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Urban water utility (UWU) regulation has been a potential practice in the water industry for years. This is because UWUs operate in an environment without competitors, and regulating them in a competitive scenario under sunshine regulation helps UWUs simulate the best management strategies. During efficiency assessment, the selection of the best, intermediate and least performing UWUs involves averaging scores of many efficiency assessment criteria analysed separately. This study expands a UWU efficiency assessment based on attaining service-level-benchmark and agreed target-level criteria using network data envelopment analysis (NDEA) for ratios. The assessment shows that the average of efficiencies of the two criteria identify a UWU with the best and worst performance in selected key indicators.

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  • Utility benchmarking in a competitive scenario using DEA for ratios.

  • Regulation with performance improvement.

  • Employment of service benchmark approach to analyze a utility's efficiency.

  • Selection of the most efficient utility using non-parametric method.

  • Application of Network DEA in regulation of a water utility.

network DEA for ratios, service level benchmark, water utility regulation, yardstick competition regime
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Gidion et al. (2019a) developed network data envelopment analysis (NDEA) models used for benchmarking urban water utility (UWU) efficiency in a competitive scenario like empirical methods considering a criterion of a UWU outperforming agreed targets. For many years empirical methods have been employed for benchmarking a UWU's performance in a competitive scenario by average scores of multiple criteria (see Gidion et al. (2019b)). This means that being benchmarked, in the first place, by outperforming targets alone as proposed by Gidion et al. (2019a) is not a guarantee that a UWU is better than others. For example, using targets alone as a criterion in assessment of UWU's efficiencies, a UWU with 60% non-revenue water (NRW) can outperform a target of 50% NRW easily compared with a UWU with 25% NRW outperforming 20% NRW. Applying a single criterion in efficiency assessment makes a UWU with 25% NRW the worst performer compared with a UWU with 60% NRW. It is well known that a UWU possesses long-term management techniques (Demerjian et al. 2012) in which regulators employ assessment criteria to benchmark the UWU's efficiency during assessment (Rezaei 2016). Thus, enumerating the best, medium and least performer using the NDEA methodology developed by Gidion et al. (2019a), the assessment should consider the level of UWU efficiency achieved by outperforming targets and other criteria in the efficiency assessment year. A UWU is considered efficient when it meets or outperforms targets and other criteria settings required by the regulator.

This study has developed a stepwise efficiency assessment methodology that is used together with Gidion et al. (2019a) to generate a UWU efficiency; the average of efficiencies generated in Gidion et al. (2019a) and a stepwise approach ascertain the best UWU score in efficiency and performance indicators. The efficiency assessment approach incorporates the outperforming of targets and the ability of a UWU to attain the service-level benchmark in efficiency assessment. DEA is a global efficiency assessment tool (Aparicio & Pastor 2014), and it is envisaged that regulators sharing the same efficiency benchmarking process can establish a platform for UWU efficiency assessment between countries and share the best management strategies among countries' UWUs for sustainable water services delivery.

To simulate the best performance, regulators employ the sunshine regulation approach to announce the best, intermediate and weakest performing UWUs in public as a harassment technique to help inefficient UWUs improve performance in the next assessment period (Revelli 2006; Savva et al. 2019). The use of empirical analysis, the competitive efficiencies benchmarking scenario and sunshine regulation has substantially improved utilities' performance. However, beside the benefit of employing performance indicators (PIs) during UWU benchmarking, empirical analysis is prone to errors and favouritism arises from assumptions which might put an inefficient UWU in first place (Berg & Lin 2008). The backlog does not allow the use of empirical methods to investigate UWU efficiencies between countries (Pinto et al. 2017a). Conversely to the weaknesses observed, regulators still employ empirical analysis as the best option rather than standard DEA (Cabrera et al. 2018). This is due to the incapability of handling PIs in standard DEA for absolute data and the efficiency clustering benchmark (Dalen 1998). Although assessing UWU efficiency based on outperforming targets is the best approach, using it alone can make an inefficient UWU the best out of a group of UWUs. Thus, assessing the performance of UWUs while incorporating multi-efficiency criteria helps identify the best, intermediate and worst performing UWUs among the assessed group. The use of NDEA for ratios can simulate regulators’ attention to use DEA in UWU efficiency assessment and improve performance even in an efficiency clustering benchmarking environment. As introduced earlier, this study aims at presenting a stepwise methodology that allows NDEA for ratios to benchmark a UWU efficiency in a competitive scenario using PIs as production variables and overcoming a situation of relying on targets alone as efficiency assessment criteria. Firstly, the current study analysis uses one year of information with targets excluded in the analysis; secondly, an analysis of Gidion et al. (2019a) that uses two years of ratio data information and targets as controlling factors is employed to produce the average of efficiencies of the same UWU. The resulting average efficiency is a UWU efficiency.

DEA is a non-parametric method that benchmarks a utility efficiency by enveloping a large number of input and output variables (Boloori et al. 2016). DEA estimates a UWU efficiency in comparison with other UWUs by prioritising highest to lowest input/output score in a black box (Li et al. 2012; Liu & Wang 2018). Constant returns to scale (CRS) and variable returns to scale (VRS) are the DEA technology most used in the water industry (Thanassoulis 2000). However, UWUs operate under VRS technology (Berg & Lin 2008). Charnes et al. (1978) and Banker et al. (1984) respectively developed the CRS and VRS models that utilise absolute data for generating the efficiency of a decision-making unit (DMU, referred to as UWU in this study); the nature of UWU operations signifies the importance of using ratios rather than absolute information in exploring efficiency- and management-specific features. DEA for absolute data uses absolute variables which do not ascertain the level of efficiency achieved when it comes to efficiency comparison in an operational environment without competitors; DEA for ratios gives regulators and researchers a holistic efficiency comparison through exploration of PIs' specific features (Gidion et al. 2019a, 2019b). A UWU operates in an environment without competitors (Pinto et al. 2017b), thus, regulating a group of UWUs requires an approach that benchmarks UWUs in a competitive scenario which identifies UWUs with outstanding PI scores to help inefficient UWUs to learn management features from the efficient UWU.

