Performance index model of simple waterworks system

This research intends to build a performance index model of the simple waterworks system, in Indonesia known as Sistem Penyediaan Air Sedehana (SiPAS). This research used 25 SiPAS located across the Brantas River Area in East Java Province, Indonesia, to build the SiPAS performance index model. The Brantas River Area is vital for East Java Province to supply clean water for all inhabitants dwelling in urban and rural areas. The Brantas River Area is a regional unit of water resources management with an area of 1,410,300 hectares that consists of 220 watersheds, including the Brantas watershed as the most significant watershed, four small watersheds in the northern and the estuary in the Java Sea, and 215 small watersheds in the southern and the estuary in the Indian Ocean. Therefore, this research used the Generalized Reduced Gradient (GRG) method to build the SiPAS performance index model using technical, social, and management variables. The results of this research derived the coefficients of technical, social, and management aspects through GRG data processing are 0.7833, 0.1011, and 0.1156, sequentially. The measurement with the SiPAS performance index model can evaluate performance and serve as a successful parameter in the operation and maintenance of SiPAS to provide clean water.


Introduction
The increasing need for limited water resources is caused by climate change, population growth, and urbanization, which causes a significant challenge to the water supply system, mainly in developed countries [1], [2].The water resources system in some regions in the world experiences difficulty in fulfilling drinking water needs and basic sanitation; even the water resources system in a region cannot support and maintain the touch one biodiversity ecosystem [3], [4].Louck and van Beek mentioned the typical causes of the disability of the water resources system for fulfilling the diverse water needs, such as the inaccuracy of infrastructure or inadequate and or damage, withdrawal of excessive river flow, change of water and sediment flow system, etc.The water resources system's inability to fulfill water needs often reflects the failure in design, management, and decision-making.
The regulation and management of water resources are essential to be regulated by a country because the development level of a country is determined by good drinking water supply for the household as a simple waterworks system (SiPAS) as industry needs [5], [6].Therefore, fulfilling water needs is the main priority, so handling the clean water sector becomes necessary to get special attention because water availability is directly related to the survival of all creatures in the world [7].The priority of the Indonesian Republic, as written in chapter 8 verses (2) and (4) 2019, is related to civilians' right over water by prioritizing the water in the river region according to their authority [8].The supply of water needed in the Brantas River Area is crucial, remembering that the need for water constantly increases from time to time.The need for water is not only because of the increasing population that needs water but also because of the increasing intensity and need for diverse water.However, the potency and utilization of available water for human needs have the remaining amount or volume [9], [10].The development of big cities that are flowed by the Brantas River flow causes the need for an increase of raw water for drinking water because the level of water needed is closely related to population growth.
The alternative solution to national strategic issues in the Brantas River Area is to make a simple waterworks system to be able to accommodate the service in the area that is unaffordable the service from the Regional Company of Drinking Water, known as Perusahaan Daerah Air Minum (PDAM).The situation needs a simple water supply system for distributing water to the downstream users [11], [12]; one of them is the technology of a simple water processing installation system on the SiPAS.Clean water supplies with SiPAS have the advantage of using natural water resources as raw water sources to provide clean water demand, which is considered convenient as it does not require complex and sophisticated infrastructure or good water quality.Thus, SiPAS can be an alternative for supplying clean water to areas not covered by PDAM services near the upstream and downstream.The success level of a simple raw water supply and processing system can be measured through the evaluation of performance [13].The simple performance index model is needed to measure and optimize the SiPAS to sustain the water supply.
Hence, this research is designed to build an equation for measuring and optimizing the water supply performance of SiPAS by evaluating SiPAS with this performance index model.This research focuses on how accurate the model built to determine the water supply performance of SiPAS is.

Research Location
Indonesian Ministry of Public Works and Housing has built 31 SiPAS spread across the Brantas River Area, East Java Province, Indonesia (see Figure 1).However, this research only used 25 SiPAS distributed in one city and five regencies in East Java Province, including Batu City and Malang, Blitar, Jombang, Kediri, and Nganjuk Regencies.
To build a performance index model of SiPAS, the first 25 SiPAS in Figure 1  Furthermore, the following study will use the rest of the five SiPAS in Tulungagung Regency (points 26 to 31) for performance index model validation.

Simple Waterworks System (SiPAS)
According to Republic Indonesia Government Regulation 16/2005, a clean water supply system is a union of physical or technical systems and non-physical drinking water infrastructure and facilities [14].Whereas SiPAS is a water supply system with no sophisticated piping network and generally can be implemented by people independently and relatively using simple technology.Water supply development is an activity to develop, expand, and/or increase the physical or technical and non-physical systems, such as institution, management, monetary, societal role, and legal.This development is a complete unit to implement the clean water supply to society towards better conditions.
The SiPAS development must be under the government's authority to equally fulfill the basic human needs of clean water [15], [16] by stimulating the government to facilitate the SiPAS development, especially in the rural areas that have not yet met PDAM services.Though the government has built a few SiPAS in several areas that have not yet been covered by PDAM, the operation, and maintenance of SiPAS need to be evaluated with a performance index that has not yet been regulated to manage the SiPAS to be sustainable.

