Waste management project\'s alternatives: A risk-based multi-criteria assessment (RBMCA) approach

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Waste Management 32 (2012) 194–212

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Waste management project’s alternatives: A risk-based multi-criteria assessment (RBMCA) approach Athanasios C. Karmperis ⇑, Anastasios Sotirchos, Konstantinos Aravossis, Ilias P. Tatsiopoulos National Technical University of Athens, School of Mechanical Engineering, Sector of Industrial Management and Operational Research, Athens, Greece

a r t i c l e

i n f o

Article history: Received 30 November 2010 Accepted 4 September 2011 Available online 5 October 2011 Keywords: Benefit-cost Monte Carlo simulation Multi-criteria assessment Project’s alternatives Risk preference Waste management projects

a b s t r a c t This paper examines the evaluation of a waste management project’s alternatives through a quantitative risk analysis. Cost benefit analysis is a widely used method, in which the investments are mainly assessed through the calculation of their evaluation indicators, namely benefit/cost (B/C) ratios, as well as the quantification of their financial, technical, environmental and social risks. Herein, a novel approach in the form of risk-based multi-criteria assessment (RBMCA) is introduced, which can be used by decision makers, in order to select the optimum alternative of a waste management project. Specifically, decision makers use multiple criteria, which are based on the cumulative probability distribution functions of the alternatives’ B/C ratios. The RBMCA system is used for the evaluation of a waste incineration project’s alternatives, where the correlation between the criteria weight values and the decision makers’ risk preferences is analyzed and useful conclusions are discussed. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The decision to proceed or not with an investment is one of the most critical issues in the development strategy of a public or private organization. Generally, projects that are implemented in the waste management (WM) field are considered as investments, due to the high initial cost and the project’s long time horizon. In most cases, each WM project has a number of alternatives based on different technical solutions, objectives, or site selection. The project’s alternatives are identified by decision makers, who compute the different costs to incur and benefits to be obtained by each one, in order to compare them and to select the optimum project’s alternative. However, these computations include a high degree of uncertainty associated with the total project’s risks. Generally, risk is defined as ‘‘the probability of an event and its consequences’’ (Hull, 1990), while a risk-based decision making process involves the quantification of the risks incurred in a project, so as to estimate their overall impact on the project’s performance. Moreover, in a risk-based decision making process, the attitude of decision makers towards risks is crucial (Xie et al., 2011), i.e. whether they are risk-neutral, risk-averse, or risk-seeking. Cost benefit analysis (CBA) is a tool that provides a specific method for the appraisal ⇑ Corresponding author. Address: National Technical University of Athens, School of Mechanical Engineering, Sector of Industrial Management and Operational Research, Iroon Polytechniou 9 Str., 15780 Zografou, Athens, Greece. Tel.: +30 210 7721066; fax: +30 210 7723571. E-mail addresses: [email protected], [email protected] (A.C. Karmperis), [email protected] (A. Sotirchos), [email protected] (K. Aravossis), [email protected] (I.P. Tatsiopoulos). 0956-053X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.wasman.2011.09.001

and evaluation of WM projects and has been widely used over the last decades. As can be seen in Fig. 1, the CBA process includes some basic steps, in which a project’s alternatives are evaluated in the third step according to economic criteria. Furthermore, the quantification of the project’s risks is considered only for the selected option in the last step. However, especially in a WM project, there are many financial, technical, environmental and social risks that maybe posed in its various alternatives. Therefore, quantification of these risks for all the identified options is crucial in a risk-based decision making process. 1.1. Scope and structure As presented in Fig. 1, the scope of the paper is the third step of the CBA process i.e. ’The study of the feasibility of the project and of alternative options’, while the other five steps are not. Specifically, this paper focuses on the correlation between a given set of alternatives of a WM project and the quantification of the project’s risks for all the identified alternatives, in order to evaluate them. A novel approach in the form of risk-based multi-criteria assessment (RBMCA) is introduced, which can be used by decision makers, in order to select the optimum alternative of a WM project according to multiple criteria. In the RBMCA system, decision makers select the evaluation criteria based on the quantitative risk analysis (RA) of the WM project’s alternatives as well as the criteria weight values according to their risk preferences. The rest of this paper includes the review of the literature on commonly used methods for a WM project’s evaluation and particularly for the evaluation of its alternatives, as well as the review on the quantitative RA methods

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Fig. 1. Flowchart of the cost benefit analysis and the risk-based multi-criteria assessment (RBMCA) system.

in Section 2. A RBMCA approach for the evaluation of a WM project’s alternatives is presented in Section 3 and is implemented in a case study for a waste incineration project in Section 4, where the results arising are further examined. Useful conclusions as well as the application of the RBMCA system are discussed in the last Section 5. 2. Literature review In the literature reviewed, several decision support systems are proposed for WM projects (Çelik et al., 2010). However, the initial evaluation process is mainly implemented through the CBA, the life cycle assessment and the multi-criteria analysis (Morrissey and Browne, 2004). 2.1. Cost benefit analysis 2.1.1. In general CBA is a widely used method for the evaluation of WM options (see for example, Aye and Widjaya, 2006; Lavee, 2010). In the early 1900, the CBA was first introduced in the United States (Hammond, 1966) and has developed rapidly since the 1950s. CBA is regarded as the main investment evaluation tool, through the quantitative summation of the investment’s anticipated impacts on consumption benefits and resource costs (Almansa and Martínez-Paz, 2011). Furthermore, as suggested by the European Commission’s (EC) guide to CBA of investment projects (EC, 2008), each investment in the WM field is examined separately, while the project’s appraisal document should be structured in six basic steps, which are illustrated in Fig. 1: (1) A presentation and discussion of the socio-economic context and the objectives. (2) The clear identification of the project. (3) The study of the feasibility of the project and of alternative options.

(4) Financial analysis. (5) Economic analysis. (6) Risk assessment. However, a WM project has a number of alternatives on the basis of technical, financial, economic, environmental and managerial constraints as well as demand opportunities, which are evaluated in the third step, during the feasibility and option analyses. As presented in Fig. 1, this third step, i.e. ‘The study of the feasibility of the project and of alternative options’, includes three sub-steps: (3a) Identification of all possible options, (3b) Feasibility analysis of these possible options, and (3c) The option selection. The specific guide to CBA (EC, 2008), suggests to carry out a simplified financial and economic analysis for each project’s alternative, in order to compare them and then to select one. The option that is selected is further assessed for its financial and economic performance in the subsequent steps. Particularly, economic analysis includes the computation of the selected option’s evaluation indicator, namely benefit/cost (B/C) ratio. The later step of the CBA is the risk assessment and consists of studying the probability that the selected option will achieve an accepted performance. This assessment is implemented through the calculation of the cumulative probability distribution function (CPDF) of the option’s B/C ratio. In this function, decision makers calculate the B/C ratio’s expected value (EV), which is a constant number that serves as the best prediction of the B/C’s value. For instance, if a B/C ratio can take value 0.8 with probability 10%, value 0.9 with probability 30%, value 1.35 with probability 35%, value 1.5 with probability 20% and value 2.0 with probability 5%, then the best prediction of the B/C ratio’s value is its EV and is calculated: EV = 0.8(10%) + 0.9(30%) + 1.35(35%) + 1.5(20%) + 2(5%) = 1.2225. Particularly, EV is the weighted average of all possible values that the B/C ratio can take on and is calculated through the sum of all possible values of the B/C ratio, where each value multiplied by its probability of occurrence. That is, when a B/C ratio can take value B/C1 with probability p1, value B/C2 with probability p2,. . ., value B/Cn with

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Table 1 List of notations, abbreviations and formulas. Cost benefit analysis Contingent valuation Analytic hierarchy process Risk analysis Present value Waste management Externalities (negative or positive)

CBA CV AHP RA PV WM

Inflows: estimated per year = t

Inflows(a)t

Consequences of the project’s activity, which result in a loss (negative externalities) or gain (positive externalities) in the welfare of unrelated third parties Summary of the total benefits (revenues and positive externalities) for each project’s alternative (a), arising through the project’s operation  Examples of revenues in WM projects: revenues through energy selling, revenues through service fees  Examples of positive externalities: the sick rate avoided, added value per m2 irrigated, saving of groundwater resources, limitation of the emission of CO2 Summary of the total costs (expenditures and negative externalities) for each project’s alternative (a), arising through the project’s operation

Outflows: estimated per year = t

Outflows(a)t  Examples of costs in WM projects: initial investment cost, operational costs  Examples of negative externalities: the water or/and air pollution by industries that adds poisons to the water or/and air, which harm plants, animals, and humans

Discounted cash flow analysis

DCFA

Project’s variables: i = 1, 2, 3, . . . , etc.

Vi

Adjustment of the future values of project cash inflows and outflows to present values (PV) using a discount rate, i.e. multiplying the future value by a coefficient that decreases with time All the appropriate parameters, which are included in the calculations of the project’s Inflowst and Outflowst, and its values is expected to have variations throughout the project’s time horizon  One example is the inflation, which is not constant during a project’s time horizon  Another example is the initial investment cost, which is initially estimated to have a specific value, however it is possible to have a higher or lower value All the appropriate parameters, which are included in the calculations of the project’s Inflows and Outflows, and is expected to have constant values throughout the project’s time horizon

Project’s fixed parameters: j = 1, 2, 3, . . ., etc.