It is well known that tackling the level of one negative PI increases the level of many positive indicators and improvement of one output variable has an impact on another input variable level (Vilanova et al. 2015). For example, the reduction of non-revenue water (NRW) improves revenue collection efficiency (González-Gómez et al. 2011) and increases service coverage (Kulshrestha & Vishwakarma 2013), and improvement of revenue collection efficiency does improve operational ratio (Marques & Monteiro 2001). The benchmarking process of this study focuses on identifying a UWU with the best production variables’ management so as to simulate management sharing strategies between weakly, intermediate and best performing UWUs and also the reliability of DEA for ratios to benchmark a utility efficiency. Liu & Wang (2018) investigated decision-making units (DMUs) using the upper and lower bounds of the normalised efficiency in DEA for absolute data. The analysis showed that the best and worst normalised efficiency interval can be achieved simultaneously when evaluating DMUs using the constructed upper and lower bounds. The analysis approach is part of an ongoing assessment debate when absolute functions are incorporated to investigate a DMU efficiency using DEA for ratios (Olesen et al. 2017).

The employment of ratios or absolute data or both information in UWU efficiency assessment consideration is undeniable. The development of DEA for ratios originally started in Hollingsworth & Smith (2003) when they spotted a negative effect of ratios used in DEA for absolute data during efficiency assessment (Hatami-Marbini & Toloo 2019) and proposed a variable-returns-to-scale DEA technology formally developed in Banker et al. (1984) to overcome the underlying ratio production functions. Later, using suggestions of Hollingsworth & Smith (2003), Emrouznejad & Amin (2009) extended the DEA models of Banker et al. (1984) for absolute data into DEA for ratios employing absolute data and ratio production functions. However, in other circumstances absolute information might not be available with ratios for analysis, thus Olesen et al. (2015) originally developed ratio-CRS and ratio-VRS models that benchmark a DMU efficiency excluding absolute data. Olesen et al. (2017) examined efficiency computation using DEA for ratios with ratio and absolute production functions, and the study observed that with absolute information it is possible for an efficient DMU to be identified as inefficient when absolute and ratio functions are used together. Based on this finding, Hatami-Marbini & Toloo (2019) revisited the ratio-VRS (R-VRS) models of Emrouznejad & Amin (2009), improved identified flaws and extended DEA for ratios to overcome the identified problem observed in Olesen et al. (2017).

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Materials/data

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This study uses information published in Gidion et al. (2019a) to present a UWU efficiency assessment. A UWU operates in an environment without competitors, and regulators use a web-based information system to collect UWUs’ operational information, convert it into PIs and rank UWUs' performance in a competitive scenario using empirical methods. For example, the Energy and Water Utilities Regulatory Authority (EWURA) of Tanzania employs MajIS (water utility information system) to collect technical, commercial and financial information and convert it to specific key PIs (KPIs) before analysing a UWU's performance. The process involves extraction of information from the web-based system, importing it into a spreadsheet, processing it and exporting the KPIs into empirical methods developed to rank UWUs’ performance. Because the process is manual, during information export and analysis, data-handling errors, tampering with information and favouritism might happen (Berg 2010).

The empirical analysis approach used by the EWURA uses information similar to that proposed in Olesen et al. (2015) during a UWU's efficiency assessment. However, Olesen et al. (2015) benchmark a utility efficiency using a black-box technology that avoids errors due to favouritism. Empirical methodologies use a fixed weighted score in an analysis to rank a utility's performance which increases chances of favouritism. Based on these descriptions, using DEA for ratios that utilise ratio production information alone is not of any importance in the water industry, and the use of DEA models that automatically convert absolute numbers into ratios, and employ absolute data and ratios to rank a UWU's efficiency is of particular importance. Thus, the study employs the models of Hatami-Marbini & Toloo (2019), improved from the study of Emrouznejad & Amin (2009), as the best approach to avoid errors of data-handling and tampering with information during UWU efficiency assessment. Beside the benefit of avoiding data-handling errors or tampering with ratios in the efficiency assessment, the use of raw and converted information creates trust in efficiency results compared with exported ratio information alone. The analysis uses the following six production variables and associated information retrieved from Gidion et al. (2019a) to demonstrate the analysis.

  • (I)A: Non-revenue water (NRW, %) is the ratio of the difference between the volume of water produced and actual revenue volume of water to the volume of water produced by a utility. The difference between the volume of the water produced and actual revenue volume of water is referred to as an absolute number.

  • (I)D: Personnel expenditure (%) is the personnel expenditure expressed as a percentage of total revenue collection. Personnel expenditure is an absolute variable.

  • (I)E: Staff/1,000 connections (FTE/1,000 Con) is an indicator that measures a ratio of staff distribution per available connections/customers. The number of staff is an absolute variable.

  • (O)A: The proportion of the population served with water (%) is the percentage of population connected to water services to the total population of the area with water service extension. The population serviced is an absolute variable.

  • (O)B: Average hours of supply (%) is the percentage of average daily hours used to pressurise the system. The actual average water supply hours are counted as an absolute variable.

  • (O)C: Metering ratio (%) is the ratio of metered customers to total customers registered in a utility database expressed as a percentage. The number of active metered connections is an absolute variable.

DEA analysis requires that the number of DMUs should be more than three times the production variables to avoid wrong efficiency benchmarking. The number of efficient UWU increases when the rule of thumb is not satisfied (Mozaffari et al. 2022). Thus, 40 UWUs and six production sets are used in the efficiency assessment.