SiPAS Performance
The success level of SiPAS management can be measured by evaluating its performance index.Performance is a work result or production that has a strong relation to the strategic aim of the organization, user satisfaction, and perhaps a contribution to the economy.The performance indicator illustrates the SiPAS in supplying clean water conditions so the local community and stakeholders can determine the current condition to make a good plan for maintaining the SiPAS performance to be sustainable [17].

Indicators and Variables of SiPAS Performance
The SiPAS performance evaluation is based on the three variable aspects of technical, social, and management.Each variable owned its chosen indicators from the data processing done by Hidayat et al. in 2023 using the Structural Equation Model based on the Partial Least Squares (SEM-PLS) method in the previous study [18].
IOP Publishing doi:10.1088/1755-1315/1311/1/0120424 2.4.1.Technical Aspect.The technical aspects in this research relate to the physical realization of a simple water supply system by reviewing the physical infrastructure, services, operational, environmental degradation, and maintenance as dimensions of the technical aspects.
2.4.2.Social Aspect.The social aspects in this study relate to the dimensions of economic and sociocultural activities of the inhabitants in the Brantas River Area as users of SiPAS.
2.4.3.Management Aspect.The management aspect is needed to show the SiPAS operational, and management run by a local organization of each SiPAS called Himpunan Penduduk Pengguna Air Minum (HIPPAM).This aspect consists of three dimensions, including water management organization, human resources, and monetary.

Modeling the SiPAS Performance Index
This research modeled the performance index of SiPAS using a linear equation to find the correlation among the three variables, specifically variables of the technical aspect, social aspect, and management aspect, based on the SEM-PLS method in the previous study.The linear equation is preferred to model the SiPAS performance index as the linear equation is more straightforward to validate, has a simple and constant form, and has more constraining assumptions than the non-linear equation.Therefore, the linear equation formula used in modeling the SiPAS performance index in this research is as follows: SiPAS Performance Index = a PI Technical + b PI Social + c PI Management (1) where: PI Technical = Performance Index Technical PI Social = Performance Index Social PI Management = Performance Index Management a = Index coefficient of Technical Aspect b = Index coefficient of Social Aspect c = Index coefficient of Management Aspect Afterward, the method used to model the SiPAS performance index is the Generalized Reduced Gradient Method (GRG), a solver for multivariable linear equation designed to optimize the value of each variable, dimension, and indicator [19], following the conditions in Brantas River Area (see Figure 2).The GRG method tries to get iteration results with the minimum relative error according to the specified statistical limits.In analyzing the GRG method, the constraint applied in this research is as follows: 1. Performance Index Technical ≤ 1 2. Performance Index Social ≤ 1 3. Performance Index Management ≤ 1 4. ∑ Technical Dimensions = 1 5. ∑ Social Dimensions = 1 6.∑ Management Dimensions = 1 7. 1 ≤ Performance Index ≤ 5 8. a + b + c = 1 In building the SiPAS performance index model, the processes are as follows: a.Each indicator multiplies by the index coefficient.b.Sum up the multiplication results of the values and coefficients on all indicators.c.Multiply the total by 20%, and the percentage calculated follows the categorization of the level of the SiPAS performance index.

Level of SiPAS Performance Index
Based on the BPPSPAM [13], the performance indicator's weight, standard, and standard value are the reference values used for analyzing the performance value with the same or different size for every performance variable.Aspect weight is the weight number of each aspect.The indicator is the performance indicator of each aspect.Weight is the weight value of each performance indicator.The indicator value is the standard value of each indicator.Evaluation is carried out in every indicator and multiplied by the weight.Then there is carried out the numbering of multiplication between the value and the weight in all of the indicator and the result is multiplied by 20% and to be compared with the criteria of performance result as follow: 100% is "Excellent", 80% -<100% is "Good", 60% -<80 is "Fair", 40% -<60% is "Poor", and <40% is "Bad".

