^{1, 2}

^{1}

^{1}

^{2}

This paper analyzes the site selection problems of water treatment plants by utilizing the set covering model. Fully consider the influence of the pipe network arrangement on the site selection when confirming the covering radius, analyze the best water supply radius of water treatment plants combining investment benefits and pipe network optimization theory, and take the best water supply radius as the covering radius. Make the pipe network optimization nest into the site selection problem meanwhile confirming the covering radius, which fully reflect the viewpoints of the integrated logistics arrangement system. Considering the multiple solutions of the set covering model, this paper introduces the model of which the cost’s present value is minimum to make the quadratic optimization and get the best site selection results of water treatment plant. At last, this paper verifies the model by combining with the cases of water supply project construction of a county; the results prove that the model is feasible and effective. This paper expects to provide some reference for the planning design of regionally centralized water supply projects concerning villages and small towns and the site selection and construction of water treatment plant.

Construction of the logistics system is of great significance to improve the level of economic development within the region and to meet the growing demand of people. Among them, the location of logistics distribution center has direct bearing on whether the logistics system is able to minimize transportation cost to the utmost, thereby reducing operating cost of the system. As a special logistics system, rural water supply project delivers special material which is water resource meeting certain health conditions for residents. This special “cargo” transportation requires special materials pipelines as transport carrier. The logistics system is composed of three subsystems, water intake engineering subsystem, the subsystem of pressuring and chlorine disinfection in water purification plant, and water distribution engineering subsystem. The section of water purification plant is equivalent to the distribution center or transfer station in general logistics system. As the location of the distribution center in the logistics system is an important decision problem, in rural water supply system, water purification plant sitting is also related to that whether to the maximum extent it can meet water demand with minimal investment in pipeline construction in rural water supply system.

Common location problem is to determine the optimal number and best location of new facilities in the candidate set of points, and the goal is to minimize the construction investment and operating cost. Since a German Weber raised the issue in the 19th century, the study on site selection was in full swing. Scholars from various countries in this field have already achieved many important results. AIKENS.CH gave nine basic site location models in his research [

Significant difference between water supply engineering system and general transport logistics system lies in its carrier medium. Layout of pipeline and diameter of pipes selection directly affect construction investment, while construction investment has a direct impact on the economic efficiency of the project. Common logistics model generally assumed that delivery route from the facility or distribution center to demand point is radial [

Whether a water supply project can achieve the expected economic benefits is closely related with its subsidiary pipeline system optimized layout. Combining the path arrangement with facility location to research has attracted more and more attention of scholars. Sun and Gao [

In this paper, covering model for the water purification plant location problem is studied. In determining the coverage radius, the impact of network optimization problems on the site selection is considered, and meanwhile economic and engineering factors based on planned investment returns during the period are taken into consideration. Combined with the water supply network system optimization design theory, the distribution network optimization and best water supply radius are connected to achieve nesting between water pipe network optimization model and location selection model, so that the coverage radius has more theoretical and practical significance and also is in line with the integrated logistics management system. Due to the characteristics of the set covering model, the results are a number of possible solutions rather than single optimal solution. Therefore, this paper introduces the model of minimum present value, in order to optimize the site selection secondly to get the best location results. Finally, through a practical calculation example, the feasibility and practicality of the nested site selection model is demonstrated.

This part firstly analyzes the investment benefits of the water treatment plant based on the income of the water treatment, the construction expenses of the water treatment plant, investment in the infrastructure of the pine network, and the energy expenses of the pump stations and establishes the present value model of project benefits during the planning period. It makes the optimization design for the affiliated pipe network of the water treatment plant when considering the investment in the infrastructure of the pine network, which achieved the combination of the engineering factor and economy analysis. It gets the hydraulic loss along the pipe network and the functional relation between the investment in the infrastructure and the water supply radius through fitting, so as to get the functional expression between the present earning value and the water supply radius during the planning period of the water treatment plant and confirms the best water supply radius. This paper expects to provide a basis for the establishment of quadratic optimization model of the site selection by using NPV maximum water supply radius or the water supply radius with the minimum average total cost.