Standard DEA model for ratios

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The VRS input oriented DEA model for ratios is used in the assessment of a UWU's efficiency because UWUs operate under VRS while considering minimising the level of input to increase the output level. Thus, consider a set of z UWUs, each consuming i input-ratio(s) to generate r output-ratios with the limitation that Let and respectively represent the vectors of m consumed input-ratio(s) and s output-ratios; and represent a numerator and denominator of the input (⁠⁠), and and represent a numerator and denominator of the output (⁠⁠) for ⁠. In the DEA model, and compose the known input-ratio and output-ratio vectors respectively of the target UWU0, is a vector describing the percentages of other producers used for constructing the virtual producer, and is the producer's efficiency score. Thus,
(1)

Stepwise efficiency assessment methodology

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A stepwise efficiency analysis employs trends of how UWU combine inputs to produce outputs that are measured to a single UWU efficiency. In the water sector, limiting an increase of input improves outputs and a considerable decrease in the level of one input has an impact on efficiency improvement as well. Wagner & Shimshak (2007) developed a stepwise variable selection in DEA under the managerial perspective to overcome a contradiction problem noted when highly correlated variables are used in DEA as production functions. In Wagner & Shimshak (2007), redundancy was considered in input and output variables respectively. However, this study uses a similar approach but keeps the number of output functions constant. It is easier to monitor risks of a single input variable and benefit from improving multiple output variables. A stepwise efficiency assessment focuses on the UWU efficiency result obtained after averaging efficiencies produced from Gidion et al. (2019a) and Wagner & Shimshak (2007) that keep the output variables constant. A methodology developed by Gidion et al. (2019a) followed a trend of reducing UWUs, input or output or both, considering the consistent analysis group formed during two years’ of variable assessment; the current method does keep the number of UWUs and output variables constant, and redundancy is made in a group of input variables only. Because the study uses a single year of information, variables with zero values included in the study of Gidion et al. (2019a) are excluded in this study. To summarise, the current study serves as a bridge between the methodologies of Wagner & Shimshak (2007) and Gidion et al. (2019a) by keeping a number of UWUs and output variables constant while reducing a number of input variables in subdivisions forming a UWU efficiency analysis (Figure 1 and Table 1 detail the concept).
Table 1

An example of an input redundant dataset in a UWU efficiency assessment

DescriptionInput (⁠⁠)Output (⁠⁠)Efficiency
 Div. 1 I(A), I(D), I(E) O(A), O(B), O(C)  
 Sub-div. 1 I(A), I(D) O(A), O(B), O(C)  
Sub-div. 2 I(A), I(E) O(A), O(B), O(C)  
Sub-div. 3 I(D), I(E) O(A), O(B), O(C)  
 Sub-div. 3 I(A) O(A), O(B), O(C)  
Sub-div. 4 I(D) O(A), O(B), O(C)  
Sub-div. 5 I(E) O(A), O(B), O(C)  
UWU overall efficiency,  
DescriptionInput (⁠⁠)Output (⁠⁠)Efficiency
 Div. 1 I(A), I(D), I(E) O(A), O(B), O(C)  
 Sub-div. 1 I(A), I(D) O(A), O(B), O(C)  
Sub-div. 2 I(A), I(E) O(A), O(B), O(C)  
Sub-div. 3 I(D), I(E) O(A), O(B), O(C)  
 Sub-div. 3 I(A) O(A), O(B), O(C)  
Sub-div. 4 I(D) O(A), O(B), O(C)  
Sub-div. 5 I(E) O(A), O(B), O(C)  
UWU overall efficiency,  
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Figure 1
Network DEA model schematic diagram.
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Network DEA model schematic diagram.

Figure 1
Network DEA model schematic diagram.
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Network DEA model schematic diagram.

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Thus, referring to exclusive features of the current study, the average of the step efficiencies score of divisions in Figure 1 produces an overall UWU stepwise efficiency. This analysis follows the UWU working environment where working on one or a set of input variables can increase the level of many output variables. For example, the decrease in NRW as discussed earlier improves many output variables, and a UWU efficiency can be measured using NRW as input to more than five output variables and identifying the UWU with the best NRW management. A stepwise analysis of this study considers that NDEA for ratios analyse efficiency in parallel and series directions through input variable(s) redundant as shown in Figure 1. Consider a with input vectors and output vectors; vector has a redundant at -step under constant at -step as shown in Figure 1.

Figure 1 presents a model development schematic diagram. is generated using all production functions selected to generate a UWU efficiency, and and are generated in two different ways: (1) is generated by omitting the first input variable (e.g. NRW in this analysis) and (2) is generated by omitting the last input variable (e.g., staff/1,000 connections in this study) but including the first variable omitted in ⁠. Efficiency assessment in and forms a parallel analysis and the average of the two efficiencies forms a single division of step 1 (⁠⁠) in series with step ⁠, and the average of efficiencies in ⁠, up to forms an overall UWU efficiency. Thus, there must be series divisions’ efficiencies containing parallel subdivisions' efficiencies analysed using standard DEA model (1) presented in the above section ‘Standard DEA model for ratios’, which make an overall efficiency analysis model as:
(2)
where,
(3)
Thus, putting model (3) in model (2), the overall efficiencies analysis model becomes:
(4)
where model (1) is used to generate and
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Dataset

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Section ‘Materials/data’ highlights three input and three output production functions coded with I and O first letters used in Figure 1 respectively as and vectors to produce a UWU efficiency. Table 1 presents a dataset arrangement to generate divisional efficiencies and overall UWU efficiency using model (4) if six production variables are used. The efficiency assessment applies basic UWU operation practices of tackling sensitive and negative input production functions to increase the level of output production functions that apparently improve a UWU efficiency. Thus, for this case, production functions for a UWU's best operation practices are investigated using an input variable redundant scenario to produce a UWU efficiency score arranged as in Table 1.

The number of divisions in series and parallel directions depends on the number of input variables selected for analysing a UWU's efficiency. For example, three input variables were selected to produce three output variables in the case of this analysis, thus there must be a starting division (⁠⁠) that analyses a UWU's efficiency using six production functions. In the first step (⁠⁠) there must be a redundancy of one input variable in each subdivision forming, and in the second division (⁠⁠) there must be a redundancy of two variables in each of the three parallel subdivisions.

Overall efficiency assessment based on attaining service level

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Efficiency assessment generally improves UWU performance. For many years, regulators ranked UWU performance using empirical methods that employed assumptions (Singh et al. 2014; Thanassoulis & Silva 2018). Recently, researchers have expanded the application of stochastic frontier analysis (SFA) and DEA to benchmark and regulate UWU performance (Goh & See 2021; Molinos-Senante & Maziotis 2021). This is due to the ability of these frontier analyses to hold a multiple input and output to benchmark UWU efficiency (Molinos-Senante & Sala-Garrido 2016). Among frontier analyses, SFA has been widely used in combination with empirical analyses to regulate UWU performance (see Berg & Lin (2008), Goh & See (2021) and Molinos-Senante & Maziotis (2021)), and in a limited environment DEA has been used (Erbetta & Cave 2007). DEA has not been widely used due to the fact that choosing the best performer among the regulated UWUs involves a combination of many criteria like attaining agreed targets, accepted service levels, and confidence grading (Gidion et al. 2019b) which employ ratios. The use of ratios as production variables was beyond the capability of CRS and VRS DEA developed in Charnes et al. (1978) and Banker et al. (1984) respectively. The extension of DEA from absolute to ratios has allowed a UWU benchmarking process using DEA to happen in the water industry.