Results and Discussion
The     2023) processed the data using the SEM-PLS method to eliminate non-or less suitable indicators for modeling a simple waterworks system performance index in the Brantas River Area.As a result, this SiPAS performance index model uses technical, social, and management aspects as variables in this research.Each aspect has several dimensions with indicators based on the data processing results using the SEM-PLS method (see Table 1).
Furthermore, the chosen indicators derived from the SEM-PLS analysis were subsequently used to model the SiPAS performance index using the Generalized Reduced Gradient (GRG) Non-Linear method.As a solver method, GRG Non-Linear can optimize the determination of the SiPAS performance index model with non-linear objectives and/or constraints, or both.The analysis with the GRG Non-Linear method is based on technical, social, and management aspects and is used to describe the relations among the variables.The results due to the process of using the GRG Non-Linear method based on each variable are as follows: a. Technical Aspect The performance index equation for the technical aspect that is formed is arranged in the formula as follows: The differentiations are as follows: T 3 = (a 3.1 x T 3.1 ) + (a 3.2 x T 3.2 ) + (a 3.3 x T 3.3 ) T 4 = (a 4.1 x T 4.1 ) + (a 4.2 x T 4.2 ) ( T 5 = (a 5.1 x T 5.1 ) + (a 5.2 x T 5.2 ) + (a 5.3 x T 5.3 ) The boundary conditions are as follows: 1. Performance Index Technical ≤ 1 (8) where: PI Technical = Performance Index Technical a n ; a n.n = Coefficients among the dimensions; and coefficients among indicators T 1 ; T 2 ; T 3 ; T 4 ; T 5 ; = Physical Infrastructure; Service; Operational; Environmental Degradation and Maintenance T 1.2 ; T 1.3 ; T 1.4 ; T b. Social Aspect The formula of the performance index for the social aspect that is formed is arranged as follows: Performance Index Social = (b 1 x S 1 ) + (b 2 x S 2 ) ( The differentiations are as follows: The boundary conditions are as follows: c. Management Aspect The formula of the performance index for the management aspect that is formed is arranged as follows: With the differentiation: (31) The process results of data analysis by using the GRG Non-Linear on the three research variables produced the performance index model of the simple waterworks system as follows: The highest to lowest performance index coefficient values from GRG Non-Linear data processing shows that the technical aspect has the highest value, followed by the management aspect, and then the social aspect with the values of 0.7833, 0.1156, and 0.1011, sequentially.The results of the GRG Non-Linear method indicate that the technical aspect has a dominant role in measuring the SiPAS performance as the indicator variants in measuring are more objective than the other two aspects so that assessment of the technical aspect can assess SiPAS performance efficiently and effectively [19], [20].Nonetheless, considering social and management aspects is also essential to improve the SiPAS operations and maintenance.This research's SiPAS performance index model has components of mutually interrelated variables that can represent SiPAS performance.These three aspects are variables that can be optimized to obtain maximum performance results.The authors believe optimizing technical aspects is the most appropriate way to achieve maximum performance, followed by management and social aspects.A system will run best if all stakeholders collaborate well together to achieve optimal performance.
Regarding the research limitations, note that the SiPAS performance index model is based on a specific set of variables and may not apply to all scenarios.In addition, the model's effectiveness may be limited by factors such as data quality and availability and the system's complexity being analyzed.For future research, it would be insightful to explore the use of alternative models or approaches to measure SiPAS performance.In addition, further research is possible by examining the accuracy of the built SiPAS performance index model with other SiPAS apart from the current model builder.

Figure 1 .
Figure 1.Distribution of SiPAS Points in Brantas River Area, East Java, Indonesia

Figure 2 .
Figure 2. Modeling Methods of SiPAS Performance Index performance index model of SiPAS in the Brantas River Area is built based on technical, social, and management variables.Each variable of this research consists of several indicators that have already been derived from the SEM-PLS process that was done in previous research by Hidayat et al. in 2023 [18].Previously, by Hidayat et al. in 2023, data processing with the SEM-PLS method used three aspects, including aspects of Technical, Social, and Management, wherein each aspect consists of several dimensions (see Figure 3).

Figure 3 .
Figure 3. Aspects and Dimensions in the Research of Hidayat et al. (2023) 3 HIPPAM's Ability to Develop the Assets or Budget for Infrastructure Needs As shown in Figure 3, the Technical Aspect is formed from five dimensions, including Physical Infrastructure with seven indicators, Service with four indicators, Operational with eight indicators, Environmental Degradation with two indicators, and Maintenance with three indicators.The Social Aspect is formed from two dimensions, including Economic with two indicators and Community Socio-Culture with four indicators.The Management Aspect is formed from three dimensions, including the dimensions of Water Management Organization with two indicators, Human Resources with two indicators, and Monetary with three indicators.Through the indicators of every dimension in these aspects, Hidayat et al. ( ConclusionsThe Performance Index Model for SiPAS in the Brantas River Area is determined from the GRG method.The Simple Water Supply System Performance Index model of each aspect is as follows: PI Technical = 0.3901 T 1 + 0.1139 T 2 + 0.1818 T 3 + 0.1503 T 4 + 0.1639 Combining the index models from the technical, social, and management aspects will result in a holistic SiPAS performance index model as follows:SiPAS Performance Index = 0.7833 PI Technical + 0.1011 PI Social + 0.1156 PI Management(39) in Laws No. 17, 1311 (2024) 012042

Table 1 .
Indicators and Variables of the SiPAS Performance Index Model in the Brantas River Area