In order to save the power expenses in rural water supply projects, we usually adopt the water supply mode which takes the plant as the center and radiates in a circular way [

Suppose that the population within the water supply area of a water treatment plant is averagely distributed and that adopted water supply mode is taking the plant as the center and radiating in a circular way; besides, suppose the water supply duration is 15 years. The model for present earning value of water treatment plants within planning periods may be expressed as follows:
^{3}; ^{2}; ^{3}/s of hydraulic pressure by 1 m H_{2}O ^{3}/s).

For any one pipe section, in the case that

As the flow distribution of each pipe section in tree-like pipe network for single-water source is unique, the formula above may be utilized to determine the relationship between water supply radius and net present value of water pipe network within one area, thereby, determining the most economical water supply radius. In rural areas, the users of water supply projects are dispersed in many spots and wide areas, and layout modes for water pipe network are various, so that it is impossible to accurately calculate the relationship between water a variety of supply pipe network and relevant hydraulic parameters [

In determining a network layout mode, we adopt the method of minimal spanning tree [

In Figure

The schematic diagram for the minimal spanning trees between each spot in need of water and the water plant within one area.

After flow of each main pipe is determined according to node flow balance condition, we may utilize investment in infrastructure construction and operating cost (electric charge of water pumps) of pipe network as objective function to determine the economical pipe diameters of each main pipe; namely, before the optimal water supply radius is determined, we should take into account the configuration and optimization of affiliated pipe network in advance. Due to various service radiuses of water treatment plants, they also have various layout modes and scale of affiliated pipe network; when water supply radiuses differ, the economical pipe diameters and head loss of pipe sections in the same position are correspondingly different. Let us take the single-water source tree-like network in Figure

The function expression of the sum between the investment in infrastructure construction and operating cost of pipe network is as follows:

To obtain the partial derivative of function

Using the formula above and the above-mentioned constraint equation, we may successively obtain the values of

The economical pipe diameter ^{3}/s), and

Use MATLAB to fit the obtained results, respectively, after getting the hydraulic loss along the pipe network and the functional relation between the investment in the infrastructure and the water supply radius; the functional expression between the present earning value and water supply radius during the planning period of the water treatment plant can also be gained according to the above mentioned present value model. Then we could obtain the best water supply radius with the maximum NPV. Similarly, according to the functional relation between the total cost of the average water production and water treatment volume, we could work out the best water production volume and the best water supply radius when the total cost of unit water production is minimum. The water supply radius under the maximal condition of NPV and the water supply radius under the minimum condition of the unit water production cost have practical significance of their own. If the maximum present earnings of the project shall be realized in the planning period, the water supply scale can be confirmed by the water supply radius under the maximum condition of NPV. If the actual project scale cannot reach this construction scale for the actual massive investment, excessive loan interest, and complexity of the construction conditions, the water supply scale can be confirmed through the water supply radius under the minimum condition of the unit water supply cost. At this moment the total unit water production reaches the minimum; the input-output ratio reaches the maximum and the economic efficiency of the water treatment plant reaches the maximum.

Applying the most economical method of water supply radius identified above, engineering factor (actual pipe network layout) and economic analysis (analysis of investment returns) can be combined reasonably to get the best water radius in sense of the practical works. Use set covering model to determine waterworks site choice of site means to use as little waterworks as possible to cover water demand points. This reduces the water treatment plant construction cost and operating cost. This model nests network optimization model with set covering secondary optimization model and the water purification plant site is built on the basis of network optimization, considering the effect of pipeline distribution layout on water plant construction and investment returns in order to make site model closer to practical engineering.