A number of studies have applied DEA for ratios to assess DMU efficiencies in various industries. For example, Akbarian (2021) developed an NDEA to assess Taiwanese non-life-insurance companies, the study of Hatami-Marbini & Toloo (2019) modified DEA for ratios from the study of Emrouznejad & Amin (2009) and extended its application in the education industry and Gidion et al. (2019a) for the first time developed an NDEA for ratios to assess UWU efficiency. The NDEA for ratio efficiency assessment presented in Gidion et al. (2019a) addresses efficiency generation based on attaining agreed performance targets. The assessment of Gidion et al. (2019a) cannot stand alone in concluding an efficient or inefficient UWU when it comes to regulating a UWU's performance using multiple criteria. An efficiencies average based on the mentioned criteria identifies the best, medium and worst performing UWUs, because it is easier for a weakly performing UWU to outperform a target than a strongly performing UWU. This study addresses a problem of attaining service level benchmarks; strong, medium, and weak UWUs are compared on their ability to attain low levels of inputs and a higher level of outputs. Thus, Table 2 presents an efficiency assessment based on a UWU attaining an acceptable level and the average of efficiencies scored in Gidion et al. (2019a) and this study for the moment ascertains the performance level of a UWU as detailed in the next section. Other UWU regulating criteria need an approach to assess them, which is beyond the scope of this study.

Table 2

Stepwise UWU overall efficiency generation

Description
UWU5 1 1 1 1 1 1 1 1 
UWU9 1 1 1 1 1 1 1 1 
UWU13 1 1 1 1 1 1 0.95 0.992857 
UWU7 1 1 1 1 1 1 0.88386 0.983409 
UWU10 1 1 1 1 1 1 0.86957 0.981367 
UWU12 1 0.91391 1 1 0.91391 0.64788 1 0.9251 
UWU3 1 0.75131 1 1 0.62506 0.75131 1 0.875383 
UWU6 1 1 0.68224 1 0.5726 1 0.65517 0.844287 
UWU1 1 1 0.73077 1 0.25098 1 0.73077 0.816074 
UWU2 0.86853 0.75837 0.83109 0.86853 0.45566 0.75837 0.82609 0.766663 
UWU15 0.85476 0.85476 0.62799 0.78105 0.48057 0.71812 0.60318 0.702919 
UWU22 0.88258 0.88258 0.60264 0.79566 0.36111 0.78947 0.58462 0.699809 
UWU4 0.79509 0.59484 0.76232 0.79509 0.37666 0.55725 0.76 0.663036 
UWU38 0.78044 0.78044 0.65 0.68 0.65 0.68 0.40425 0.660733 
UWU37 0.70019 0.70019 0.70019 0.6424 0.70019 0.54424 0.62295 0.658621 
UWU33 0.8 0.8 0.8 0.55814 0.8 0.55814 0.15625 0.638933 
UWU8 0.75 0.52974 0.74017 0.75 0.39663 0.45116 0.73077 0.62121 
UWU35 0.76 0.45724 0.76 0.76 0.39179 0.40448 0.76 0.613359 
UWU11 0.69284 0.55986 0.68028 0.69284 0.41187 0.48112 0.66667 0.597926 
UWU21 0.70298 0.70298 0.53146 0.64315 0.53146 0.62083 0.44706 0.597131 
UWU39 0.66365 0.64452 0.62527 0.66365 0.41935 0.51724 0.60318 0.59098 
UWU14 0.625 0.625 0.51578 0.625 0.41935 0.625 0.49351 0.561234 
UWU16 0.60857 0.51499 0.60857 0.59055 0.51499 0.30024 0.58462 0.53179 
UWU17 0.60221 0.57257 0.49885 0.60221 0.28758 0.55333 0.48718 0.514847 
UWU20 0.54054 0.54054 0.5 0.54054 0.5 0.54054 0.27143 0.490513 
UWU34 0.55145 0.54559 0.47609 0.53463 0.3421 0.44118 0.45783 0.47841 
UWU28 0.69552 0.69552 0.22034 0.65217 0.22034 0.65217 0.1155 0.464509 
UWU30 0.56522 0.56522 0.56522 0.35503 0.56522 0.2 0.34546 0.451624 
UWU19 0.56564 0.31742 0.56564 0.55073 0.31707 0.2381 0.55073 0.443619 
UWU18 0.49178 0.49178 0.43333 0.46073 0.43333 0.375 0.4 0.44085 
UWU36 0.45899 0.45899 0.45899 0.42493 0.45899 0.24594 0.41304 0.417124 
UWU29 0.58621 0.58621 0.20757 0.58621 0.20757 0.58621 0.08636 0.40662 
UWU31 0.45214 0.45214 0.43333 0.34091 0.43333 0.34091 0.1704 0.374737 
UWU23 0.40261 0.40261 0.40261 0.36759 0.40261 0.28045 0.33333 0.370259 
UWU25 0.38461 0.38461 0.37143 0.38461 0.37143 0.38461 0.09223 0.339076 
UWU27 0.36111 0.36111 0.36111 0.30513 0.36111 0.2459 0.26761 0.323297 
UWU40 0.34642 0.32226 0.34543 0.34642 0.28918 0.2459 0.33043 0.318006 
UWU24 0.3533 0.24913 0.3533 0.34546 0.24913 0.21306 0.34546 0.301263 
UWU32 0.34719 0.34719 0.18066 0.3085 0.18066 0.3085 0.10857 0.254467 
UWU26 0.27999 0.216 0.27999 0.2695 0.216 0.10076 0.2695 0.233106 
Description
UWU5 1 1 1 1 1 1 1 1 
UWU9 1 1 1 1 1 1 1 1 
UWU13 1 1 1 1 1 1 0.95 0.992857 
UWU7 1 1 1 1 1 1 0.88386 0.983409 
UWU10 1 1 1 1 1 1 0.86957 0.981367 
UWU12 1 0.91391 1 1 0.91391 0.64788 1 0.9251 
UWU3 1 0.75131 1 1 0.62506 0.75131 1 0.875383 
UWU6 1 1 0.68224 1 0.5726 1 0.65517 0.844287 
UWU1 1 1 0.73077 1 0.25098 1 0.73077 0.816074 
UWU2 0.86853 0.75837 0.83109 0.86853 0.45566 0.75837 0.82609 0.766663 
UWU15 0.85476 0.85476 0.62799 0.78105 0.48057 0.71812 0.60318 0.702919 
UWU22 0.88258 0.88258 0.60264 0.79566 0.36111 0.78947 0.58462 0.699809 
UWU4 0.79509 0.59484 0.76232 0.79509 0.37666 0.55725 0.76 0.663036 
UWU38 0.78044 0.78044 0.65 0.68 0.65 0.68 0.40425 0.660733 
UWU37 0.70019 0.70019 0.70019 0.6424 0.70019 0.54424 0.62295 0.658621 
UWU33 0.8 0.8 0.8 0.55814 0.8 0.55814 0.15625 0.638933 
UWU8 0.75 0.52974 0.74017 0.75 0.39663 0.45116 0.73077 0.62121 
UWU35 0.76 0.45724 0.76 0.76 0.39179 0.40448 0.76 0.613359 
UWU11 0.69284 0.55986 0.68028 0.69284 0.41187 0.48112 0.66667 0.597926 
UWU21 0.70298 0.70298 0.53146 0.64315 0.53146 0.62083 0.44706 0.597131 
UWU39 0.66365 0.64452 0.62527 0.66365 0.41935 0.51724 0.60318 0.59098 
UWU14 0.625 0.625 0.51578 0.625 0.41935 0.625 0.49351 0.561234 
UWU16 0.60857 0.51499 0.60857 0.59055 0.51499 0.30024 0.58462 0.53179 
UWU17 0.60221 0.57257 0.49885 0.60221 0.28758 0.55333 0.48718 0.514847 
UWU20 0.54054 0.54054 0.5 0.54054 0.5 0.54054 0.27143 0.490513 
UWU34 0.55145 0.54559 0.47609 0.53463 0.3421 0.44118 0.45783 0.47841 
UWU28 0.69552 0.69552 0.22034 0.65217 0.22034 0.65217 0.1155 0.464509 
UWU30 0.56522 0.56522 0.56522 0.35503 0.56522 0.2 0.34546 0.451624 
UWU19 0.56564 0.31742 0.56564 0.55073 0.31707 0.2381 0.55073 0.443619 
UWU18 0.49178 0.49178 0.43333 0.46073 0.43333 0.375 0.4 0.44085 
UWU36 0.45899 0.45899 0.45899 0.42493 0.45899 0.24594 0.41304 0.417124 
UWU29 0.58621 0.58621 0.20757 0.58621 0.20757 0.58621 0.08636 0.40662 
UWU31 0.45214 0.45214 0.43333 0.34091 0.43333 0.34091 0.1704 0.374737 
UWU23 0.40261 0.40261 0.40261 0.36759 0.40261 0.28045 0.33333 0.370259 
UWU25 0.38461 0.38461 0.37143 0.38461 0.37143 0.38461 0.09223 0.339076 
UWU27 0.36111 0.36111 0.36111 0.30513 0.36111 0.2459 0.26761 0.323297 
UWU40 0.34642 0.32226 0.34543 0.34642 0.28918 0.2459 0.33043 0.318006 
UWU24 0.3533 0.24913 0.3533 0.34546 0.24913 0.21306 0.34546 0.301263 
UWU32 0.34719 0.34719 0.18066 0.3085 0.18066 0.3085 0.10857 0.254467 
UWU26 0.27999 0.216 0.27999 0.2695 0.216 0.10076 0.2695 0.233106 
View Large

