beneficial by integrating two approaches into one framework and overcoming the limitations of each. This study integrates GA with LP and determines the structural component sizes and operational decisions simultaneously. This approach is beneficial than the stochastic programming in terms of computational efficiency and simplicity in real-life implementation and anticipated to find better solutions than the individual optimization approaches. 1.2. Problem statement In a long-term planning of water supply system, providing required water for each end user with minimum cost is a goal of water providers. To that end, climate-related changes are critical issues and spatiotemporal demand variations should also be considered when planning the system. Deciding component sizes and allocating water for each demand sector for entire operation period is complex task, thus required assistance by optimization tools. The proposed coupled decision model combines a heuristic search algorithm (GA) and a linear programming (LP) model to simultaneously determine the component sizes and time-varying water allocation decisions. That is, a GA determines the component sizes in an outer-loop and the decisions from GA are provided to the inner-model (LP) in which flow allocations along the links are determined based on the GA-proposed component sizes and unit costs to minimize the operation cost over the scheduled operation period. Note the unit costs in LP are determined based on the component sizes suggested by the GA. In this way, GA and LP are coupled to find the most economic decisions overall. Operational decisions and costs from LP are sent back to GA and total costs (¼capital cost þ operation cost) and constraints are evaluated in GA. Potentially new solutions for system component sizes are regenerated from GA and transmitted to LP to determine new flow allocations. This process is repeated until the GA termination criteria are met or optimal decisions are found. To determine optimal flow allocations in LP, transmission pipe system hydraulics (which is
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linearized) is directly embedded in the model to better estimate the operation cost. The operational constraint is to meet the system demand at all consumer locations with appropriate end node pressure requirements. All supply sources are limited by flow capacity and allowable minimum flow is to be maintained over the simulation period. A water supply system typically includes multiple sources and demand sectors and its purpose is to deliver adequate amount of water with minimal economic costs. The decision should be made subject to uncertainties induced by future growth rates and demand locations, water resources availability, and changing institutional regulations and public sentiments. The design of the component size, layout, and operation is usually based on predictions of future population and climate conditions. Decisions based on a deterministic model without consideration of future uncertainties may result in system failure. Here the system failure is defined as not meeting a required demand or paying additional cost (generally, costly than scheduled) to supply the unexpected demand. This study considers multiple plausible futures and final optimal decisions are determined based on the acceptance as common elements obtained from the multiple future scenarios. Thus, the model can assist decision makers to plan a long-term sustainable water supply to cope with the future changes in water demands. The important features of this study as compared to the previous studies mentioned above are: (1) GA-LP combination to solve not only structural decisions but also long-term annual allocations (2) Adopting and applying a scenario-based planning approach for long-term water system design/planning (3) Applying a deterministic optimization algorithm in an intuitive way to solve the complex stochastic problem 2. Model formulation
agricultural and domestic outdoor uses is not required to be treated. Wastewater returned from domestic and industrial users must be treated at wastewater treatment plants (WWTP). After treatment, the reclaimed water could be reused for agricultural irrigation, domestic outdoor uses, or discharged to the aquifer for groundwater replenishment or released to the river. 2.2. A GA-LP coupled optimization model Fig. 1 illustrates the GA-LP coupled model components and their interactions. The outer-model is a component investment decision model, in which GA determines water infrastructure sizes. The decisions are passed to the second component (inner-model), in which optimal water allocation decisions are made using a LP model. The purpose of this component is to determine the least-cost distribution of water along the links over the simulation period. Water will be transported from sources to end users given infrastructure availability decided by GA and associated unit operation/ management cost. Communities and other major water users will be represented as sink nodes and water sources are denoted as supply nodes. The conveyance system comprises the links in the network flow LP model. The decisions are the flow rates in each link with constraints of the water volume at each source and demand point over a planning time period. The decisions obtained from the GA and LP models are fed into the post-processor to calculate economic cost and the constraints applied. The process continues with the communication of the objective values to the major investment model (GA) in order to update the infrastructure decisions and consequently the flow allocations for the links. The procedure is repeated until the GA convergence criteria are met. In the proposed model, the capacities of the water transmission structures such as pipes, pumps, and treatment plants are described as structural variables determined in GA. Flow
2.1. Water supply network Water supply network can be schematically represented by nodes and links. Potential flow paths connected with transmission links are shown between sources and users while sources and users are denoted as nodes. Water uses generally include agricultural, domestic and industrial demands. Available water supply sources include groundwater aquifer and surface water supply from reservoir and river. In addition, locally produced reclaimed water that is mainly supplied for agricultural irrigation and domestic outdoor uses is receiving a spotlight as a valuable alternative source at water shortage areas. If these local supplies fail to meet demands in the service area, water importation from outer sources should be pursued, which is in general more costly than local supplies. Due to rapid urbanization in some areas with limited supplies, the inter-basin water transfer becomes a growing trend. Regarding water/wastewater treatment within the basin, any flow provided to domestic and industrial users from surface water sources (e.g., river and reservoir) must be treated at water treatment plants (WTP), while surface water provided to
3
Fig. 1. A GA-LP coupled optimization model.