Fj  One example of a fixed parameter is the SDR, which is used in the adjustment of future values of project cash inflows and outflows to present values and is constant  Another example is the parameter of energy production: MWh/ton of waste burned in an incinerator It reflects the social view on how net future benefits should be valued against present ones

Social discount rate

SDR

Present value of inflows

PVInflows(a)

Present value of outflows

PVOutflows(a)

Monte Carlo simulation

MCS

Cumulative probability distribution function

CPDF

 In this paper: SDR = 5.5% (see EC, 2008) Pr InflowstðaÞ t¼1 ð1þSDR%Þt , r = time horizon, t = years, for each project’s alternative (a)

PVInflowsðaÞ ¼

PVOutflowsðaÞ ¼

Pr

t

OutflowsðaÞ t¼1 ð1þSDR%Þt ,

r = time horizon, t = years, for each project’s alternative (a)

An analytical technique for calculating the probability distribution of possible outcomes for the selected output/s, which are functioned with the selected input/s, by performing a large number of trail runs, called simulations in the inputs. In the RBMCA, all the project’s variables Vi are defined as inputs in the MCS model, by assigning a specific probability distribution to each one, while the alternatives’ B/C ratios are defined as outputs A function that shows the probability that the random variable will attain a value less than or equal to each value that the random variable can take on. In the RBMCA, all the alternatives’ B/C ratios are defined as outputs and thus, there is a specific CPDF for each alternative’s B/C ratio, which is calculated through the MCS For instance, assume a B/C ratio (output) that is calculated with the Variables V1, V2 (inputs), which follow the triangular probability distributions presented in the Table, according to the function: V1 + V2 = B/C: Variables

Minimum value

Most probable value

Maximum value

V1

0.5

0.75

1.0

V2

0.2

0.80

1.2

In each simulation (run) there is a stochastic value allocated to each of the V1, V2 in the range of their lower and upper bounds (0.5–1.0 and 0.2–1.2, respectively), e.g.:  Simulation 1: V1 = 0.51, V2 = 0.88 ? B/C = 1.39  Simulation 2: V1 = 0.95, V2 = 0.25 ? B/C = 1.20  ...  Simulation 5000: V1 = 0.50, V2 = 0.30 ? B/C = 0.80 Through the 5000 simulations, the CPDF of the B/C ratio that will be illustrated, will have as lower bound of the B/C ratio the B/C = 0.5 + 0.2 = 0.7 and as upper bound the B/C = 1.0 + 1.2 = 2.2, while most calculations of the B/C values will be closely to the inputs’ most probable values: B/C = 0.75 + 0.8 = 1.55 WM project’s alternatives Benefit cost (B/C) ratio for each project’s alternative a = 1, 2, 3, . . ., n

a = 1, 2,. . ., n B/Ca

The ratio of the present value (PV) of project inflows to the PV of project outflows over the project’s time horizon B/Ca = PVInflows(a)/PVOutflows(a)

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Table 1 (continued) Evaluation criteria

c = 1, 2, . . ., k

Expected value of the B/C ratio of the project’s alternatives a = 1, 2, 3, . . ., n

EVa

c = 1: EVs of the alternatives’ B/C ratios; c = 2, 3, 4,. . ., k: probability for B/C > 1, probability for B/ C > 1.2, . . ., etc. The weighted average of all possible values that the B/C ratio can take on. It is calculated through the sum of all possible values of the B/C ratio, where each value multiplied by its probability of occurrence. For instance, if a B/C ratio can take value B/C1 with probability p1, value B/C2 with probability p2, . . . , value B/Cm with probability pm, where: p1 + p2 + . . . + pm = 100%, then the B/C ratio’s EV is a constant number, calculated with: P EV ¼ m r¼1 B=Cr ðpr Þ

EVHighest: the highest one between the project alternatives’ EVs For each project’s alternative a = 1, 2, 3, . . ., n, there is: A specific CPDF of its B/C ratio A specific EVa of the alternative’s B/C ratio, which is constant and is calculated through its CPDF P c 0 6 weightc 6 100 and kc¼1 weight ¼ 100 Example: In the c = 3 criterion (probability of B/C > 1.5), the probability of the a = 4th alternative’s B/ C ratio for higher than 1.5 value, is estimated through the analysis of its CPDF in 26%. In this case: p34 ¼ 26%    

Weight values of the criteria c = 1, 2, 3, . . . ,k

weightc

Probability of the alternatives’ B/C ratios for higher values than the criteria B/C values

pca

Alternatives’ scores in the c = 1 criterion: (EVs of the alternatives’ B/C ratios) Alternatives’ scores in the c = 2, 3, . . ., k criteria

score1a

score1a ¼ EV a ðweight Þ=EV Highest , for each project’s alternative a = 1, 2, 3, . . . ,n

scoreca

Alternatives’ total scores

total scorea

scoreca ¼ pca ðweight Þ, for each project’s alternative a = 1, 2, 3, . . ., n, in each of the evaluation criteria c = 2, 3, 4,. . ., k P total scorea ¼ kc¼1 scoreca , for each project’s alternative a = 1, 2, 3, . . . ,n

1

c

probability pn, where: p1 + p2 +    + pn = 100%, then the B/C ratio’s EV is given:

B=C1 ðp1 Þ þ B=C2 ðp2 Þ þ    þ B=Cn ðpn Þ () EV p1 þ p2 þ    þ pn n X B=C i ðpi Þ ¼

EV ¼

ð1Þ

i¼1

Furthermore, the CPDF can be further analyzed in order to estimate the probability of the B/C ratio to have higher values than specific target values, e.g. the probability of B/C > 1, or/and the probability of B/C > 1.2. Through this process, the decision makers have the necessary results and can use different evaluation criteria, in order to decide to proceed on the investment or not. The evaluation criteria that can be used are illustrated in the subsequent sections, while a complete list of definitions, abbreviations, notations and formulas used in this paper is presented in Table 1. 2.1.2. Investment evaluation in the cost benefit analysis Generally, the commonly used method for the investment evaluation is the discounted cash flow analysis (DCFA), where the cash flows arising in different years are adjusted in present value (PV) with the use of the discount rate (Karmperis et al., 2010; Sotirchos et al., 2011). The DCFA is used in the financial analysis, which is implemented on behalf of the investment’s owners, as well as in the economic analysis, which is implemented on behalf of the whole society and takes into consideration the social and environmental externalities (positive or negative). The WM projects are examined in a case by case basis and it is crucial to distinguish the resulting costs and benefits of the project. For instance, in the wastewater treatment sector, boundaries for downstream effects should be clear, either including the area affected immediately, or consider the impacts on irrigation, fishing and drinking water (ADB, 1997). However, due to the fact that in most cases the WM projects are classic cases of a monopoly market, the revenues collected by the operator, even if corrected by means of appropriate conversion factors do not represent the project’s social and environmental externalities. As presented in Table 1, externalities can be positive or negative (Nahman, 2011), e.g. the safeguarding of human health and the integrity of human species, or the noise, odours, aesthetic and landscape impacts of the plant, respectively. In the case that market prices do not exist, relevant approaches can be followed (Aravossis and Karydis, 2004). The

most common approach is the use of the contingent valuation (CV) method, which is a survey-based method frequently used for placing monetary values on goods and services not bought and sold in the marketplace. CV method has been used in many studies for the evaluation of a consumer’s willingness to pay for different product/services attribute (Fu et al., 1999). Additionally, in the appraisal of non-market goods, there is also the benefittransfer approach specifically for environmental goods and services (Pearce et al., 2006), while several approaches are also suggested in valuing time, health benefits, landscape or water (HM Treasury, 2004). However, economic analysis focuses on the calculation of the B/ C ratio that is the ratio of the PV of project inflows (summary of the total revenues and positive externalities), which is divided by the PV of project outflows (summary of the total costs and negative externalities), over the investment’s time horizon (EC, 2008; Nahman, 2011):

B=C ¼ PVinflows =PVoutflows

ð2Þ

Particularly, according to the CBA methodology, the criterion for evaluation result to be positive for a specific investment, the value of the B/C ratio is to be higher than unity i.e. 1. If B/C > 1, then the project is feasible, as the benefits, measured by the PV of the total inflows, are greater than the relative costs, measured by the PV of the total outflows. In the literature, several authors use the B/C ratio (Yang et al., 2004) and examine its application in the fuzzy set theory (Kahraman et al., 2000) as well as in the analytic hierarchy process (AHP) (Wedley et al., 2001), while Campbell and Brown (2005) propose a spreadsheet-based multiple account framework for the investment evaluation with the CBA. Further, as mentioned by Nagel (1983) a program’s alternatives evaluation consists of finding the alternative that has the highest score on a combination of benefits and costs. Thus, when comparing a WM project’s alternatives, the alternative that is preferred is the one whose B/C ratio has positive evaluation (i.e. greater than unity/one) and also has higher value than the corresponding B/C ratios of the other alternatives (Wedley et al., 2001). For instance, let’s consider a WM project which has two alternatives, namely A and B. In the CBA, it is established that cost-benefit ratio for the alternative A, B/CA = 1.4 and that for the alternative B, B/CB = 1.25. Thus the alternative A should be preferred to the alternative B because the alternative A satisfies both conditions, i.e. B/CA = 1.4 > 1 and B/CA = 1.4 > B/CB = 1.25.