Efficiency generation in Table 2 indicates that at the start (⁠⁠) nine UWUs were efficient, in step 1 (⁠⁠) the number of efficient UWUs decreased to five (when averaging subdivisional efficiencies) and the number of efficient UWU's drastically reduced to two in the second step (⁠⁠). This is due to the analysis target investigating the ability of a UWU using a low number of input variables to produce a high number of output variables. Thus, when reducing the number of inputs, a few inputs are utilised with existing outputs to produce a UWU efficiency; in this regard, a UWU with the best service levels among a few input variables is analysed and benchmarked as efficient (Zhu 2009). Nine UWUs were efficient because they scored low/high indicative service levels in input/output variables respectively; the number of efficient UWUs is reduced as the number of inputs is reduced to show the effort of a UWU's management in utilising a few input variables to produce many output variables. An average of the efficiencies analysed in the steps produces a UWU's overall efficiency; for this case, UWU5 and UWU9 were identified as efficient and UWU26 was benchmarked in last position.

The data and codes cited under ‘Data Availability Statement’ at the end of this paper highlight the hidden concept of efficiency assessment based on the production set used which on the other hand is also used by regulators to explore best management features (Vilanova et al. 2015); the NDEA for ratios used in this analysis prioritises access to this information. For example, comparing NRW levels in the top and bottom five UWUs respectively indicates that the top five UWUs have attained the service level. The acceptable NRW service levels in developing countries and developed countries are 20% and 15% of production respectively (Kanakoudis et al. 2013; Al-Washali et al. 2020); the NDEA for ratios assessment has identified UWUs with improved NRW reduction arranged from the top chronologically. Thus, the NRW reduction strategies employed by these UWUs can help other UWUs improve their operational performance; for the least performing UWUs, their NRW level is higher compared with the top five benchmarked UWUs. Moreover, there is a substantial improvement of the output production variables of outperforming UWUs compared with underperforming UWUs. Thus, this suggests the proposed approach performs well in the regulation process to identify the best, intermediate and worst UWUs during efficiency assessment, and regulators applying the proposed approach will avoid the favouritism and errors generated when using parametric methods to benchmark a UWU's efficiency.

