Embracing data uncertainty in water decision-making: an application to evaluate water supply and sewerage in Spain

1 7 ©IWA Publishing [2019]. The definitive peer-reviewed and edited version of this article is published in Water Supply vol. 19, isuue 3, p. 778-788, 2019. doi: 10.2166/ws.2018.122 and is available at www.iwapublishing.com. 2 Embracing data uncertainty in water decision-making: an application to 8 evaluate water supply and sewerage in Spain. 9 Fatine Ezbakhe1, Agustí Pérez-Foguet1 10 11 1Research group on Engineering Sciences and Global Development (EScGD), Department of Civil and 12 Environmental Engineering, Barcelona School of Civil Engineering (ETSECCPB), Universitat Politècnica de 13 Catalunya. Barcelona, Spain 14 *Corresponding author: [email protected] 15 16 Abstract 17 Analyses of complex water management decision-making problems, involving tradeoffs 18 amongst multiple criteria, are often undertaken using multi-criteria decision analysis 19 (MCDA) techniques. Various forms of uncertainty may arise in the application of MCDA 20 methods, including imprecision, inaccuracy or ill determination of data. The ELECTRE 21 family methods deal with imperfect knowledge of data by incorporating ‘pseudo-criteria’, 22 with discrimination thresholds, to interpret the outranking relation as a fuzzy relation. 23 However, the task of selecting thresholds for each criterion can be difficult and 24 ambiguous for decision-makers. In this paper, we propose a confidence-interval-based 25 approach which aims to reduce the subjective input required by decision-makers. The 26 proposed approach involves defining the uncertainty in the input values using confidence 27 intervals and expressing thresholds as a function of the interval estimates. The usefulness 28 of the approach is illustrated by applying it to evaluate the water supply and sewerage 29 services in Spain. Results show that the confidence interval approach may be interesting 30 in some cases (e.g. when dealing with statistical data from surveys or measuring 31 equipment), but should never replace the preferences or judgments of the actors involved 32 in the decision process. 33 34 Keywords: ELECTRE; Multi-criteria decision analysis; Outranking methods; 35 Uncertainty; Water supply; Sewerage. 36 3 INTRODUCTION 37 Decision-making in water management is inherently complex. Water decisions often 38 involve large numbers of alternatives, competing objectives, and participation of multiple 39 stakeholders with conflicting interests (Hyde et al. 2005). Consequently, a formal 40 framework to water resources decision-making is required. Multi-criteria decision 41 analysis (MCDA) provides a structured approach for analyzing decision problems with 42 multiple objectives and criteria (Mutikanga et al. 2011). MCDA can assist decision43 makers in identifying critical issues, assigning relative priorities to those issues, selecting 44 best compromise solutions, and enhancing communication in the evaluation of decision 45 problems (Flug et al. 2000). 46 Numerous MCDA methods have been developed over the years, and are commonly 47 classified in three classes: full aggregation approach, outranking approach, and goal, 48 aspiration or preference-level approach (Ishizaka & Nemery 2013). The elimination and 49 choice expressing the reality (ELECTRE) methods developed by Roy (1991) belong to 50 the group of outranking approaches and are one of most well known and widely applied 51 methods, especially in Europe (Wang & Triantaphyllou 2006). This is evident by their 52 broad use in wide-ranging decision-making situations, from natural resources and 53 environmental management to structural engineering, logistics and supply chain 54 management, and public planning and policy decisions (Govindan & Jepsen 2016). In 55 water management, the specific application areas include ranking water allocation 56 strategies (Bella et al. 1996, Zardari et al. 2010), assessing projects for river basin 57 planning and development (Duckestein et al. 1982, Raj 1995), selecting alternative 58 strategies for managing irrigation systems (Raju et al. 2000, Pedras & Pereira 2009), 59 choosing operation rules for reservoir systems (Ko et al. 1994, Malekmohammadi et al. 60 2011), prioritizing pipe rehabilitation projects in water and sewer networks (Carrico et al. 61 2012, Tscheikner-Gratl et al. 2017), comparing watershed management schemes (Tecle 62 et al. 1988, Ceccato et al. 2011) or identifying priority water users or regions for future 63 inversions (Roy et al. 1992, Morais & Almeida 2006). However, despite their extensive 64 application, the drawbacks of ELECTRE methods are still discussed by researchers 65 (Figueira & Roy 2009, Figueira et al. 2013), mainly what their theoretical limitations are 66 and whether they aid the decision-making process. 