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allocations over the water supply network are operational variables determined in LP. The objective function consists the construction cost of all system components (pipes, pumps, and treatment facilities) and operation cost over the simulation time period including pumping, water/wastewater treatment, and water importing expenditures if needed. Details of the cost functions and applied constraints are described in the following sections.
3. Optimization formulation 3.1. Cost functions Here the economic cost functions of system components and operation are summarized. The cost functions employed in this study are mainly appropriate for planning level design. All costs are updated using the Engineering News-Record (ENR) construction cost index for 2011 and expressed in US dollars. The annual operation costs are converted to present worth value based on the defined planning time horizon and discount rate. Details of the cost functions can be found in the noted references and they are briefly summarized as below.
2.3. Scenario-based system planning Predictions of future conditions contain unavoidable uncertainties. The most significant uncertainty in water supply planning occurs in water demand predictions and available water supply estimates. In deterministic optimization process, it is commonly assumed that all parameters are known in advance at planning stage. However, future conditions can never be predicted with accuracy and uncertainties must be considered in decision making process, especially for a largescale and long-term infrastructure planning. One way to deal with uncertainties is to consider multiple scenarios that represent plausible futures and to determine system components based on the potential scenarios (Schwartz, 1991). By doing so, the system remains feasible and operates in a satisfactory condition for a range of future circumstances with possibly minimal adjustments. Here the scenario-based planning scheme has been incorporated to find optimal decisions hedging against future uncertainties. Deterministic models select decision variables with perfect knowledge of the future (in other words, it is a single-scenario planning), while (multiple) scenario-based planning approach considers a number of possible futures to reduce the risk of system failure and prohibitive system adjustment costs. Preparing for a range of possible futures provides flexibility and adds robustness to the system so it can respond to uncertain events at reasonable costs while satisfying service requirements. Large-scale and long-term planning should be carefully analyzed and decisions should account for uncertainties in future water uses change and source availability. By incorporating multiple scenarios in the planning stage, the system planners could have better chance to obtain robust decisions that are supposed to perform satisfactorily across a range of possible future conditions. Thus the decisions would be costeffective, reliable, and sustainable across a wide range of future realities.
3.1.1. Pipe construction cost Ductile iron pipe is assumed to be used for transmission lines. The general form of the pipe construction cost function developed by Clark et al. (2002) is: y ¼ fa þ bðxc Þ þ dðue Þ þ f ðxuÞg
ð1Þ
where y ¼ cost of a particular component (USD/ft, 1ft ¼ 0.3048m); x ¼ pipe diameter in inch (1inch ¼ 2.54 cm); u ¼ indicator variable; and a, b, c, d, e, and f are parameter values estimated using regression methods. Pipe construction costs are the sum of the base installation cost, trenching and excavation cost, embedment, backfill, and compaction cost. Parameters for each component are listed in Table 1. 3.1.2. Pump construction cost The general equation for pump construction cost is function of the rated pump discharge and head and is taken from Walski et al. (1987): PumpCC ¼ 500 Q0:7 H 0:4
ð2Þ
where Q ¼ rated discharge in GPM (gallons per minute, 1 gallon ¼ 3.78 L); H ¼ rated head in feet (1ft ¼ 0.3048 m). 3.1.3. Water treatment plant construction cost Water treatment plant (WTP) construction cost is given below (Davis and USBR, 2009) as a function of plant capacity. In this study, the WTP treatment type is assumed to be conventional treatment; if needed, more cost functions for other types of treatment can be found from the reference (Davis and USBR, 2009).