Competitive efficiency assessment and the new issue puzzle

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Average efficiency assessment

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The preceding section ‘Overall efficiency assessment based on attaining service level’ discusses results of the proposed approach by generating an overall efficiency based on attaining service level; this section extends UWU efficiency generation based on the combination of attaining performance targets proposed in Gidion et al. (2019a) and service levels as the road to select the most efficient UWU among the UWUs. The importance of the process benchmarking methodology can be explored in the associated package of data and codes cited under ‘Data Availability Statement’ at the end of this paper. Using the same input and output production variables, Gidion et al. (2019a) for the first time developed NDEA for ratios in the water industry and generated UWU efficiencies in a competitive scenario addressing one of the criteria used for UWU efficiency analysis. Table 3 presents an overall efficiency and NDEA for ratios efficiencies (retrieved from Gidion et al. (2019a)) averaged to produce a UWU average efficiency which is constructed to arrange the inefficient UWUs in a competitive scenario. The NDEA for ratios developed in Gidion et al. (2019a) produced UWU3 ranked efficient in the first position; UWU12 and UWU13 ranked inefficient in the second and third positions respectively. The NDEA for ratios extended in this study produce UWU5 and UWU9 ranked efficient in the first position and UWU13 ranked in the second position while the third position went to UWU7. Interchangeably, UWU32 and UWU26 were ranked in the last positions using NDEA for ratios developed in Gidion et al. (2019a) and this study respectively.