67 In addition, as in every other MCDA method, uncertainty is ubiquitous in the ELECTRE 68 decision-making process. According to French (1995), different forms of uncertainty may 69 arise in decision analysis from imprecision, ambiguity or lack of clarity. One form is the 70 uncertainty about the selection of criteria that adequately represent the objectives of the 71 decision problem. Another is the uncertainty surrounding the assignment of criteria 72 weights. There is also uncertainty related to the numerical accuracy of input data. Data 73 uncertainty (i.e. degree to which data is inaccurate, imprecise or unknown) can be due to 74 many factors, such as inherent variability (from the natural processes that continually 75 affect water resources), measurement errors (caused by equipment or random sampling 76 effects) and boundary conditions (from external factors that cannot be accounted for 77 explicitly) (Klauer et al. 2006). However, as stated by Xu and Tung (2008), MCDA 78 methods are often applied without much consideration given to the uncertainty in the 79 input data and its propagation into the problem solution. As can be expected, data 80 4 uncertainty may have an important influence on the ranking of alternatives (Eastman et 81 al. 1991), which thus casts significant doubt on the decision analysis results. 82 Dealing with inaccurate, imprecise, uncertain or ill-determined data is one of the foremost 83 strong features of ELECTRE family methods (Figueira & Roy 2005). Instead of ‘true84 criteria’, ELECTRE methods include ‘pseudo-criteria’, with discrimination thresholds, to 85 account for the imperfect knowledge of the data (Figueira et al. 2013). However, fixing 86 the discrimination thresholds for each criterion can be a difficult and ambiguous task for 87 decision-makers, and remains a problematic issue (Govindan & Jepsen 2016). A number 88 of researchers have addressed the need for more comprehensive approaches for selecting 89 appropriate threshold values. Rogers and Bruen (1998) described a methodology for 90 choosing realistic threshold values for use in environmental appraisal systems. The 91 method took into account the effect on human beings of the difference between criterion 92 scores. Hokkanen and Salminem (1997) provided another approach for selecting 93 thresholds in the context of solid waste management systems. It associated thresholds 94 with the possible error range in criteria, which was inferred with the help of regression 95 analyses. On the other hand, Banias et al. (2010) overcame the subjectivity issue by 96 connecting the thresholds to the performance values range (i.e. difference between the 97 maximum and minimum values), divided by the number of alternatives. The idea behind 98 this was to emphasize the discrimination power of the method: the more alternatives there 99 were, the more necessary was to have finer thresholds to discriminate among them. This 100 approach, which echoed others in the literature (Haralambapoulous & Polatidis 2003, 101 Polatidis & Morales 2006), provided a simple way for determining the thresholds, but 102 ignored the uncertainty underlying the data. More works needs to be done in order to 103 assist decision-makers in choosing thresholds in a rational and defendable manner. 104 In this paper, we introduce an extension of the ELECTRE III method to address the issue 105 of fixing discrimination thresholds. We propose a ‘confidence interval-based’ approach, 106 where uncertainty in the input data is defined using confidence intervals and thresholds 107 are expressed as a function of the interval estimates. Our objectives are to: (i) introduce 108 a new approach for thresholds determination, which provides a means of reducing the 109 degree of subjectivity; and (ii) test the proposed approach by applying it to a priority 110 ranking of water supply and sewerage services in Spain. 