Table 1 Parameters for pipe installation cost. Description
Type
Pipe material Trenching and excavation
Ductile iron pipe Concrete cylinder pipe Sandy gravel soil with 1:1 side slope
Embedment Backfill and compaction
Ordinary embedment Sandy gravel soil with 1:1 side slope
Parameter values a
b
c
d
e
f
44.0 11.7 24.0 2.9 1.6 0.094
0.33 0.51 0.32 0.0018 0.0062 0.062
1.72 1.38 0.67 1.90 1.83 0.73
2.87 0.0 16.7 0.13 0.20 0.18
0.74 0.0 0.38 1.77 1.00 2.03
0.0 0.0 0.0 0.0 0.07 0.02
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WTPCC ¼ e14:444þ
0:5372 2
1:314667 Q0:881 WTP
ð3Þ
where QWTP is the capacity of the plant in MGD (million gallons per day, 1 million gallon ¼ 3785.4 m3). 3.1.4. Wastewater treatment plant construction cost Wastewater treatment plant (WWTP) construction cost is a function of the plant capacity and the treatment type (Davis and USBR, 2009). Here a sequencing batch reactor is assumed as the treatment type and more information of the WWTP construction costs for other treatment types could be found from the reference. WWTPCC ¼ ð1 þ fs Þ 12; 892; 000 Q0:6289 WWTP
ð4Þ
where QWWTP is the capacity of the plant in MGD (million gallons per day) and fs is a factor accounting for on-site solids handling (here, fs ¼ 0.0). 3.1.5. Operation unit cost The pump operation cost includes energy consumption for lifting water to demand nodes using a flat rate of $0.20/kWh. The annual required pumping energy (P ¼ Ku*Q*H/h in kW, where Ku ¼ unit conversion factor, h ¼ pump efficiency) is first estimated using the pumping flow rate (Q, operational decision) and head gained (H ); then annual pumping cost is computed by multiplying the flat rate. Unit cost of potable water treatment was assumed to be $0.30/m3. Two different unit costs were assumed for the wastewater treatment; $0.40/ m3 was assigned for river effluent treatment and slightly higher unit cost of $0.50/m3 was assigned for water reuse treatment that could be supplied to domestic non-potable uses and agricultural irrigation. Imported water from external sources was priced at unit cost of $0.75/m3. Potential conveyance structures for water importation were not explicitly considered as economic cost but included implicitly in the unit cost applied. Note the water importation cost would be system specific depending on the conveyance distance and market conditions. Here the unit cost of importing water was Table 2 Input parameters and system data for application study. Parameter
Value
Unit
Simulation period Discount rate Darcy-Weisbach friction factor, f Energy tariff Pump efficiency Water treatment unit cost Wastewater treatment unit cost For river effluent For non-potable reuse Water importation unit cost Initial population of municipal 1 at year 1 Initial population of municipal 2 at year 1 Population growth rate Per-capita water use Agricultural consumptive water use Required downstream river flow
20 5 0.02 0.20 75 0.30
year % e USD/kWh % USD/m3
0.40 0.50 0.75 100,000 150,000 2.0 400 1.2 1.0
USD/m3 USD/m3 USD/m3 e e % Liter/capita/day m3/sec m3/sec
5
assumed to be higher than local service costs; thus water importation will occur only if the local supplies are limited. The annual operation costs are converted to present worth value based on the defined planning time horizon and discount rate. The parameters used in the annual cost calculations are summarized in Table 2. 3.2. Objectives and constraints The model aims to minimize the overall system costs while meeting operation constraints. The total cost is the sum of the costs for system construction and operation over the simulation period; thus the objective function is expressed as: Minimize F ¼ CCðXconst;
t¼1 Þ þ
T X
OC Xoprt; t
ð5aÞ
t¼1
Subject to G Xconst;
t¼1 ;
Xoprt;
t
>0
ð5bÞ
where CC and OC are the system construction (capital) and operation costs, respectively. Xconst, t¼1 denotes structural decisions at initial time (t ¼ 1) and Xoprt, t denotes annual operation decisions at time t. G represents constraints for the flow requirements for all users and pressure requirements on that supply and mass balance at each location. The formulated optimization problem is a mixed integer nonlinear problem and is solved using the proposed GA-LP coupled model. GAs are stochastic search techniques based on the evolutionary mechanisms inspired by biological evolution processes, such as elitism, crossover, and mutation (Goldberg, 1989). Regarding GA processes, the best 10% of the current population are preserved as elite children to survive to the next generation. Here, varieties of crossover and mutation functions were tested as a preliminary