Table 3

Overall, NDEA for ratios, average and normalised UWU efficiencies

Descr.
UWU13 1 1 1 1 1 1 0.9500 0.9929 0.9900 0.9914 1 
UWU10 1 1 1 1 1 1 0.8696 0.9814 0.9735 0.9774 0.9859 
UWU12 1 0.9139 1 1 0.9139 0.6479 1 0.9251 0.9900 0.9576 0.9658 
UWU5 1 1 1 1 1 1 1 1 0.9131 0.9566 0.9648 
UWU9 1 1 1 1 1 1 1 1 0.9013 0.9507 0.9589 
UWU3 1 0.7513 1 1 0.6251 0.7513 1 0.8754 1 0.9377 0.9458 
UWU7 1 1 1 1 1 1 0.8839 0.9834 0.8529 0.9182 0.9261 
UWU1 1 1 0.7308 1 0.2510 1 0.7308 0.8161 0.9462 0.8811 0.8888 
UWU6 1 1 0.6822 1 0.5726 1 0.6552 0.8443 0.9074 0.8758 0.8834 
UWU2 0.8685 0.7584 0.8311 0.8685 0.4557 0.7584 0.8261 0.7667 0.8547 0.8107 0.8177 
UWU22 0.8826 0.8826 0.6026 0.7957 0.3611 0.7895 0.5846 0.6998 0.7891 0.7445 0.7509 
UWU15 0.8548 0.8548 0.6280 0.7811 0.4806 0.7181 0.6032 0.7029 0.7711 0.7370 0.7434 
UWU4 0.7951 0.5948 0.7623 0.7951 0.3767 0.5573 0.7600 0.6630 0.7871 0.7251 0.7313 
UWU8 0.7500 0.5297 0.7402 0.7500 0.3966 0.4512 0.7308 0.6212 0.7462 0.6837 0.6896 
UWU37 0.7002 0.7002 0.7002 0.6424 0.7002 0.5442 0.6230 0.6586 0.6746 0.6666 0.6724 
UWU38 0.7804 0.7804 0.6500 0.6800 0.6500 0.6800 0.4043 0.6607 0.6494 0.6551 0.6607 
UWU11 0.6928 0.5599 0.6803 0.6928 0.4119 0.4811 0.6667 0.5979 0.6876 0.6428 0.6483 
UWU39 0.6637 0.6445 0.6253 0.6637 0.4194 0.5172 0.6032 0.5910 0.6511 0.6210 0.6264 
UWU33 0.8000 0.8000 0.8000 0.5581 0.8000 0.5581 0.1563 0.6389 0.5359 0.5874 0.5925 
UWU14 0.6250 0.6250 0.5158 0.6250 0.4194 0.6250 0.4935 0.5612 0.5875 0.5744 0.5793 
UWU16 0.6086 0.5150 0.6086 0.5906 0.5150 0.3002 0.5846 0.5318 0.5967 0.5642 0.5691 
UWU17 0.6022 0.5726 0.4989 0.6022 0.2876 0.5533 0.4872 0.5148 0.5757 0.5453 0.5500 
UWU35 0.7600 0.4572 0.7600 0.7600 0.3918 0.4045 0.7600 0.6134 0.4560 0.5347 0.5393 
UWU20 0.5405 0.5405 0.5000 0.5405 0.5000 0.5405 0.2714 0.4905 0.4461 0.4683 0.4724 
UWU21 0.7030 0.7030 0.5315 0.6432 0.5315 0.6208 0.4471 0.5971 0.3321 0.4646 0.4686 
UWU18 0.4918 0.4918 0.4333 0.4607 0.4333 0.3750 0.4000 0.4409 0.4612 0.4510 0.4549 
UWU30 0.5652 0.5652 0.5652 0.3550 0.5652 0.2000 0.3455 0.4516 0.4444 0.4480 0.4519 
UWU29 0.5862 0.5862 0.2076 0.5862 0.2076 0.5862 0.0864 0.4066 0.4652 0.4359 0.4397 
UWU36 0.4590 0.4590 0.4590 0.4249 0.4590 0.2459 0.4130 0.4171 0.4348 0.4260 0.4296 
UWU28 0.6955 0.6955 0.2203 0.6522 0.2203 0.6522 0.1155 0.4645 0.2909 0.3777 0.3810 
UWU23 0.4026 0.4026 0.4026 0.3676 0.4026 0.2805 0.3333 0.3703 0.3679 0.3691 0.3723 
UWU31 0.4521 0.4521 0.4333 0.3409 0.4333 0.3409 0.1704 0.3747 0.3500 0.3624 0.3655 
UWU40 0.3464 0.3223 0.3454 0.3464 0.2892 0.2459 0.3304 0.3180 0.3432 0.3306 0.3335 
UWU25 0.3846 0.3846 0.3714 0.3846 0.3714 0.3846 0.0922 0.3391 0.3071 0.3231 0.3259 
UWU27 0.3611 0.3611 0.3611 0.3051 0.3611 0.2459 0.2676 0.3233 0.3224 0.3228 0.3256 
UWU34 0.5515 0.5456 0.4761 0.5346 0.3421 0.4412 0.4578 0.4784 0.1067 0.2926 0.2951 
UWU19 0.5656 0.3174 0.5656 0.5507 0.3171 0.2381 0.5507 0.4436 0.1101 0.2769 0.2793 
UWU24 0.3533 0.2491 0.3533 0.3455 0.2491 0.2131 0.3455 0.3013 0.0691 0.1852 0.1868 
UWU26 0.2800 0.2160 0.2800 0.2695 0.2160 0.1008 0.2695 0.2331 0.0539 0.1435 0.1447 
UWU32 0.3472 0.3472 0.1807 0.3085 0.1807 0.3085 0.1086 0.2545 0.0217 0.1381 0.1393 
Descr.
UWU13 1 1 1 1 1 1 0.9500 0.9929 0.9900 0.9914 1 
UWU10 1 1 1 1 1 1 0.8696 0.9814 0.9735 0.9774 0.9859 
UWU12 1 0.9139 1 1 0.9139 0.6479 1 0.9251 0.9900 0.9576 0.9658 
UWU5 1 1 1 1 1 1 1 1 0.9131 0.9566 0.9648 
UWU9 1 1 1 1 1 1 1 1 0.9013 0.9507 0.9589 
UWU3 1 0.7513 1 1 0.6251 0.7513 1 0.8754 1 0.9377 0.9458 
UWU7 1 1 1 1 1 1 0.8839 0.9834 0.8529 0.9182 0.9261 
UWU1 1 1 0.7308 1 0.2510 1 0.7308 0.8161 0.9462 0.8811 0.8888 
UWU6 1 1 0.6822 1 0.5726 1 0.6552 0.8443 0.9074 0.8758 0.8834 
UWU2 0.8685 0.7584 0.8311 0.8685 0.4557 0.7584 0.8261 0.7667 0.8547 0.8107 0.8177 
UWU22 0.8826 0.8826 0.6026 0.7957 0.3611 0.7895 0.5846 0.6998 0.7891 0.7445 0.7509 
UWU15 0.8548 0.8548 0.6280 0.7811 0.4806 0.7181 0.6032 0.7029 0.7711 0.7370 0.7434 
UWU4 0.7951 0.5948 0.7623 0.7951 0.3767 0.5573 0.7600 0.6630 0.7871 0.7251 0.7313 
UWU8 0.7500 0.5297 0.7402 0.7500 0.3966 0.4512 0.7308 0.6212 0.7462 0.6837 0.6896 
UWU37 0.7002 0.7002 0.7002 0.6424 0.7002 0.5442 0.6230 0.6586 0.6746 0.6666 0.6724 
UWU38 0.7804 0.7804 0.6500 0.6800 0.6500 0.6800 0.4043 0.6607 0.6494 0.6551 0.6607 
UWU11 0.6928 0.5599 0.6803 0.6928 0.4119 0.4811 0.6667 0.5979 0.6876 0.6428 0.6483 
UWU39 0.6637 0.6445 0.6253 0.6637 0.4194 0.5172 0.6032 0.5910 0.6511 0.6210 0.6264 
UWU33 0.8000 0.8000 0.8000 0.5581 0.8000 0.5581 0.1563 0.6389 0.5359 0.5874 0.5925 
UWU14 0.6250 0.6250 0.5158 0.6250 0.4194 0.6250 0.4935 0.5612 0.5875 0.5744 0.5793 
UWU16 0.6086 0.5150 0.6086 0.5906 0.5150 0.3002 0.5846 0.5318 0.5967 0.5642 0.5691 
UWU17 0.6022 0.5726 0.4989 0.6022 0.2876 0.5533 0.4872 0.5148 0.5757 0.5453 0.5500 
UWU35 0.7600 0.4572 0.7600 0.7600 0.3918 0.4045 0.7600 0.6134 0.4560 0.5347 0.5393 
UWU20 0.5405 0.5405 0.5000 0.5405 0.5000 0.5405 0.2714 0.4905 0.4461 0.4683 0.4724 
UWU21 0.7030 0.7030 0.5315 0.6432 0.5315 0.6208 0.4471 0.5971 0.3321 0.4646 0.4686 
UWU18 0.4918 0.4918 0.4333 0.4607 0.4333 0.3750 0.4000 0.4409 0.4612 0.4510 0.4549 
UWU30 0.5652 0.5652 0.5652 0.3550 0.5652 0.2000 0.3455 0.4516 0.4444 0.4480 0.4519 
UWU29 0.5862 0.5862 0.2076 0.5862 0.2076 0.5862 0.0864 0.4066 0.4652 0.4359 0.4397 
UWU36 0.4590 0.4590 0.4590 0.4249 0.4590 0.2459 0.4130 0.4171 0.4348 0.4260 0.4296 
UWU28 0.6955 0.6955 0.2203 0.6522 0.2203 0.6522 0.1155 0.4645 0.2909 0.3777 0.3810 
UWU23 0.4026 0.4026 0.4026 0.3676 0.4026 0.2805 0.3333 0.3703 0.3679 0.3691 0.3723 
UWU31 0.4521 0.4521 0.4333 0.3409 0.4333 0.3409 0.1704 0.3747 0.3500 0.3624 0.3655 
UWU40 0.3464 0.3223 0.3454 0.3464 0.2892 0.2459 0.3304 0.3180 0.3432 0.3306 0.3335 
UWU25 0.3846 0.3846 0.3714 0.3846 0.3714 0.3846 0.0922 0.3391 0.3071 0.3231 0.3259 
UWU27 0.3611 0.3611 0.3611 0.3051 0.3611 0.2459 0.2676 0.3233 0.3224 0.3228 0.3256 
UWU34 0.5515 0.5456 0.4761 0.5346 0.3421 0.4412 0.4578 0.4784 0.1067 0.2926 0.2951 
UWU19 0.5656 0.3174 0.5656 0.5507 0.3171 0.2381 0.5507 0.4436 0.1101 0.2769 0.2793 
UWU24 0.3533 0.2491 0.3533 0.3455 0.2491 0.2131 0.3455 0.3013 0.0691 0.1852 0.1868 
UWU26 0.2800 0.2160 0.2800 0.2695 0.2160 0.1008 0.2695 0.2331 0.0539 0.1435 0.1447 
UWU32 0.3472 0.3472 0.1807 0.3085 0.1807 0.3085 0.1086 0.2545 0.0217 0.1381 0.1393 
View Large