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2.2. Quantitative risk analysis The risk assessment follows the economic analysis and supports the total investment’s evaluation process, simply by weighting the economic performance with the incurred risk. Generally, a WM project’s performance is mainly influenced by financial risks, such as the energy prices and demand, as well as by environmental risks, e.g. the noises and aesthetic impact on landscape, or the impact of the project on human health, linked to pollutant emissions and contamination of the environment. Furthermore, the design and construction of the infrastructure and the operational WM procedures are some technical risks associated with projects in the WM field. However, the most critical issue in the risk assessment is the quantification of risks (Brookhart et al., 1997), which is mainly implemented with the Monte Carlo Simulation (MCS) technique (see Alonso-Conde et al., 2007; Ng et al., 2007a; Chou, 2010). The flowchart of the MCS process is illustrated in Fig. 2. Initially, all appropriate project’s parameters are identified, which are included in the calculation of the B/C ratio in Eq. (2) and thus their variations have a positive or negative impact on the project’s performance. Depending on the expectation for their values to be constant or to have variations throughout the project’s time horizon, the project’s parameters are classified as fixed parameters or variables, respectively. Typical fixed parameters associated with WM projects is the discount rate and the energy produced by the waste burned in an incinerator (MWh/ton), while typical variables is the inflation, the operational costs and the positive and negative externalities. Furthermore, the probability distribution of the variables’ range around the best estimate value is used (Balcombe and Smith, 1999; Moreno and Navas, 2003; Rentizelas et al., 2007), in order to assess their overall impact on the B/C ratio. Specifically, decision makers select the appropriate distribution and the range values for each variable and develop a MCS model, in which all project’s variables are defined as inputs and the B/C ratio is defined as output. According to the project’s size and the importance of risks, the decision makers select the number of runs that the simulation

should be performed, i.e. 1000, 2000, 5000, or 10,000 (Rezaie et al., 2007), taking into consideration that a higher number of runs provides more accurate results. The simulation is performed using random values of the inputs, so that the overall impact of the project’s variables is taken into account and the possible range of the B/C ratio is calculated, graphically expressed as the CPDF. However, the CPDF can be further analyzed by decision makers, in order to assess the project’s risks (Chou et al., 2009). As shown by Ng et al. (2007b), in case that the probability of B/C < 1, is higher than a pre-defined level, then the examined scenario should be considered as risky and is not preferred, otherwise it should be followed. For instance, consider a scenario with two different projects, namely A and B, where the CPDFs of their B/C ratios are illustrated in Figs. 3 and 4, respectively. As can be seen in Fig. 3, there is 11.44% probability for the B/CA < 1 and thus project A can be considered as low risk project and be followed. On the other hand, the relative CPDF of project’s B B/C ratio illustrated in Fig. 4, shows that there is 18.11% probability for the B/CB < 1 and thus, it depends on the decision makers’ risk preferences, whether this probability value is acceptable or not.

2.3. Evaluation of a waste management project’s alternatives 2.3.1. Multi-criteria decision making methods Multi-criteria decision making theory consists of techniques and tools developed in the specific field that help the decision makers to solve problems. In most cases, these tools provide the appropriate steps that the decision makers should follow in order to analyze and compare alternative solutions and to select the optimum one according to their decision criteria. In the environmental field there are various decision-making tools that are suggested by the literature, such as the multi-criteria analysis, the analytic hierarchy process (AHP) (Karagiannidis et al., 2010), the Electre III method (Ohman et al., 2007) and the PROMETHEE and GAIA methods (Aravossis et al., 2001).

Fig. 2. Flowchart of the Monte Carlo simulation (MCS).

Fig. 3. Cumulative probability distribution function of the B/C ratio (Project A).

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Fig. 4. Cumulative probability distribution function of the B/C ratio (Project B).

2.3.2. Analytic hierarchy process AHP is a quite simple and flexible technique first introduced by Saaty in the 1970s, which provides a framework for evaluating alternative solutions of complex problems (Saaty, 1978). The AHP supports the decision makers through the hierarchical structure of the identified alternatives and the use of quantitative or/and qualitative criteria (Ramanathan, 2002) that are defined as well as the weight of each criterion (Lin et al., 2010), in order to compare the alternatives and to select the optimum one (De Feo and De Gisi, 2010). Many applications of the AHP are examined in the literature for WM projects. Specifically, Sener et al. (2010) combine the AHP with GIS techniques, in order to determine the optimum landfill site for the Lake Beysehir catchment area, while Hung et al. (2007) proposes a decision-making model, which uses the fuzzy AHP to prioritize the WM project’s alternatives. Promentilla et al. (2006) propose the generalization of AHP in the analytic network process, which is a multi-criteria decision analysis tool for the evaluation of the remedial of contaminated sites in Japan and Khan and Faisal (2008) propose an analytic network process model that is based on the generalization of the AHP, in order to select the optimum alternative for solid waste disposal. Furthermore, Garfi et al. (2009) use the multi-criteria analysis to compare alternatives and present optimum solutions for waste management in Saharawi refugee camps and Hsu et al. (2008) develop a method for selecting medical waste disposal firms, where the AHP is combined with the modified Delphi method and supports the decision-making process. 2.3.3. Decision makers’ risk preferences Generally, when comparing a WM project’s alternatives, namely 1, 2, 3,. . ., a, according to their B/C ratios, namely B/C1, B/C2, B/ C3, . . ., B/Ca, respectively, the preferred alternative is the one, in which:  Its B/C ratio has the highest EV compared with the relative EVs of the other alternatives (see criterion 1 in par. 3.2.4 and par. 4.2.4). For instance, if the EV1 = 1.4, the EV2 = 1.3, . . ., and the EVa = 1.45, then alternative a is preferred, because: EVa = 1.45 > EV1 = 1.4 >    > EV2 = 1.3.  There is lower probability p for its B/C < 1 or/and higher probability for its B/C > 1, against the relative probability of the other alternatives’ B/C ratios (see criterion 2 in par. 3.2.4 and par. 4.2.4). For example, if the probability for B/C1 < 1 is p1 = 15%, the relative probability for B/C2 < 1 is p2 = 35%,. . ., the relative probability for B/Ca < 1 is pa = 40%, then alternative 1 is preferred, because: p1 = 15% < p2 = 35% p1 = 40% >, . . ., > pa = 25%. However, in a risk-based decision making process where the evaluation criteria along with their weight values are defined by the decision makers, the attitude of decision makers towards risks is crucial. Specifically, it is mentioned that the decision makers’ risk preferences, i.e. whether they are risk-neutral, risk-averse, or risk-seeking, have an impact on their optimal decisions (see Yang et al., 2009; Wu et al., 2010; Zhao et al., 2010). In the literature, a decision maker’s risk preference, which is defined as the attitude of the decision maker towards risk, is classified as follows: (1) Risk-neutral: a decision maker who ignores risk in making investment decisions and considers only the expected profit from each investment. (2) Risk-averse: a decision maker who prefers a certain profit to an uncertain profit (Gan et al., 2004). (3) Risk-seeking: a decision maker who is willing to take big risks, in order to increase the potential profit of an investment. For instance, if the B/C ratio of a WM project has the CPDF presented in Fig. 3, then a risk-averse decision maker will consider the probability of B/CA < 1, which is estimated in 11.44%. Moreover, a risk-neutral decision maker will give a higher priority in the B/C ratio’s expected value that is EVA = 1.2, while a risk-seeking decision maker will consider to increase the potential profit, e.g. the probability of B/C > 1.5, which is estimated in 100–93.52 = 6.48%. However, if the CPDFs illustrated in Figs. 3 and 4 represent the A and B alternatives of a WM project, then the analysis of their B/C ratios’ CPDFs gives:  For alternative A, the probability p (0.5 < B/CA < 1.0) = 11.44%, the p (1.0 < B/CA < 1.5) = 82.08%, the p (1.5 < B/CA < 2.0) = 6.48%, while the EVA = 1.20.  For alternative B, the relative probability is estimated in p (0.5 < B/CB < 1.0) = 18.1%, the p (1.0 < B/CB < 1.5) = 59.46%, the p (1.5 < B/CB < 2.0) = 22.43% and the EVB = 1.27.

(€/year) (€/year)

V1  V 2 + V 3 + V 1  F 4  V 4

–

(€/MWh)

V1  V 2 + V 3 + V 1  F 3  V 4 + V 1  F 5  V 5

–

(MWh/ton)

(€/year)

22.50

(€/MWh)

V1  V 2 + V 3 + V 1  F 2  V 4

F1 = 0.66

(MWh/ton)

–

–

–

Inflowsð1Þ ¼ 30; 270; 000:00

2

1,300,000.00

(€/year)

(€/year)

200,000.00 130.00 26,000,000.00

–

(€/year)

(ton/year) (€/ton) (€/year)

–

(€/year)

V1  V2 + V3 + V1  F 1  V4

V5

F5

V4

Fa

V3

V1 V2 V1  V2

2nd year Inflows t=2

–

(€/year)

1

Outflowsð1Þ ¼ 86; 785; 000:00

1

Inflowsð1Þ ¼ 0

(€/year)

(€/year)

Units

–

2

–

–

Inflowsð2Þ ¼ 29; 280; 000:00

–

–

–

22.50

F2 = 0.44

1,300,000.00

200,000.00 130.00 26,000,000.00

–

–

–

–

2

–

Inflowsð3Þ ¼ 30; 666; 000:00

–

–

6.00

1.98

22.50

F3 = 0.22

1,300,000.00

200,000.00 130.00 26,000,000.00

–

1

2

Inflowsð4Þ ¼ 29; 280; 000:00

–

–

–

–

–

22.50

F4 = 0.44

1,300,000.00

200,000.00 130.00 26,000,000.00

Outflowsð4Þ ¼ 81; 000; 000:00

1

Inflowsð4Þ ¼ 0

Project’s 4th Alternative (a = 4) Firing system, electrostatic precipitator, precipitation, activated coke absorber and catalytic plant with power generation (Steam extraction turbine applying steam parameters: 50 bar, 400 °C)