test. The single-point crossover operator is adopted with a crossover fraction of 0.60. A Gaussian mutation operator is used for the mutation operation for the remaining individuals to introduce diversity in the population. The random nature of GAs implies that the global optimum is not guaranteed to be found, but with sufficient function realizations, near-optima are expected to be found. Several system operation constraints are posed here: (1) satisfy water demand for each end user; (2) satisfy conservation of mass at nodes; (3) meet flow requirement at defined source points; (4) restrict the amount of reclaimed water use for specified users; (5) satisfy required minimum allowable water pressure at demand nodes if needed; (6) do not exceed the capacity of the water and wastewater treatment plants; and (7) maintain minimum river flow rate at downstream location. 4. Applications 4.1. Study network The proposed GA-LP coupled optimization model was applied to a simplified water supply network. The system was simplified by lumping demand sectors and removing local distribution lines; thus only the large transmission lines were
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Fig. 2. Schematic of study network (note the numbers beside the links and nodes are pipe length (km) and elevation (m) respectively); the links are denoted from X1 to X11.
considered. However, overall system topography and component layout were remained realistic. A schematic of the study network is depicted in Fig. 2. The water system is composed of surface, and imported water sources, residential and agricultural irrigation users, and water and wastewater treatment plants. External water source can be imported at a cost per unit volume that includes the cost of conveyance system. It is assumed that the highly treated reclaimed water can be supplied to domestic users for non-potable uses, and agricultural irrigation, and to meet the downstream community's needs or environmental flows. However, the maximum limit of reclaimed water uses has been set for domestic users. That is, up to 20% of municipal demands and 30% of agricultural uses can be supplied by the reclaimed water. The objective function of the problem is to minimize the cost of construction and operation of system components as well as the cost of treating, conveying, or importing water to meet water demand. Design decisions are pipe diameters, pump design flows and heads, water and wastewater treatment plant capacities. Flow allocations for each link over the simulation period are operational decisions. Total 20-year simulation is conducted. The years are not hydrologically linked and there is no storage carryover between years, because only yields of river water supplies with no storage facilities are modeled. The infrastructure construction occurs in a first stage (i.e., current time step, t ¼ 1) in anticipation of water resources needs for subsequent years. The application network has 11 links with lengths given in Fig. 2. Eight of which are pipe connections (X1 ~ X8) along
which pump station could be built depending on energy requirement. Three potential importation paths (X9 ~ X11) from external sources are included. There are 2 treatment facilities (1 WTP and 1 WWTP) in the system. Thus, total number of structural design variables are 26 (¼8 pipe diameters þ 16 decisions for pump (¼design flow (Q) and head (H ) for each of 8 potential pumps) þ 2 treatment plant capacities). Flow allocations through 11 links are defined as operational decisions determined by mass balance constraints and unit cost of water transportation for each link. The simulation periods are 20 years thus total 220 operation decisions (¼11 links 20 years) should be determined. In total, the problem consists of 246 decision variables. Note the input parameters for the problem and system data are summarized in Table 2. 4.2. Results 4.2.1. Optimal decisions for base condition (Scenario 1) The model is programmed and simulated using MATLAB (MathWorks R2012a). The problem was run on an Intel Core i5 3.2 GHz with 4 GB of RAM and was solved in 30.8 min after twenty thousand function evaluations. Fig. 3 depicts the optimal component designs for the base condition (Scenario1, S1) in which the population growth rate, per-capita water use, and agricultural consumptive demand are assumed to be remained constant throughout the 20-yr simulation period as listed in Table 2. Based on the optimization results, link X5 is
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Fig. 3. Optimal decisions of system components for the base condition scenario.