111 5 METHODS 112 ELECTRE III 113 The ELECTRE III method is based upon developing a preference relation, called 114 ‘outranking relation’, among alternatives evaluated on several criteria. The outranking 115 relation is defined as a binary relation, S, between two alternatives, a1 and a2, such that 116 a1Sa2 if there are enough arguments to declare that ‘alterative a1 is at least as good 117 alternative a2’ (Bouyssou 1996). To build the outranking relation, a series of pairwise 118 comparisons of the alternatives is done using the concordance-discordance principle. It 119 represents, in a sense, the reasons for and against an outranking situation (Roy 1996): a1 120 outranks a2 if a majority of criteria support this assertion (concordance condition) and if 121 the opposition of the other criteria is not ‘too strong’ (non-discordance condition). The 122 method, in the second phase of outranking relation exploitation, derives two pre-orders: 123 downward, Z1, and upward, Z2. Both pre-orders Z1 and Z2 are constructed through 124 descending and ascending distillation procedures, respectively (for details of these 125 procedures, see Roy 1996). A final pre-order of alternatives is finally suggested as the 126 intersection of Z1 and Z2. Figure 1 illustrates a summary of the method. 127 128 Figure 1. General structure of ELECTRE III method. 129 6 The construction of the concordance and discordance indexes requires the definition of 130 three discrimination thresholds for each criterion: 131 • The indifference threshold, qi, beneath which the decision-maker is indifferent to 132 two alternatives. 133 • The preference threshold, pi, above which the decision-maker shows a clear 134 preference of one alternative over the other. 135 • The veto threshold, vi, above which the decision-maker negates any possible 136 outranking relationship indicated by the other criteria. 137 Choosing realistic values for each threshold involves a high degree of subjectivity. In 138 order to facilitate this task for decision-makers, we propose an approach that allows for 139 less subjective input through defining thresholds as a function of the confidence intervals 140 of the alternatives performances. Hence, we address two concerns that may affect the 141 validity of the rankings: (i) the uncertainty in choosing threshold values, and (ii) the 142 imprecision in performance values due to measurement error. The idea behind the 143 approach is explained in Figure 2. 144 145 Figure 2. Confidence-interval approach. 146 147 This way, our approach will provide a different set of q-p-v thresholds for each pair of 148 alternatives and criterion. The equations for the proposed approach are as follows: 149 !" ( $%, $' ) =*$+ { - | /" ( $% ) 0− /" ( $% )| -, | /" ( $' ) 2− /" ( $' )| - } Eq.1 150 4" ( $%, $' ) =- | /" ( $% ) 0− /" ( $% )| + | /" ( $' ) 2− /" ( $' )| Eq. 2 151 6" ( $%, $' ) = -2 ∙ 4" ( $%, $' ) Eq. 3 152 where Vi(aj) is the performance value of alternative aj for criterion i, and Vi(aj)U and Vi(aj)L 153 the upper and lower limits of its confidence interval. 154 155 7 Case study 156 We selected a real case study to test the proposed approach. It consisted in a priority 157 ranking of water supply and sewerage services in Spain. The objective was to prioritize 158 the different regions of Spain according to their need for better water supply and sewerage 159 services. This prioritization could be used to support current or future political actions 160 regarding water management in Spain. 161 The alternatives in the decision problem were the 17 Autonomous Communities of Spain 162 (Andalucía, Aragón, Asturias, Baleares, Canarias, Cantabria, Castilla y León, Castilla-La 163 Mancha, Catalunya, Comunitat Valenciana, Extremadura, Galicia, Madrid, Murcia, 164 Navarra, País Vasco and Rioja). The 11 criteria used to rank the regions consisted of 165 water supply, wastewater, economic and structural factors. A description of each criterion 166 is contained in Table 1. 167 Table 1. Criteria used in the case study. 168 Criteria Definition Units Direction C1: Volume of drinkable water available Water treated in drinking water treatment plants. Liters/ inhabitant/ day + C2: Volume of water supplied to the public network Water entering the distribution network from drinking water treatment plants or service deposits. Includes both registered and non-registered water. Liters/ inhabitant/ day + C3: Percentage of water losses Water not registered or distributed to the users. It includes both physical losses (i.e. water leaks, breakages and faults in the distribution network and outlets) and apparent losses (i.e. undercounting, fraud and other non-physical losses). Percentage over total volume - C4: Volume of treated wastewater Wastewater treated in treatment plants. All types of treatment are considered (primary, secondary or biological, and tertiary treatments; and soft technologies and septic tanks). m3/ inhabitant/ day + C5: Volume of reused wastewater Wastewater reused, including all types of uses (agriculture, industry, watering gardens, leisure sports areas, cleaning of streets and sewage, etc.). m3/ inhabitant/ day + C6: Unit cost of water supply Cost charged to users for the full amount of water supplied on the network. It includes both the rates and tariffs paid for water supply. Euros/ m3 - C7: Unit cost of sewage Cost charged to users for the full amount of wastewater collected and treated. It includes both the municipal sewerage fees and taxes of an ecological nature collected for third parties. Euros/ m3 - C8: Length of the water supply network Total length of the distribution network. It excludes transmission lines and service pipes. kilometer/ inhabitant + C9: Length of the sewerage network Total length of the sewerage network. It excludes service connections. kilometer/ inhabitant + C10: Volume of water leaked Water leaked due to water pipe breaks in the distribution network. It excludes leaks from active leakage control. m3/ kilometer/ year - C11: Number of storm water tanks Storm water retention tanks included in the sewer system. nº + *Note: direction of the criterion refers to whether it needs to be maximized (+) or minimized (-). 169 8 Data on the regions was obtained from the “Survey on Water Supply and Sewerage” done 170 by the Spanish National Institute of Statistics. The survey is framed within the National 171 Statistic Plan 2013-2016 (INE 2014), and aims to provide access to reliable and regular 172 data regarding water management in Spain. The survey consists in a questionnaire on the 173 collection, purchase, sale, supply and distribution of water, as well as collection and 174 treatment of wastewater, by companies or institutions in the same Autonomous 175 Community. The sample for the survey is extracted based on a geographical coverage: it 176 covers all municipalities with a population of more than 15,000 inhabitants, which is 177 nearly two thirds of the Spanish population. The sampling error is estimated to be 5%. 178 The data for year 2014 is shown in the following table (Table 2). This data constituted 179 the performance values for ELECTRE III (note: we considered that all criteria had the 180 same importance, and thus the same weight coefficients). The application of the 181 mathematical model was undertaken with the use of R software (v3.3.1). 182 9 Table 2. Criteria performance values for the Autonomous Communities, with their confidence interval. 183 184 Criteria C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 Regions A1: Andalucía 282 ±14 253 ±13 19.6 ±0.98 0.239 ±0.012 0.019 ±0.001 1.06 ±0.05 0.75 ±0.04 5.5 ±0.28 3.8 ±0.19 3281 ±164 8 ±0.4 A2: Aragón 332 ±17 281 ±14 19.9 ±1.00 0.416 ±0.021 0.003 ±0.000 0.69 ±0.03 0.76 ±0.04 3.9 ±0.20 3.3 ±0.17 5170 ±259 12 ±0.6 A3: Asturias 428 ±21 297 ±15 17.4 ±0.87 0.524 ±0.026 0.036 ±0.002 0.6 ±0.03 0.72 ±0.04 8.1 ±0.41 4.9 ±0.25 2317 ±116 0 ±0.0 A4: Baleares 284 ±14 272 ±14 16.7 ±±0.84 0.299 ±0.015 0.136 ±0.007 1.08 ±0.05 1.11 ±0.06 3.7 ±0.19 3.3 ±0.17 4527 ±226 0 ±0.0 A5: Canarias 327 ±16 264 ±13 20.3 ±1.02 0.181 ±0.009 0.036 ±0.002 1.72 ±0.09 0.37 ±0.02 7.4 ±0.37 2.6 ±0.13 2650 ±133 2 ±0.1 A6: Cantabria 373 ±19 347 ±17 25.1 ±1.26 0.455 ±0.023 0.009 ±0.000 1 ±0.05 0.75 ±0.04 6.7 ±0.34 4.2 ±0.21 4761 ±238 62 ±3.1 A7: Castilla y León 418 ±21 329 ±16 16.5 ±0.83 0.431 ±0.022 0.004 ±0.000 0.54 ±0.03 0.41 ±0.02 6.6 ±0.33 4.3 ±0.22 3000 ±150 21 ±1.1 A8: Castilla-La Mancha 318 ±16 265 ±13 19 ±0.95 0.255 ±0.013 0.007 ±0.000 0.82 ±0.04 0.46 ±0.02 6.7 ±0.34 3.9 ±0.20 2738 ±137 6 ±0.3 A9: Catalunya 263 ±13 219 ±11 11.2 ±0.56 0.233 ±0.012 0.009 ±0.000 1.41 ±0.07 1.34 ±0.07 5.4 ±0.27 1.9 ±0.10 1669 ±83 16 ±0.8 A10: Comunitat Valenciana 279 ±14 271 ±14 15.8 ±0.79 0.232 ±0.012 0.138 ±0.007 1.21 ±0.06 0.86 ±0.04 7.6 ±0.38 2.9 ±0.15 2043 ±102 9 ±0.5 A11: Extremadura 310 ±16 262 ±13 24 ±1.20 0.406 ±0.020 0 ±0.000 1 ±0.05 0.52 ±0.03 6.4 ±0.32 3 ±0.15 3594 ±180 2 ±0.1 A12: Galicia 304 ±15 243 ±12 16.4 ±0.82 0.33 ±0.017 0 ±0.000 0.67 ±0.03 0.44 ±0.02 5.8 ±0.29 4.9 ±0.25 2504 ±125 54 ±2.7 A13: Madrid 220 ±11 217 ±11 4.6 ±0.23 0.264 ±0.013 0.006 ±0.000 1.31 ±0.07 0.77 ±0.04 2.8 ±0.14 2.2 ±0.11 1295 ±65 63 ±3.2 A14: Murcia 235 ±12 235 ±12 13.5 ±0.68 0.249 ±0.012 0.125 ±0.006 1.84 ±0.09 0.89 ±0.04 7.5 ±0.38 4.1 ±0.21 1535 ±77 10 ±0.5 A15: Navarra 307 ±15 261 ±13 17.6 ±0.88 0.34 ±0.017 0 ±0.000 0.74 ±0.04 0.67 ±0.03 4.8 ±0.24 5.2 ±0.26 3470 ±174 21 ±1.1 A16: País Vasco 265 ±13 234 ±12 8.9 ±0.45 0.539 ±0.027 0.008 ±0.000 0.84 ±0.04 0.91 ±0.05 5.6 ±0.28 2.1 ±0.11 1350 ±68 28 ±1.4 A17: Rioja 308 ±15.4 299 ±15.0 14 ±0.700 0.471 ±0.024 0 ±0.000 0.55 ±0.028 0.6 ±0.030 3.4 ±0.17 3 ±0.15 4539 ±227 0 ±0.0 16 Hokkanen, J., Salminen, P., 1997. 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