1 Outflowsð3Þ ¼ 88; 810; 000:00 –

1

Inflowsð3Þ ¼ 0

Project’s 3rd alternative (a = 3) Firing system, dry, wet and catalytic flue gas treatment with cogeneration (CHP) (applying steam parameters: 50 bar, 400 °C)

1 Outflowsð2Þ ¼ 86; 110; 000:00 –

–

1

Inflowsð2Þ ¼ 0

Project’s 2nd alternative (a = 2) Firing system, dry, wet & catalytic flue gas treatment with power generation (Steam extraction turbine applying steam parameters: 50 bar, 400 °C)

200

Demand Service fees Revenues (fees) Positive externalities Electricity production Electricity selling price Heat production Heat selling price

In the 1st year, the waste incineration plant is under construction and thus there are no inflows (revenues or positive externalities), while the relative outflows are equal to the initial investment costs Initial V18 investment costs(1) Initial V19 investment costs(2) Initial V20 investment costs(3) Initial V21 investment costs(4)

1st year t = 1

Description

Variables/functions

Year

Project’s 1st alternative (a = 1) Firing system, dry, wet and catalytic flue gas treatment (water steam cycle: comprising a steam extraction turbine in combination with the steam system of an adjacent power plant)

Table 2 t t Expected inflows ðInflowsðaÞ Þ and outflows ðOutflowsðaÞ Þ of the project’s alternatives: a = 1, 2, 3, 4 in the 1st (t = 1) and 2nd year (t = 2) of the project’s time horizon.

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2nd year Outflows t=2

8.19

–

(€/ton)

(€/ton)

(€/year) (€/year) (€/year)

V1  (V7 + V8 + V9 + V14 + V16 + V17) + V6 + V10

1.50

(%) (€/year)

–

–

–

Outflowsð1Þ = 15,698,000.00

–

(€/ton)

2

5.48

(€/ton)

–

7.21

(€/ton)

(€/ton)

1,800,000.00

(€/year)

–

3.20

(€/ton)

(€/ton)

36.42

4.24

(€/ton)

(€/ton)

950,000.00

(€/year)

V1  (V7 + V8 + V9 + V11 + V12 + V15) + V6 + V10

Negative externalities Discharge and storage costs Firing system and boiler Catalytic flue gas cleaning Personnel costs Dry flue gas cleaning Gypsum scrubber Steam extraction turbine (thermal) Steam extraction turbine Cogeneration (CHP) applying steam Electrostatic precipitator and scrubber Activated coke absorber Inflation

V1  (V7 + V8 + V9 + V11 + V12 + V14) + V6 + V10

V22 V1  (V7 + V8 + V9 + V11 + V12 + V13) + V6 + V10

V17

V16

V15

V14

V13

V12

V11

V10

V9

V8

V7

V6

–

–

2

Outflowsð2Þ = 14,664,000.00

1.50 –

–

–

–

3.02

–

5.48

7.21

1,800,000.00

3.20

36.42

4.24

950,000.00

2

–

Outflowsð3Þ = 15,674,000.00

–

1.50 –

–

–

8.07

–

–

5.48

7.21

1,800,000.00

3.20

36.42

4.24

950,000.00

2

Outflowsð4Þ = 15,510,000.00

–

–

1.50 –

4.92

12.00

–

3.02

–

–

–

1,800,000.00

3.20

36.42

4.24

950,000.00

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¼ 315; 596; 842

t

t

ðV1 ðV2 þF4 ðV4 ÞÞþV3 Þð1þV22 Þt2 ð1þ5:5%Þt

¼ 305; 275; 042

PVoutflowsð2Þ ¼

t

Outflowsð4Þ t¼1 ð1þ5:5%Þt

P16

ð1Þ

t

Outflowstð3Þ t¼1 ð1þ5:5%Þt

P16

Outflowsð2Þ t¼1 ð1þ5:5%Þt

P16

V21 ¼ 1þ5:5% þ

V20 ¼ 1þ5:5% þ

V19 ¼ 1þ5:5% þ

V18 ¼ 1þ5:5% þ

B=C1 ¼ PVOutflowsð1Þ ¼ 315;596;842 245;928;956 ¼ 1:2833

PVInflows

PVoutflowsð4Þ ¼

PVoutflowsð3Þ ¼

Outflowsð1Þ t¼1 ð1þ5:5%Þt

t

t¼2

P16

t¼2

t¼2

P16

P16

t¼2

P16

ðV1 ðV7 þV8 þV9 þV14 þV16 þV17 ÞþV6 þV10 Þð1þV22 Þt2 ð1þ5:5%Þt

ðV1 ðV7 þV8 þV9 þV11 þV12 þV15 ÞþV6 þV10 Þð1þV22 Þt2 ð1þ5:5%Þt

ðV1 ðV7 þV8 þV9 þV11 þV12 þV14 ÞþV6 þV10 Þð1þV22 Þt2 ð1þ5:5%Þt

ðV1 ðV7 þV8 þV9 þV11 þV12 þV13 ÞþV6 þV10 Þð1þV22 Þt2 ð1þ5:5%Þt

¼ 245; 928; 956

¼ 238; 485; 445

¼ 247; 598; 162

¼ 234; 508; 600

t

(V1  (V7 + V8 + V9 + V14 + V16 + V17) + V6 + V10)  (1 + V22)t2

P16

t

(V1  (V7 + V8 + V9 + V11 + V12 + V15) + V6 + V10)  (1 + V22)t2

PVoutflowsð1Þ ¼

t

(V1  (V7 + V8 + V9 + V11 + V12 + V14) + V6 + V10)  (1 + V22)t2

ð2Þ

B=C2 ¼ PVOutflowsð2Þ ¼ 305;275;042 234;508;600 ¼ 1:3018

PVInflows

Outflowsð4Þ

Outflowsð3Þ

Outflowsð2Þ

t

Outflowsð1Þ

(V1  (V7 + V8 + V9 + V11 + V12 + V13) + V6 + V10)  (1 + V22)t2

0

15,510

15,674

14,664

15,698

984

2400

1614

604

1638

1096

1442

1800

640

7284

848

950

0

0

0

PVInflows

ð3Þ

B=C3 ¼ PVOutflowsð3Þ ¼ 319;725;061 247;598;162 ¼ 1:2913

alternatives’ B/C ratios

Computation of the project’s

PVInflows

ð4Þ

B=C4 ¼ PVOutflowsð4Þ ¼ 305;275;042 238;485;445 ¼ 1:2801

Computation of the project’s alternatives’ outflow in present value (PVOutflows)

81,000

88,810

86,110

86,785

0

0

Activated coke absorber

V14  V1  (1 + V22)t2

0 0 0

V17  V1  (1 + V22)t2

Steam extraction turbine (thermal power plant)

V13  V1  (1 + V22)t2 0

Gypsum scrubber

V12  V1  (1 + V22)t2 0

Dry flue gas cleaning

V11  V1  (1 + V22)t2

0

Electrostatic precipitator, scrubber with precipitator

Personnel costs

V10  (1 + V22)t2

0

0 0

Cogeneration applying steam (50 bar, 400 °C)

Catalytic flue gas cleaning

V9  V1  (1 + V22)t2

Steam extraction turbine (50 bar, 400 °C)