The averaging of efficiencies from NDEA for ratios by Gidion et al. (2019a) and this study put UWU13, UWU10 and UWU12 in the first, second and third positions respectively and UWU32 was ranked in the last position. From thorough investigation of data used in the efficiency assessment, UWU13, UWU10 and UWU12 had 13%, 16% and 21% NRW, which are the best NRW management compared with the others; UWU26 and UWU32 had 66% and 78% NRW respectively, which are the worst performance levels. Although the benchmarking approach proposed in this study has shown the significance of using NDEA for ratios in UWU efficiency assessment and regulation, still other benchmarking criteria (depending on the regulator's priorities; Gidion et al. (2019b) presented benchmarks for priorities of the EWURA of Tanzania) are important to select the best among the best, and thus more efficiency exploration expansion is needed.

Reliability of NDEA for ratios over empirical methods

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The preceding section ‘Average efficiency assessment’ presents UWU efficiencies generation using NDEA for ratios. The type and number of KPIs (production variables) used for analysing a UWU's efficiencies in NDEA for ratios were also employed to generate UWU efficiency using empirical analysis, thus making the efficiency scores comparison shown in Figure 2. The two curves indicate that UWUs identified as efficient in NDEA for ratios were observed to be inefficient in empirical method analysis and the inefficient UWU1 in Table 3 was observed to be efficient using empirical analysis. The investigation shows that UWU1 and UWU22 had 53% and 35% NRW respectively. The efficiencies variation and biased relationship between NDEA for ratios and empirical results necessitate either the significance of including an analysis of other criteria to draw a concrete conclusion about the two benchmarking methods or the weakness of the empirical analysis when production variables are reduced. Because efficiency assessment using empirical analysis include criteria mentioned in the preceding section, the said section indicates that the proposed NDEA for ratios (using two criteria) has the strength of identifying UWUs with the best management strategies even without the consideration of other criteria. Thus, referring to Figure 2, an empirical method used by the EWURA has shown a weakness in efficiency assessment and is not reliable for a UWU's efficiency assessment and management strategies improvement. Moreover, the proposed NDEA for ratios has the benefit of working on individual input production variables, criteria, and benchmarks for a UWU in the yardstick competition regime to improve a UWU's production while the empirical method does not specify variables to deal with.
Figure 2
Comparison of normalised DEA and empirical efficiencies.
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Comparison of normalised DEA and empirical efficiencies.

Figure 2
Comparison of normalised DEA and empirical efficiencies.
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Comparison of normalised DEA and empirical efficiencies.

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The yardstick competition regime has been used globally to investigate the underlying management features among the regulated DMUs. Regulators use the yardstick competition benchmarking process and sunshine regulation in addition for exposing a UWU's performance in public as the best harassment strategy that improves UWU performance (Dalen 1998; Marques 2006). However, the majority of UWUs underperform, and this is due to the wrong benchmarking process employed in investigating efficiency- and management-specific features, as observed in Figure 2. Bogetoft (1997) employed various types of DEA for absolute data to present the optimality of the best practice regulation under the yardstick competition regime; for the first time, the author observed that DEA is suitable for a regulatory practice particularly in cost estimation. However, regulators employ SFA as the best tool for cost estimation (Lampe & Hilgers 2015). The development of NDEA for ratios takes a regulatory industry to another milestone of employing KPIs in DEA for ratios as the production function to generate a UWU's efficiency in a competitive scenario by including targets and service-level problems in the efficiency assessment without considering cost estimation alone.

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DEA have been widely expanded to address specific industries' efficiencies. This paper has expanded the application of NDEA for ratios to assess a UWU's efficiency in a competitive scenario as a regulating tool in combination with NDEA for ratios developed in Gidion et al. (2019a). In addition, this study extends the application of a non-parametric technology to assess a UWU's efficiency; UWU efficiency assessment involves a combination of many criteria to overcome a UWU's operating environment problem. For example, the majority of UWU regulators use performance targets to monitor UWU operations and use the same targets as one of the criteria to rank a UWU's performance in combination with other criteria.

The UWU efficiency assessment proposed in this study aims to apply the EWURA efficiency assessment approach where a utility's efficiency is estimated based on the ability to attain target setup and acceptable service levels, confidence grading and an ability to outperform acceptable service levels (see Gidion et al. (2019b) for details). Among the criteria mentioned, Gidion et al. (2019a) addressed efficiency assessment based on the ability to attain agreed performance targets, and the current study addresses a UWU efficiency assessment problem based on attaining the acceptable service level. The average of the efficiencies generated in Gidion et al. (2019a) and this study produces an overall UWU efficiency.

The assessment shows that the developed efficiency assessment methodology outperforms the empirical method and the analysis approach proposed in Gidion et al. (2019a) in many ways and has an advantage of selecting a UWU with best management in production variables. This has been observed when the methods' reliabilities in efficiency assessment using six production set variables were tested; the empirical method failed to identify a UWU with the best management strategies while NDEA identified and benchmarked them in the first position. Even though the current study discussed the issues of methods and reliability, the analysis proposed in this study is limited to the extension of NDEA for ratios in efficiency assessment under the yardstick regime and exploration of management-specific features using acceptable service-level benchmark and targets. Future researchers may wish to expand this study by developing a non-parametric approach that (1) incorporates confidence grading in NDEA for ratios to assess a UWU's efficiency; and (2) incorporates efficiency analysis based on the ability of a UWU to outperform the acceptable level; as well as (3) exploring and including any other necessary efficiency assessment approach in addition to the criteria mentioned.

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All relevant data and codes are available from: http://dx.doi.org/10.17632/m96sxh95kd.1.

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The authors declare there is no conflict.

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