not installed (through which the reclaimed water was supposed to be supplied to agricultural area), because treating/conveying effluent is more costly than acquiring surface water directly from the river. Hence, all the agricultural demand is satisfied by the raw water from the river for the entire simulation period. In addition, no pumping unit will be required for link X8 (transporting WWTP effluent to downstream river), since sufficient elevation difference is secured for gravity flow. Regarding water importation, Municipal Area1 is receiving outer source water from year 9 to the end of simulation period. Note the imported flow rate at year 20 is 0.19 cm, which is almost 30% of the total demand of Municipal Area 1. However, no water importation is required for Municipal Area 2 for entire period; thus, all demand is supplied from WTP for potable uses and WWTP for non-potable purposes. Total construction and operation cost for 20-year period with discount rate of 5% was $512 million as a present value. Detailed cost breakdowns for each system component are shown in Fig. 4. It is seen that the system construction costs (i.e., pipe, pump, WTP and WWTP construction costs) comprise 48.5% of total cost, while system operation costs (i.e., WTP/WWTP operation, pump operation, and water importation costs) are 51.5% of overall system cost. Among the operation costs, water and wastewater treatment facilities operation cost comprises the majority while pumping and water importation costs are relatively low. 4.2.2. Multiple scenarios and common elements Future water demand projections are inherently uncertain. As such, two more scenarios were simulated representing
potential future conditions, such as community growth projections represented by per capita water use and agricultural consumptive water demand. Scenario2 (S2) represents a severe future condition in which the per capita water use of municipal area is kept increasing over time to reach 450 lpcd at year 20 and agricultural consumptive use is assumed to be linearly increased by 10% at year 20. In contrast, Scenario3 (S3) simulates mild future condition for which the municipal water demand is decreased due to demand management and water conservation (350 lpcd at year 20) and agricultural demand is also linearly decreased by 10% at year 20. Therefore, the uncertain parameters are water demands for municipal and agricultural sectors reflected in the per capita water use and consumptive demand, respectively. Note the potential
Fig. 4. Optimal design costs for the base condition scenario.
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Table 3 Economic costs for individual scenarios. System construction cost ($M)
S1 (Base) S2 (Severe) S3 (Mild)
System operation cost ($M)
Pipe
Pump
WTP
WWTP
Pump
WTP/ WWTP
Water import
Total Cost ($M)
81.2
27.2
59.6
80.2
23.0
228.5
12.3
512.0
73.1
28.1
59.6
86.3
27.0
231.9
36.4
542.5
77.9
24.6
59.6
73.7
26.9
220.3
0.0
483.1
uncertainties in water availability caused by climate-related changes or uncertainties in imported water availability due to water market variations were not simulated in this study but can be incorporated if information is available without altering design framework. Overall system costs for the three scenarios are summarized in Table 3. For S2 (severe condition), water importation was initiated at year 6 for Municipal Area1 and continued till the end of the simulation period due to the increased water demand. For S3 (mild condition), however, no water importation was required and local demands during the simulation years were met by local supplies. Comparing system costs, S2 requires $542.5M, which is $30.5M higher than the base condition (S1, $512.0M) and the difference is mostly from the water importation cost. Total cost of S3 is $483.1 M ($28.9 M less than S1) and the reductions are from the system operation savings (e.g., no water importation). It is interesting to note that overall system construction costs (pipe, pump, WTP, and WWTP construction costs) of the three scenarios are similar; that is, $248.2M, $247.1M, and $235.9M for S1, S2, and S3, respectively. The main differences in total costs are observed from the system operation costs (WTP/WWTP and pump operation costs and water importation cost); that is, $263.7M, $295.4M, and $247.2M for S1, S2, and S3, respectively. The similarity in system construction costs of the different scenarios are confirmed in Table 4 that summarizes the optimal component sizes of the obtained three scenario designs. As seen, the optimal pipe diameters and WTP/WWTP