Firing system and boiler

V8  V1  (1 + V22)t2

V15  V1  (1 + V22)t2

Discharge and storage costs

V7  V1  (1 + V22)t2

81,000 0

V16  V1  (1 + V22)t2

Negative externalities

V6  (1 + V22)t2

86,785

15,742

15,909

14,883

15,933

998

2436

1638

613

1662

1112

1463

1827

649

7393

860

964

0

0

0

0

29,719

31,125

29,719

30,724

2009

3416

2009

3014

1319

26,390

t=3

15,978

16,147

15,107

16,172

1013

2472

1662

622

1687

1129

1485

1854

659

7504

873

978

0

0

0

0

30,164

31,592

30,164

31,184

2039

3467

2039

3059

1339

26,785

t=4

16,218

16,389

15,333

16,415

1028

2509

1687

631

1712

1146

1507

1882

669

7616

886

993

0

0

0

0

30,617

32,066

30,617

31,652

2070

3519

2070

3105

1359

27,187

t =5

16,461

16,635

15,563

16,661

1044

2547

1713

641

1738

1163

1530

1910

679

7730

900

1008

0

0

0

0

31,076

32,547

31,076

32,127

2101

3572

2101

3152

1379

27,595

t=6

16,708

16,885

15,797

16,911

1060

2585

1738

650

1764

1180

1553

1939

689

7846

913

1023

0

0

0

0

31,542

33,035

31,542

32,609

2133

3626

2133

3199

1400

28,009

t=7

16,959

17,138

16,034

17,164

1075

2624

1764

660

1791

1198

1576

1968

699

7964

927

1038

0

0

0

0

32,016

33,531

32,016

33,098

2165

3680

2165

3247

1421

28,429

t=8

17,213

17,395

16,274

17,422

1092

2663

1791

670

1817

1216

1600

1997

710

8084

941

1054

0

0

0

0

32,496

34,034

32,496

33,595

2197

3735

2197

3296

1442

28,855

t=9

17,471

17,656

16,518

17,683

1108

2703

1818

680

1845

1234

1624

2027

720

8205

955

1070

0

0

0

0

32,983

34,545

32,983

34,098

2230

3791

2230

3345

1464

29,288

t = 10

17,733

17,921

16,766

17,948

1125

2744

1845

690

1872

1253

1648

2058

731

8328

969

1086

0

0

0

0

33,478

35,063

33,478

34,610

2263

3848

2263

3395

1486

29,728

t = 11

17,999

18,190

17,018

18,218

1141

2785

1873

700

1900

1271

1673

2088

742

8453

984

1102

0

0

0

0

33,980

35,589

33,980

35,129

2297

3906

2297

3446

1508

30,174

t = 12

18,269

18,463

17,273

18,491

1159

2827

1901

711

1929

1291

1698

2120

753

8580

998

1119

0

0

0

0

34,490

36,122

34,490

35,656

2332

3964

2332

3498

1531

30,626

t = 13

18,544

18,740

17,532

18,768

1176

2869

1929

722

1958

1310

1724

2152

765

8708

1013

1135

0

0

0

0

35,007

36,664

35,007

36,191

2367

4024

2367

3550

1554

31,086

t = 14

18,822

19,021

17,795

19,050

1194

2912

1958

732

1987

1330

1749

2184

776

8839

1029

1152

0

0

0

0

35,532

37,214

35,532

36,734

2402

4084

2402

3604

1577

31,552

t = 15

19,104

19,306

18,062

19,336

1212

2956

1988

743

2017

1350

1776

2217

788

8972

1044

1170

0

0

0

0

36,065

37,773

36,065

37,285

2438

4146

2438

3658

1601

32,025

t = 16

202

t = 2, 3, 4, . . ., 16

29,280

30,666

29,280

30,270

1980

3366

1980

2970

1300

26,000

t=2

Computation of the project’s alternatives’ outflows in present value (PVOutflows)

Initial investment costs(4)

t¼2

P16

V21

¼ 0þ

0

88,810

t

Inflowsð4Þ t¼1 ð1þ5:5%Þt

P16

¼ 305; 275; 042

86,110

PVInflowsð4Þ ¼

ðV1 ðV2 þF2 ðV4 ÞÞþV3 Þð1þV22 Þt2 ð1þ5:5%Þt

Initial investment costs(3)

¼ 319; 725; 061

t¼2

P16

Initial investment costs(2)

ðV1 ðV2 þF3 ðV4 ÞþF5 ðV5 ÞÞþV3 Þð1þV22 Þt2 ð1þ5:5%Þt

¼ 0þ

V20

t¼2

P16

Inflowstð2Þ t¼1 ð1þ5:5%Þt

P16

V19

¼0þ

Inflowsð4Þ

PVInflowsð2Þ ¼

0

0

0

0

0

0

Initial investment costs(1)

Inflowsð3Þ t¼1 ð1þ5:5%Þt

P16

ðV1 ðV2 þF1 ðV4 ÞÞþV3 Þð1þV22 Þt2 ð1þ5:5%Þt

t

0

0

0

t=1

Computation of the project’s alternatives’ inflows in present value (PVInflows)

V18

PVInflowsð3Þ ¼

t¼2

P16

t

Inflowstð1Þ t¼1 ð1þ5:5%Þt

¼0þ

(V1  V2 + V3 + V1  F4  V4)  (1 + V22)t2

P16

t

PVInflowsð1Þ ¼

t

Inflowsð3Þ

Inflowsð2Þ

t Inflowsð1Þ

Electricity selling

(V1  V2 + V3 + V1  F3  V4 + V1  F5  V5)  (1 + V22)t2

t2

t revenuesð4Þ

Electricity heat selling revenuesð3Þ

(V1  V2 + V3 + V1  F2  V4)  (1 + V22)t2

(V1  V2 + V3 + V1  F1  V4)  (1 + V22)

V1  F4  V4  (1 + V22)

t2

Electricity selling revenuesð2Þ

V1  F2  V4  (1 + V22)t2

(V1  F3  V4 + V1  F5  V5)  (1 + V22)t2

t

Electricity selling revenuesð1Þ

Positive externalities

V1  F1  V4  (1 + V22)t2

V3  (1 + V22)d

Revenues (fees)

V1  V2  (1 + V22)t2

t2

Description

Variables/functions t = 2, 3, 4, . . ., 16

Table 3 Spreadsheet for the computation of the project’s alternatives B/C ratios (base case values of the variables) (1000.00 €/year).

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According to these estimations, it is concluded that decision makers with different risk preferences will probably use different evaluation criteria and select a different alternative, as follows: (a) A risk-neutral decision maker considers only the EVs of the alternatives’ B/C ratios and thus, he prefers alternative B against alternative A, as the EVB = 1.27 > EVA = 1.20. (b) A risk-averse decision maker prefers the alternative with lower probability for its B/C < 1 against the relative probability of the other alternative. Thus, he selects alternative A instead of alternative B, as there is 11.44% probability for B/CA < 1 that is lower than the probability for B/CB < 1, estimated in 18.11%. (c) A risk-seeking decision maker considers increasing the potential profit, e.g. the B/C > 1.5. In this case, he prefers alternative B against alternative A, because the probability for B/CA > 1.5 is 100–93.52 = 6.48%, which is lower than the relative probability for B/CB > 1.5 estimated in: 100– 77.57 = 22.43%.

2.4. Aims and objectives Generally, the selection of the optimum alternative is based on the evaluation criteria set by the decision makers and specifically on the weight that each criterion has (Benedetti et al., 2008). To the best of our knowledge, there is no specific system in the literature for the evaluation of a WM project’s alternatives, in which the evaluation criteria as well as their weight values are based on the decision makers’ risk preferences. Therefore, the major objectives of this paper can be stated as:  To present a risk-based decision making system for the evaluation of a WM project’s alternatives. The system includes multiple criteria, in order to take into account the decision makers’ risk preferences i.e. whether they are risk-neutral, risk-averse, or risk-seeking.  To examine the proposed system in an illustrative case study for a waste incineration project, with real market values.

3. Risk-based multi-criteria assessment (RBMCA) 3.1. Application of the RBMCA approach Consider a scenario where a specific investment in the WM field is evaluated according to the CBA methodology. This project has a = 1, 2, 3,. . ., n different alternatives, which ensure the achievement of the desired objectives and are based on different disposal methods, i.e. land filling, composting, incineration, or combinations of them. Thus, each alternative has different initial investment cost, energy requirements, labor cost and revenues, while there may be different costs to incur and benefits to be obtained by each one. Target of this paper, is to present a risk-based system that can be followed by decision makers, in order to evaluate these alternatives and come up with the optimum solution according to multiple criteria, which are based on their risk preferences. The proposed system applies in cases where the identified WM alternatives satisfy the project’s objectives and each one has different financial, environmental or social benefits and costs. The RBMCA system presents the appropriate stages that the decision makers should follow, in order to evaluate a WM project’s alternatives according to c = 1, 2, 3, . . ., k evaluation criteria that are based on the CPDFs of the alternatives’ B/C ratios. Clearly, there is no constraint in the number of alternatives or in the number of evaluation criteria that the decision makers can use.

3.2. The basic stages of the RBMCA system The proposed system consists of seven basic stages, as illustrated in Fig. 1. 3.2.1. Stage 1: alternatives’ identification and spreadsheet development In the first stage, decision makers identify all the project’s alternatives that provide the desired result of satisfying or meeting the WM project’s objectives. At this point, a spreadsheet is developed for the computation of the alternatives’ B/C ratios. The spreadsheet includes all appropriate parameters (fixed or variables), which are used once and are functioned with the alternatives’ B/C ratios (see example in Table 3). 3.2.2. Stage 2: probability distribution of the variables According to the second stage of the system, the decision makers assign probability distributions to all the appropriate project’s variables, by selecting their distributions as well as the range of their values around the base case value. 3.2.3. Stage 3: development of a Monte Carlo simulation model In the third stage, a MCS model is developed, where the defined distributions of the variables are used as inputs and the B/C ratios of the a = 1, 2, 3, . . ., n project’s alternatives, namely B/C1, B/C2, B/ C3, . . ., B/Cn, respectively, are defined as outputs. 3.2.4. Stage 4: definition of the decision-making criteria with their weights In the fourth stage, decision makers define the evaluation criteria c = 1, 2, 3, . . ., k and select the weight (weightc) for each one (see also Table 1), as follows:  The weights satisfy: c

0 6 weight 6 100 and

k X

c

weight ¼ 100

ð3Þ

c¼1

 c = 1: expected values (EVs) of the alternatives’ B/C ratios: ? weight1  c = 2, 3, . . ., k: probability p for the alternatives’ B/C ratios to have higher values than specific values: B/C > 1, B/C > 1.2, . . ., B/C > 2.3 ? weight2, weight3, . . . , weightk. 3.2.5. Stage 5: illustration of the cumulative probability distribution functions According to the fifth stage, decision makers run the MCS model, so that the CPDFs of the alternatives’ B/C ratios are illustrated in one graph. 3.2.6. Stage 6: analysis of the cumulative probability distribution functions and calculation of each alternative’s score in each criterion In the sixth stage of the system, the EVs of the alternatives’ B/C ratios are estimated and the CPDFs are further analyzed in the B/C values of the selected criteria, in order to estimate for each alternative the probability pa to has higher than these B/C values. In this point, the score for each of the alternatives a = 1, 2, 3, . . ., n in each of the criteria c = 2, 3, 4, . . ., k is calculated: c

scoreca ¼ pca ðweight Þ

ð4Þ

Especially for the c = 1 criterion, i.e. the EVs of the alternatives’ B/C ratio, the alternatives’ EVs are compared and the highest one (EVHighest) is distinguished, e.g.:

EV4 > EV3 > EVa >    > EV2

ð5Þ

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In this case, EVHighest = EV4 and the score1a for each alternative a = 1, 2, . . ., n is given: 1

score1a ¼ EVa ðweight Þ=EVHighest ) score1a 1

¼ EVa ðweight Þ=EV4

ð6Þ

Further, decision makers summarize each alternative’s score in each criterion c = 1, 2, 3, . . ., k and get the total score for each project’s alternative a = 1, 2, . . ., n:

total scorea ¼ score1a þ score2a þ    þ scoreka ¼

k X

scoreca

ð7Þ

c¼1

3.2.7. Stage 7: selection of the optimum alternative with the RBMCA system In the seventh stage of the system, the alternatives’ total scores are compared and the alternative with the highest total score is selected, e.g. project’s 3rd alternative:

total score3 > total score1 > total score2 >    > total scoren 4. Case study: a waste incineration project In this section, an illustrative case study is presented, in order to guide the reader towards how to implement the proposed RBMCA system. A waste incineration project is examined, which will be implemented in Southeast Europe and includes the construction and operation of a new waste incineration plant. The design capacity is fixed and the plant will have a waste throughput of 200,000 ton per year of urban waste. Initially, there are four different alternatives of the waste incineration project identified, i.e. a = 1, 2, 3, 4, which are based on different technical solutions, such as the water-steam cycle and the energy utilization, i.e. electricity or combined heat power (CHP) (Damgaard et al., 2010).

4.1. Assumptions The basic assumptions in the specific case study are:  It is assumed that other WM alternatives e.g. land-filling, landraising etc were already considered and it was concluded that such options were not feasible for the WM scenario under consideration, and eventually WM incineration was pointed out. However, within incineration four alternatives are identified and these are on which RBMCA is to be applied to choose the most optimum solution. This is illustrated in Section 4.2 below.  The four project’s alternatives are examined in the same time horizon that is one year as the construction phase and 15 years as the operational phase.  The social discount rate that is used in the case study is 5.5%, while the conversion factor, which converts the variables’ market prices to accounting prices, is the standard conversion factor: 0.96, as suggested by the EC’s guide to CBA of investments projects (EC, 2008).  The cost of noise, aesthetic and landscape impact are considered as negative externalities, which impact the market value of the rent for the buildings in the area of the plant. The difference of the market value of the rent without the incinerator and the relative value with the incinerator is estimated in €950,000.00 in the 1st year of the project’s operational phase and is equal for all the project’s alternatives.

 The positive externalities are equal to the benefits due to the greenhouse gas emissions (CO2 and CH4) that would be produced without the waste incineration project, i.e. through the solid waste land-filling (see Nahman, 2011). These benefits are estimated in €6.50/ton of the waste burned in the incinerator and thus, the positive externalities for the 1st year of the operational phase are estimated as: 6.50 (€/ton)  200,000 (ton/year) = 1,300,000€, which is equal for all the project’s alternatives.  The personnel costs are equal for the four alternatives, while the residual value and the value added tax are not taken into consideration, not as a limitation of the proposed system, but for the sake of simplicity. 4.2. Evaluation of the project’s alternatives with the use of the RBMCA system 4.2.1. Stage 1: alternatives’ identification and spreadsheet development According to the proposed system (refer to Fig. 1), there are four project’s alternatives identified, which are presented in Table 2. These alternatives have the same waste throughput that is 200,000 ton/year and the revenues arising through the service fees are equal. However, due to the fact that each alternative presents a different technical solution, the electricity or heat production performance as well as the total estimated inflows for each alternative are different. Moreover, there are certain variables, which influence one or more alternatives, e.g. the heat selling price is applied only to project’s 3rd alternative, while the dry flue gas cleaning cost is applied to project’s 1st, 2nd and 3rd alternatives. A complete list of the variable (Vi) and the fixed parameters (Fj) used in the case study is illustrated in Table 2. These parameters, namely V1, V2, V3,. . .,V22 the variables and F1, F2, . . ., F5 the fixed parameters, which have different units (i.e. €/MWh, MWh/ton, €/year, €/ton, ton/year and %), are functioned properly, in order to calculate for each alternative the inflows and outflows in the same units (€/year), for the first (t = 1) and second year (t = 2) of the project’s time horizon. These are t t t the Inflowsð1Þ and Outflowsð1Þ for the 1st, Inflowsð2Þ and t t t Outflowsð2Þ for the 2nd, Inflowsð3Þ and Outflowsð3Þ for the 3rd t t and Inflowsð4Þ and Outflowsð4Þ for the 4th project’s alternative. Furthermore, a spreadsheet is developed for the computation of the alternatives’ B/C ratios. Clearly, there is one B/C ratio per each WM incineration alternative that is the B/C1 for the 1st, B/C2 for the 2nd, B/C3 for the 3rd and B/C4 for the 4th project’s alternative. Each of these B/C ratios is a cumulative figure, which indicates combined effect of all variables and fixed parameters for that one alternative. The spreadsheet is illustrated in Table 3, where the alternatives’ initial investment costs are considered in the first year of the time horizon. Moreover, the alternatives’ inflows and outflows (calculated in Table 2), are used in the second year of the project’s horizon and increased annually by inflation, which is regarded 1.5%. As can be seen in Table 3, for each project’s alternative present value (PV) is calculated of its inflows and outflows, e.g. the 1st alternative:

PVinflows ð1Þ ¼

t 16 X Inflowsð1Þ t¼1

¼ 0þ

ð1 þ 5:5%Þt 16 X ðV1 ðV2 þ F1ð1Þ ðV4 ÞÞ þ V3 Þð1 þ V22 Þt2 t¼2

ð1 þ 5:5%Þt

ð8Þ

These inflows are placed in the numerator, while the relative outflows:

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PVoutflowsð1Þ ¼

16 Outflowst X ð1Þ t¼1

ð1 þ 5:5%Þ

t

¼

V18 1 þ 5:5%

16 X ðV1 ðV7 þ V8 þ V9 þ V11 þ V12 þ V13 Þ þ V6 þ V10 Þð1 þ V22 Þt2 þ ð1 þ 5:5%Þt t¼2

ð9Þ are placed in the denominator of the 1st alternative’s B/C ratio:

B=C1 ¼

PVInflowsð1Þ

ð8Þ

PVOutflowsð1Þ

ð9Þ

P16 ¼

t¼2

V18 1þ5:5%

þ

P16

t¼2

4.2.5. Stage 5: illustration of the cumulative probability distribution functions According to the fifth stage, the MCS is performed with 10,000 runs, which is a high number, in order to ensure the accuracy of the results. The CPDFs of the B/C1, B/C2, B/C3 and B/C4 are illustrated in Fig. 5, where their EVs, namely EV1, EV2, EV3 and EV4 are calculated with Eq. (1) and further compared:

EV2 ¼ 1:2271 > EV3 ¼ 1:2269 > EV4 ¼ 1:2208 > EV1 ¼ 1:2185 ) EVHighest ¼ EV2

¼

ðV1 ðV2 þF1ð1Þ ðV4 ÞÞþV3 Þð1þV22 Þt2 ð1þ5:5%Þt

ðV1 ðV7 þV8 þV9 þV11 þV12 þV13 ÞþV6 þV10 Þð1þV22 Þt2 ð1þ5:5%Þt

ð10Þ

4.2.2. Stage 2: probability distribution of the variables According to the second stage, decision makers assign the probability distributions to the variables. We take into account that in cases where no details exist for the variables’ past behavior, the probability distribution that is preferred is the triangular one (ADB, 2002; EC, 2008; PMI, 2008). The triangular distribution is developed with the use of the three point estimate for each variable as inputs, i.e. the base case value, the minimum and the maximum one (Salling and Leleur, 2011). In the specific case study, the base case values as well as the range of the minimum and maximum values for each variable included in the spreadsheet are presented in Table 4.

4.2.3. Stage 3: development of a Monte Carlo simulation model In the third stage of the system, a MCS model is developed, where the variables presented in Table 4, which follow specific probability distributions, are defined as inputs and the alternatives B/C ratios, namely B/C1, B/C2, B/C3 and B/C4, are defined as outputs, respectively.