Assume that within a water area, there are m water demand points, set covering model is as follows:

In the formula,

The objective function is to select preferably site which can cover m waterworks points in the minimum quantity from the existing m water demand points; constraint equation (

To solve the above set covering model with constraints extremes, branch and bound method can be used for accurate calculation [

When solving scale becomes larger, the collection of site selection of plant solved by set covering model is nonunique. After the position and the number of water purification plant initially identified, use the minimum model of present value to make secondary optimization of water purification plant sitting point and coverage. With this model, a number of possible solutions can be further optimized, resulting in the rank of present value of the water site collection, where we can choose the present value of the minimum cost as the optimal solution. When calculating the length of pipeline lying, this model is unlike the general logistics distribution center location model which assumes that distribution from the facility or distribution center to demand points (customer sites) is radiation-like, otherwise, it is based on the minimum spanning tree model taking optimization of water distribution pipelines into consideration.

The minimum cost model of present value is as follows:

Constraint equation is as follows:
^{3}/km) where ^{3}/d) ^{3}/km); ^{3}/d) which plant ^{3}/d); ^{3}/d);

The objective function is the minimum model of present value in planned useful life, covering the present value of water costs in rural water supply and distribution system (including the cost of water demand point of water distribution from water purification plants and the present value of taking water from water source), the present value of the investment and present value of construction investment of water distribution network infrastructure. Constraint (

Set the feasible solution achieved by set covering model as minimum cost optimization model, the best result of purification plant siting can be obtained. The following example demonstrates the feasibility and practicality on basis of secondary optimization model of the most economical water supply radius.

A county plans to build water supply system within geographic scope and needs to establish some water treatment plants within water supply region. According to population distribution within the region, permanent residents of the county are clustered as per township into Jinjiang town

Firstly, determine the most economical water supply radius of the county’s water supply project. Assume that county distribution within the water supply range and the water demand situation are known. By calculating hydraulic parameters for each pipe segment in different water radius, we get loss value on water conservancy project and cost of the pipe network of radius of 4 km, 6 km, 8 km, and 10 km. The functional relationship between loss value on water conservancy project and investment in infrastructure and water supply radius is calculated as follows:

Set

Figure ^{3}/s, NPV reaches its maximum, the corresponding water radius is about 20 km, and the present value of the project revenue is approximately 1.2 × 104 million. As water radius continues to increase, NPV decreases. When ^{3}/s, and the corresponding water radius is 12.4 km.

Functional relationships between water volume and NPV, total cost, and unit total cost.

Taking into account the initial investment to maximize present value of earnings in the realization of the project within planning period is huge, in order to adapt to the water demand size of the county, water supply radius of 12.4 km achieves smallest total cost of the unit water supply as set covering model coverage radius. In the above set covering model, screened plant ^{3}/s. Take the average integrated unit price of UPVC pipeline construction is 130 yuan/m and the average integrated unit price of ductile iron pipeline construction is 950 yuan/m, ^{3}/km. Write programs using MATLAB to solve optimization. The result shows that the total cost of water supply system in planned life (15 years) within the county

Specific location of water purification plant and its services range.

In this paper, set covering model represents water purification plant location problem. In determining its coverage radius, impact of pipeline layout on the site selection is taken into consideration, and investment returns and the pipe network optimization theory are combined to analyze the best radius of the water purification plant, which is set as the coverage radius. In rural water supply project, as a kind of special logistics system, determination of the coverage radius is not based on transcendental experience, which is more theoretical and practical. When determining the radius of coverage, we should fully reflect the views of integrated logistics management system and combine pipelines optimization and location. Taking into account of multiple solutions of set covering model, this paper introduces secondary optimization of minimum cost model of the present value to obtain the best waterworks site. Finally, this paper combines with a county water supply project example to validate the model and the experimental results show that the proposed model is feasible and effective. So due to the advantages, decision authorities can introduce the specific model to assist them to arrange the county-level water supply infrastructure, which is more scientific and precise than depending just on experience. This model assumes that there is no other water plant in the region; that is, this water plant is the first entrant to the market in the region without other competitors. Actually, competitors are prevalent and, therefore, the existing water treatment plant competitors need to be taken into account. Thus, the model needs to be furthermost developed to accommodate to a wider range of circumstances.

The authors declare that there is no conflict of interests regarding the publication of this paper.