sizes for the three scenario designs are similar. These common construction decisions (listed in the bottom row of Table 4) from the multiple scenarios are the robust solutions that remain viable for a range of potential futures if implemented (Schwartz, 1991). These common elements narrow down the planners' decision ranges and, once implemented, ensure system's reliability against the future uncertainties. Identifying the common projects across the scenarios in planning stage helps to prioritize the capital investments and reduce potential regret and risk. The goal of scenario-based optimization is to identify sets of projects that will be viable for all potential futures and avoid over-investment and costly retrofitting. The proposed optimization model and the scenario-based planning approach will assist to make proper decisions in time-varying conditions. It should be noted that, however, there is no guarantee that the exactly common solutions would be found for all decisions across the scenarios considered. Some decisions could be common across the scenarios, some are partly common, and some decisions could be variable over the scenarios. In our simulations, it is seen that only some structural decisions are common across the scenarios and the obtained common elements would be robust over the futures considered. The point is that the process of identifying the common elements helps to narrow down the decision ranges and aids decision makers' on system planning process. This whole process is called “scenario planning” (Schwartz, 1991) and it aims for a sustainable system planning in a changing environment.
Table 4 Optimal designs for individual scenarios and common ranges. Scenarios y parameters S1 (Base) S2 (Severe) S3 (Mild) Range
Plants (m3/s)
Links X1
X2
X3
X4
X5
X6
X7
X8
WTP
WWTP
Diameter (mm) Pump (kW) Diameter (mm) Pump (kW) Diameter (mm) Pump (kW) Diameter (mm)
1200 196.0 1200 117.6 1200 117.6 1200
900 235.2 900 441.0 900 274.4 900
900 156.8 900 235.2 900 196.0 900
900 274.4 900 156.8 900 196.0 900
900 e 900 e 900 e 900
1.20
0.80
1.20
0.90
1.20
0.70
1.20
0.70 ~0.90
117.6 ~196.0
1200 441.0 900 548.8 1200 294.0 900 ~1200 294.0 ~441.0
e e e e e e No Link
Pump (kW)
1800 294.0 1500 411.6 1500 264.6 1500 ~1800 264.6 ~411.6
No Pump
156.8 ~235.2
156.8 ~274.4
No pump
235.2 ~441.0
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Fig. 5. Projected demands and water supplies for municipal areas.
4.2.3. Projected water demands/supplies and downstream river flows One of the advantages of the proposed model is to estimate annual flow allocations for each link; thus projected water demands and supplies over the simulation period can be obtained for interesting nodes. Fig. 5 shows projected water demands and supplies (broken down by supplying sources) of municipal areas for 20yr simulation period under scenarios 1 and 2 conditions. For Municipal Area 1, demands are met by three different water sources, such as potable, reclaimed, and imported water. Under base condition (S1) (Fig. 5a), water importation is initiated at year 9 and kept increasing. Overall, the majority of supplies is potable water from the river flow and portions of reclaimed and imported water increase in later years. Notably, under severe condition (S2) (Fig. 5b), the water importation starts at year 6 and the amount rapidly increases. At year 20, more than half of the demand is supplied by the imported water and portion of potable water from river decreases dramatically. The results indicate that under the rapid community growing conditions, Municipal Area 1 largely depends on imported water in the future. This is because more river flows are provided for Municipal Area 2 and agricultural demands. For Municipal Area 1, proactive demand management plans should be prepared and/or uses of reclaimed water should be encouraged by modifying the current regulations in order to reduce the dependence on the imported water. Note
that the reclaimed water can only be supplied up to 20% of municipal demands for outdoor uses following current regulations. Looking at the projected supplies for Municipal Area 2, no water importation is needed for the next 20 years (even under S2 condition). However, this area also needs efforts of demand management and stimulating reclaimed water usage to save river water source and reduce system-wide water importing expenditure. Although not presented here, under mild condition (S3), all municipal demands are supplied by local sources (river flow and reclaimed water) thus no importation is required. Fig. 6 shows projected flow rates of river at downstream for three scenarios. The minimum flow rate should be maintained for downstream community supplies and the required amount is set for 1.0 m3/s for the entire simulation period as hard constraint. As seen, the minimum flow is satisfied for entire period under three future scenarios. Under the mild condition (S3) (Fig. 6c), some surplus can flow for the next 20 years, while under severe scenario (S2) (Fig. 6b), there is no left-over flow after year 5. The downstream river flow is composed of the left-over upstream river flow (after supplying the upstream study area) and WWTP effluent produced from the upstream community. The composition of the river water would be critical for the downstream community since it is related to the water quality of the source. Under the severe (S2) scenario, the proportion of WWTP effluent is kept increasing and at year 20
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5. Conclusions
Fig. 6. Projected composition of downstream river flows.