4.2.4. Stage 4: definition of the decision-making criteria with their weights In the fourth stage, decision makers define the evaluation criteria as well as the criteria weight values, which are presented in Table 5. As can be seen, there are five criteria used, whereas the first criterion (c = 1) is the EVs of the alternatives’ B/C ratios calculated by their CPDFs. Specifically, the higher EV an alternative’s B/C ratio has, the higher score this alternative gets in the first criterion (c = 1). Moreover, the other four criteria used is the probability of the alternatives’ B/C ratios to have higher values than the criteria B/C values and that is: B/Ca > 1 (c = 2); B/Ca > 1.15 (c = 3); B/ Ca > 1.25 (c = 4) and B/Ca > 1.35 (c = 5). It is mentioned that the probability pca is estimated for each one of the alternatives B/C ratios (B/Ca): a = 1, 2, 3, 4 in each of these four criteria: c = 2, 3, 4, 5. Obviously, the higher probability an alternative’s B/C ratio has in taking higher values than a criterion’s B/C value, the higher score the specific alternative gets in this criterion. Furthermore, the criteria weight values used is: weight1 = 30; weight2 = 35; weight3 = 15; weight4 = 15; weight5 = 5 for the 1st, 2nd, 3rd, 4th and 5th criteria, respectively. The EVs of the alternatives’ B/C ratios as well as the probability for each alternative’s B/C ratio to have higher values in each of the criteria B/C values are estimated in the subsequent stages through the MCS and the analysis of the CPDF for each alternative’s B/C ratio. Clearly, the specific criteria as well as their weight values are arbitrarily chosen. However, the sensitivity analysis of the alternatives’ total scores in the criteria weight values is presented in Section 4.3.

205

ð11Þ

4.2.6. Stage 6: analysis of the cumulative probability distribution functions and calculation of each alternative’s score in each criterion According to the sixth stage, the CPDFs of the project’s alternatives, which are presented separately in four different graphs in Fig. 5, are put together in a single diagram, which is presented in Fig. 6(6). In this diagram, all the possible values of all the alternatives’ B/C ratios are illustrated in the x-axis. However, graph (6) is analyzed in the B/C values of the evaluation criteria (B/C = 1; 1.15; 1.25; 1.35), in order to estimate with accuracy the probability pca for the alternatives’ B/C ratios to have higher values than these. Specifically, as presented in the enlarged sub-graphs (6a) and (6b) in Fig. 6, the CPDFs of the alternatives’ B/C ratios are analyzed in the B/C values:  c = 2: B/Ca 6 1 and c = 3: B/Ca 6 1.15 in the sub-graph (6a) and  c = 4: B/Ca 6 1.25 and c = 5: B/Ca 6 1.35 in the sub-graph (6b) As can be seen, the points where each of the CPDFs cuts through the vertical axes present the probability of its B/C ratio to have lower values than the values in the x-axis. For instance, the B/C1 that is the 1st alternative’s B/C ratio and its function is illustrated with the black line, has 0.51% probability for B/C1 6 1, i.e. the probability for B/C1 > 1, is p21 ¼ 100  0:51 ¼ 99:49%. Moreover, the relative probability for B/C1 6 1.15, B/C1 6 1.25 and B/C1 6 1.35, is estimated in 23.10%, 61.48% and 93.79%, respectively and thus: p31 ¼ 100  23:10 ¼ 76:90%; p41 ¼ 100  61:48 ¼ 38:52% and p51 ¼ 100  93:79 ¼ 6:21%. The results through the analyses of CPDFs of the alternatives’ B/C ratios are presented in Table 6. Further, decision makers calculate the score for each alternative in each one of the evaluation criteria, as presented in Table 7. Due to the fact that EVHighest = EV2 from Eq. (11), the alternatives’ scores in the first criterion (c = 1: EVs of the alternatives’ B/C ratios), are calculated for each a = 1, 2, 3, 4 with (12): 1

score1a ¼ EVa ðweight Þ=EV2

ð12Þ

while the alternatives’ scores in the second to fifth criteria: c = 2, 3, 4, 5 are calculated for each a = 1, 2, 3, 4 with (13): c

scoreca ¼ pca ðweight Þ

ð13Þ

These calculations are presented in Table 7, in which the total score for each alternative i.e. a = 1, 2, 3, 4, is calculated with Eq. (7): P total scorea ¼ 5c¼1 scoreca . 4.2.7. Stage 7: selection of the optimum alternative with the RBMCA system In the seventh stage of the system, decision makers compare the alternatives’ total scores and select the one with the highest total score. According to the calculations, which are presented in Table 7, there is:

total score3 ¼ 83:38 > total score2 ¼ 83:29 > total score4 ¼ 82:44 > total score1 ¼ 82:23

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Table 4 Variables of the four waste incineration project’s alternatives in triangular distributions. Variable

Description

Applied to

Units

Triangular probability distributions Minimum value

Base case value

Maximum value

(%) (€/MWh) (€/ton) (ton/year) (€/ton) (€/ton) (€/ton) (€/year) (€/year) (€/year)

1.00 20.00 100.00 165,000.00 4.00 32.00 3.00 1,750,000.00 1,200,000.00 900,000.00

1.50 22.50 130.00 200,000.00 4.24 36.42 3.20 1,800,000.00 1,300,000.00 950,000.00

1.50 27.00 145.00 210,000.00 5.00 40.00 4.00 1,900,000.00 1,400,000.00 1,000,000.00

Variables common to all alternatives V22 Inflation V4 Electricity sell price V2 Service fee V1 Demand V7 Discharge-storage costs with vehicles V8 Firing system and boiler V9 Catalytic flue gas cleaning V10 Personnel costs V3 Positive externalities V6 Negative externalities

1st 1st 1st 1st 1st 1st 1st 1st 1st 1st

Variables uncommon 1st V13 V11 V12 V18 2nd V14 V19 3rd V15

1st 1st to 3rd 1st to 3rd 1st 2nd, 4th 2nd 3rd

(€/ton) (€/ton) (€/ton) (€) (€/ton) (€) (€/ton)

8.00 6.00 4.00 83,000,000.00 2.00 82,000,000.00 6.00

8.19 7.21 5.48 86,785,000.00 3.02 86,110,000.00 8.07

8.40 8.00 7.00 92,000,000.00 4.00 95,000,000.00 10.50

3rd 3rd 4th

(€/MWh) (€) (€/ton)

5.00 82,500,000.00 9.50

6.00 88,810,000.00 12.00

9.00 100,000,000.00 16.00

4th 4th

(€/ton) (€)

3.30 70,000,000.00

4.92 81,000,000.00

5.70 87,000,000.00

4th

V5 V20 V16 V17 V21

and specific to any one alternative Steam extraction turbine (thermal power plant) Dry flue gas cleaning Gypsum scrubber Initial investment costs(1) Steam extraction turbine (50 bar and 400 °C) Initial investment costs(2) Cogeneration (CHP) applying steam (50 bar and 400 °C) Heat selling price Initial investment costs(3) Electrostatic precipitator & Scrubber with precipitator Activated coke absorber Initial investment costs(4)

to to to to to to to to to to

4th 4th 4th 4th 4th 4th 4th 4th 4th 4th

Table 5 Definition of the evaluation criteria and selection of their weight values. Criteria c

Description

c=1

EVs of the alternatives’ B/C ratios

c=2

Probability

c=3

Probability

c=4

Probability

c=5

Probability

p2a p3a p4a p5a

Weights weightc

Alternatives’ scores calculation a = [1, 2, 3, 4]

weight1 = 30

score1a ¼ EVa ðweight Þ=EVHighest

of the alternatives’ B/C ratios >1.00

weight2 = 35

of the alternatives’ B/C ratios >1.15

weight3 = 15

of the alternatives’ B/C ratios >1.25

weight4 = 15

of the alternatives’ B/C ratios >1.35

weight5 = 5 P5 c c¼1 weight ¼ 100

score2a score3a score4a score5a

Thus, the project’s 3rd alternative is selected, i.e. the waste incineration plant that consist of a grate firing system with delivery by vehicles, dry, wet and catalytic flue gas treatment with cogeneration (CHP). 4.3. Discussion The selection of the project’s 3rd alternative in the specific case study is based on the specific criteria that were used as well as on the arbitrarily chosen criteria weight values. Taking into consideration that other decision makers would probably select different criteria weight values, the following statements are pointed out: (1) A multi-criteria evaluation process should be preferred against the one-criterion evaluation process. As can be seen in Table 6, irrespective of how high or low is a criterion’s weight value, there is a different alternative that is distinguished through the comparison of the four alternatives’ scores in a single criterion:

1

¼ ¼ ¼ ¼

2 p2a ðweight Þ 3 p3a ðweight Þ 4 p4a ðweight Þ 5 5 pa ðweight Þ

 In the first criterion that is the EVs of the alternatives’ B/C ratios, the project’s 2nd alternative gets the highest score as

EV2 ¼ 1:2271 > EV3 ¼ 1:2269 > EV4 ¼ 1:2208 > EV1 ¼ 1:2185  In the second and third criteria that is the probability of B/ C > 1.00 and B/C > 1.15, respectively, the project’s 3rd alternative gets the highest score due to

p23 ¼ 99:58% > p21 ¼ 99:49% > p22 ¼ 99:46% > p24 ¼ 99:29% p33 ¼ 78:91% > p32 ¼ 78:15% > p34 ¼ 77:03% > p31 ¼ 76:90%  In the fourth and fifth criteria that is the probability of B/ C > 1.25 and B/C > 1.35, respectively, the project’s 2nd alternative gets the highest score due to

p42 ¼ 42:10% > p43 ¼ 41:85% > p44 ¼ 39:43% > p41 ¼ 38:52% p52 ¼ 9:08% > p53 ¼ 8:49% > p54 ¼ 7:92% > p51 ¼ 6:21%

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Fig. 5. Cumulative probability distribution functions of the alternatives’ B/C ratios.

(2) The attitude of decision makers towards risks is taken into account in the RBMCA system. Specifically, let’s consider a risk-neutral, a risk-averse and a risk-seeking decision maker, who evaluate the waste incineration project’s alternatives using the RBMCA approach. Taking into consideration that the alternatives’ B/C ratios include not only the financial, but also the environmental and social profits and costs (i.e.