about 45% of river water is composed of the effluent. This is because the amount of effluent increases with the demand growth in municipal area (44% of municipal demand returns to WWTP); but the reuse of reclaimed water is limited as maximum 20% of the demand. Since more river water is consumed in upstream area, the required downstream flow is increasingly supplemented by the WWTP effluent. If needed, the amount of effluent released to the downstream river should be regulated based upon the request of downstream users. In terms of the water quality and water right issues, comprehensive discussions involving a diverse group of stakeholders and system planners are required and the proposed model can aid to provide projected quantities under various future scenarios and assist the decision making process.
In a changing environment, water system planners face difficult challenges regarding significant investments of infrastructure construction and its operation for long-term sustainability. The investments are significant and poor decisions are costly in terms of economics and public confidence. Community growth rate is a key projection for construction and operation planning. In addition, the regional imbalance of community growth makes providing an adequate water supply more difficult. If a lower than expected growth occurs, constructed infrastructure will likely be oversized; while, if the implemented components are under-sized due to rapid growth, the system may be inadequate to deliver the desired level of service. In both cases, regret cost occurs and the public will lose trust in the service providers. Large-scale, long-term, and high-budget investments should be carefully determined and the sophisticated decision tools are needed to assist this highly consequential decision process. Since future conditions change, it becomes less likely to predict the future accurately. So the goal becomes to choose cost efficient robust solutions that allow flexibility as future conditions unfold. Therefore, the decision process should account for the uncertainties in the future, and the tools should be developed based on that need. The objective of this study is to develop a water infrastructure planning/management tool for long-term water sustainability with emphasis on needs for new infrastructure that is necessary to meet increasing demands. The proposed modeling tool will be able to evaluate various future scenarios and suggest potential optimal policy. As a decision supporting tool, an intelligent optimization model is proposed by coupling a genetic algorithm (GA) with linear programming (LP) model, in which one-time structural decisions and long-period operational decisions are determined simultaneously. The model was demonstrated using a simplified water supply network to find optimal policy of construction and operation decisions minimizing overall capital and operation costs. Decision variables are component sizes at the beginning year and the water allocations for each of the flow links for entire simulation time period. To account for the system uncertainties, various plausible future conditions were produced as multiple scenarios and common elements (¼decisions) over the scenarios were suggested preparing for the diverse future conditions. In addition, timevarying projected demands/supplies and river flows were predicted to investigate the potential issues of water shortage and water quality/right in coming years and suggest proactive actions for preparedness. The proposed model has several advantages for water system planning: (1) GA-LP coupled framework provides construction decisions and long-term operation schedules simultaneously; (2) it provides stakeholders and system planners with intuitive solutions; (3) the framework is intuitive and easy to implement in practice and does not require specialized optimization technique such as stochastic programming; (4) it provides view of multiple futures and solutions using scenario-based planning; (5) the common solutions found across scenarios would remain valid
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for a wide range of plausible futures; (6) it can aid in developing preparedness plans for future water shortage and water right issues involving diverse stakeholders; and (7) the model can be tailored to the specific system and various regulations and conditions can be incorporated within the model without adding complexity to the optimization framework. This study has several limitations that future research must address to improve the proposed approach; (1) uncertainties addressed here were limited to the demand projections; clearly the uncertainties in source availability will be crucial for future water planning thus must be addressed in the further study; (2) the optimization framework considers that the system design is completed in current stage (t ¼ 1) with assumption of future modifications to adapt to the evolving conditions. In practice, this process will likely be multi-staged as conditions change over time. In this case, multi-stage design and construction should be considered leading to a multi-staged optimization framework. The model proposed here is a first step for long-term planning of water supply system. It allows for the design in the relatively near future based on the best projections at the current time. The multistaged optimization approaches should be pursued since it is a fruitful area of research; (3) this study was initiated by the request of a city planner to develop a simulation model for city-wide capital improvement planning (CIP). The project is on-going and here some preliminary results were presented. Note that the researches are under way applying the proposed model to large scale water networks in order to include better representation of the system while minimizing network simplification; (4) the proposed model is mainly appropriate for the preliminary system planning under various future scenarios. Our approach would suggest better results than early LP models, but still detailed hydraulic simulations are needed to provide final solutions to be implemented; and finally (5) intensive scenario analyses should be conducted on a variety of system parameters, such as population growth patterns, water demand variations (per-capita use and spatial distribution), water source availability due to climate changes, and drought conditions.
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Acknowledgments This research was supported by Seokyeong University in 2011. References Chung, G., Lansey, K., 2009. Application of the shuffled frog leaping algorithm for the optimization of a general large-scale water Supply system. Water Resour. Manag. 23 (4), 797e823. Chung, G., Lansey, K., Bayraksan, G., 2009. Reliable water supply system design under uncertainty. Environ. Model. Softw. 24 (4), 449e462. Clark, R.M., Sivaganesan, M., Selvakumar, A., Sethi, V., 2002. Cost model for water supply distribution systems. J. Water Resour. Plan. Manag. 128 (5), 312e321. Davis, S., U.S. Bureau of Reclamation (USBR), 2009. Decision Support System for Selection of Satellite Vs. Regional Treatment for Reuse. Water Reuse Foundation, Alexandria, VA. Goldberg, D.E., 1989. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, New York. Hsiao, C., Chang, L., 2002. Dynamic optimal groundwater management with inclusion of fixed costs. J. Water Resour. Plan. Manag. 128 (1), 57e65. Krapivka, A., Ostfeld, A., 2009. Coupled genetic algorithm e linear programming scheme for least-cost pipe sizing of water distribution systems. J. Water Resour. Plan. Manag. 135 (4), 298e302. Lansey, K., Pasha, F., Pool, S., Elshorbagy, W., Uber, J., 2007. Locating satellite booster disinfectant stations. J. Water Resour. Plan. Manag. 133 (4), 372e376. Ocanas, G., Mays, L.W., 1981a. A model for water reuse planning. Water Resour. Res. 17 (1), 25e32. http://dx.doi.org/10.1029/WR017i001p00025. Ocanas, G., Mays, L.W., 1981b. Water reuse planning models: extensions and applications. Water Resour. Res. 17 (9), 1311e1327. http://dx.doi.org/ 10.1029/WR017i005p01311. Pallottino, S., Sechi, G.M., Zuddas, P., 2005. A DSS for water resources management under uncertainty by scenario analysis. J. Environ. Model. Softw. 20, 1031e1042. Ray, P.A., Kirshen, P.H., Watkins, D.W., 2012. Staged climate change adaptation planning for water supply in Amman, Jordan. J. Water Resour. Plan. Manag. 138 (5), 403e411. Schwartz, P., 1991. The Art of the Long View. Doubleday, New York. Walski, T.M., et al., 1987. Battle of the network models: Epilogue. J. Water Resour. Plan. Manag. 113 (2), 191e203. Watkins, D., McKinney, D., Lasdon, L., Nielsen, S., Martin, Q., 2000. A scenario-based stochastic programming model for water supplies from the highland lakes. Intl. Trans. Op. Res. 7, 211e230.
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