These results demonstrate that if a decision maker uses only one criterion for the evaluation of the WM project’s alternatives, there is a different alternative selected in each criterion. The WM project’s alternatives that are selected, if there was only one criterion used, are illustrated in Fig. 7, where it is shown the unique project’s alternative that is selected through the RBMCA approach.

Table 6 Analysis of the cumulative probability distribution functions of the alternatives’ B/C ratios. Criteria Description

c c=1

c=2

c=3

c=4

c=5

EVs of the alternatives’ B/C ratios Probability of B/C ratios 61.00 Probability of B/C ratios >1.00 Probability of B/C ratios 61.15 Probability of B/C ratios >1.15 Probability of B/C ratios 61.25 Probability of B/C ratios >1.25 Probability of B/C ratios 61.35 Probability of B/C ratios >1.35

Analysis of the Project’s 1st alternative CPDFs of the alternatives’ B/C ratios a=1

Project’s 2nd alternative

Project’s 3rd alternative

Project’s 4th alternative

a=2

a=3

a=4

EVa

EV1 = 1.2185

EV2 = 1.2271

EV3 = 1.2269

EV4 = 1.2208

0.51%

0.54%

0.42%

0.71%

p21 ¼ 100  0:51 ¼ 99:49%

p22 ¼ 100  0:54 ¼ 99:46%

p23 ¼ 100  0:42 ¼ 99:58%

p24 ¼ 100  0:71 ¼ 99:29%

23.10%

21.85%

21.09%

22.97%

p2a

p3a

p4a

p5a

p31 ¼ 100  23:10 ¼ 76:90% p32 ¼ 100  21:85 ¼ 78:15% p33 ¼ 100  21:09 ¼ 78:91% p34 ¼ 100  22:97 ¼ 77:03% 61.48%

57.90%

58.15%

p41

p42

p43

¼ 100  61:48 ¼ 38:52%

¼ 100  57:90 ¼ 42:10%

60.57%

¼ 100  58:15 ¼ 41:85% p44 ¼ 100  60:57 ¼ 39:43%

93.79%

90.92%

91.51%

92.08%

p51 ¼ 100  93:79 ¼ 6:21%

p52 ¼ 100  90:92 ¼ 9:08%

p53 ¼ 100  91:51 ¼ 8:49%

p54 ¼ 100  92:08 ¼ 7:92%

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total score4 = 82.44 total score3 = 83.38

¼ 8:49%ð5Þ ¼ 0:42

total score2 = 83.29

core44 ¼ 39:43%ð15Þ ¼ 5:91

score54 ¼ 7:92%ð5Þ ¼ 0:39

¼ 41:85%ð15Þ ¼ 6:28

¼ 9:08%ð5Þ ¼ 0:45

score34 ¼ 77:03%ð15Þ ¼ 11:55 ¼ 78:91%ð15Þ ¼ 11:84

According to the above statements, the sensitivity of the alternatives’ total scores in the weight values of the evaluation criteria is examined and the sensitivity analysis diagrams are illustrated in Fig. 8. As can be seen in Fig. 8, each diagram presents the alternatives’ total scores, when a specific criterion’s weight takes values from 0 to 100 and the other criteria take equal weight values. Total scores of the 1st, 2nd, 3rd, 4th alternatives, namely total score1, total score2, total score3, total score4, are calculated with Eq. (7), i.e. for all a = 1, 2, 3, 4 asX 5follows:

scoreca () total scorea

ð7Þ : total scorea ¼

ð12Þ

¼ score1a þ score2a þ score3a þ score4a þ score5a () total scorea ð13Þ

total score1 = 82.23

¼ 6:21%ð5Þ ¼ 0:31

¼ 38:52%ð15Þ ¼ 5:78

score31 score41 score51

¼ 76:90%ð15Þ ¼ 11:53

¼ 42:10%ð15Þ ¼ 6:31

score24 ¼ 99:29%ð35Þ ¼ 34:75

score33 score43 score53 score32 score42 score52

¼ 78:90%ð15Þ ¼ 11:72

score14 ¼ 1:2208 1:2271 30 ¼ 29:84 score13 ¼ 1:2269 1:2271 30 ¼ 29:99

score23 ¼ 99:58%ð35Þ ¼ 34:85

score12 ¼ 1:2271 1:2271 30 ¼ 30:00

score22 ¼ 99:46%ð35Þ ¼ 34:81

score11 ¼ 1:2185 1:2271 30 ¼ 29:79

weight4 = 15

weight5 = 5

c=4

c=5

c c¼1 scorea

P5

total scorea ¼

¼

¼

¼

3 p3a ðweight Þ 4 4 pa ðweight Þ 5 p5a ðweight Þ

weight3 = 15 c=3

score3a score4a score5a

weight2 = 35 c= 2

2

1

score2a ¼ p2a ðweight Þ

weight1 = 30 c= 1

EVa score1a ¼ EV weight 2

Project’s 3rd alternative a=3 Project’s 2nd alternative a=2 Project’s 1st alternative a=1

 A risk-neutral decision maker (who ignores risk and considers only the expected profit from an investment), will probably give a higher weight value in the first criterion that is the EVs of the alternatives’ B/C ratios.  A risk-averse decision maker (who prefers a certain profit to an uncertain profit) will probably give a higher weight value in the second criterion that is the probability of B/C > 1 and  A risk-seeking decision maker (who is willing to take big risks, in order to increase the potential profit of an investment) will probably give a higher weight value in the third, fourth or fifth criteria that is the probability of B/C > 1.15, B/C > 1.25 and B/ C > 1.35, respectively.

1

EVa ðweight Þ 2 3 4 ¼ þ p2a ðweight Þ þ p3a ðweight Þ þ p4a ðweight Þ EV 2 5

þ p5a ðweight Þ It is mentioned that in the above equation, the alternatives’ EVs as well as the probability values pca for all alternatives’ B/C ratios, which are estimated through the analysis of CPDFS and presented in Table 6, are constant. That is, the alternatives’ total scores are calculated with the following Eqs. (14)–(17) for the 1st, 2nd, 3rd, and 4th project’s alternatives, respectively:

1:2185 1 2 weight þ 99:49%ðweight Þ 1:2271 3 4 5 þ 76:90%ðweight Þ þ 38:52%ðweight Þ þ 6:21%ðweight Þ 1:2271 1 2 weight þ 99:46%ðweight Þ total score2 ¼ 1:2271 3 4 5 þ 78:15%ðweight Þ þ 42:10%ðweight Þ þ 9:08%ðweight Þ 1:2269 1 2 weight þ 99:58%ðweight Þ total score3 ¼ 1:2271 3 4 5 þ 78:91%ðweight Þ þ 41:85%ðweight Þ þ 8:49%ðweight Þ 1:2208 1 2 weight þ 99:29%ðweight Þ total score4 ¼ 1:2271 3 4 5 þ 77:03%ðweight Þ þ 39:43%ðweight Þ þ 7:92%ðweight Þ

total score1 ¼

Criteria weight values weightc

Calculations of each alternative’s score in each criterion scoreca

the positive and negative externalities), these decision makers will select different weight values for the evaluation criteria, as follows:

c¼1

Criteria c

Table 7 Risk-based multi-criteria assessment (RBMCA) of the waste incineration project’s alternatives.

score21 ¼ 99:49%ð35Þ ¼ 34:82

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Project’s 4th alternative a=4

208

ð14Þ

ð15Þ

ð16Þ

ð17Þ

(i) Specifically, the first diagram (8a) is illustrated with Eqs. (14)–(17), when the weight1 takes values from 0 to 100 2 and the other criteria weights take equal values: weight ¼ 3 4 5 100weight1 weight ¼ weight ¼ weight ¼ . For instance, 4 when weight1 = 100 , weight2 = weight3 = weight4 = weight5 = 0, Eqs. (14)–(17) give: total score2 = 100.0 > total score3 = 99.98 > total score4 = 99.48 > total score1 = 99.29. Moreover, if: weight1 = 60 , weight2 = weight3 = weight4 = weight5 = 10,

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Fig. 6. Analysis of the CPDFs in the B/C values of the evaluation criteria.

Fig. 7. One criterion assessment and the RBMCA of the project’s alternatives.

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then (14) to (17) give: total score2 = 82.87 > total score3 = 82.86 > total score4 = 82.05 > total score1 = 81.69 However, according to the risk-neutral definition (a decision maker who ignores risk and considers only the expected profit from an investment), we consider that the more risk-neutral a decision maker is, the higher weight value the first criterion (EVs of the alternatives’ B/C ratios) takes, e.g. 40 6 weight1 6 100. Therefore, according to diagram (8a), it is concluded that the project’s 2nd alternative will be preferred by a risk-neutral decision maker. (ii) In the second diagram (8b), the second criterion’s weight, namely weight2 takes values from 0 to 100, while the other 1 3 criteria take equal weight values: weight ¼ weight ¼ 4 5 100weight2 weight ¼ weight ¼ in Eqs. (14)–(17). We con4 sider that the more risk-averse a decision maker is (i.e. he prefers a certain profit to an uncertain one), the higher weight value the second criterion (probability of the alternatives’ B/C > 1) will take: 40 6 weight2 6 100. Therefore, as presented in (8b), it is concluded that the project’s 3rd alternative will be preferred by a risk-averse decision maker. (iii) Moreover, a risk-seeking decision maker (who is willing to take big risks, in order to increase the potential profit of an investment), will probably give a high weight value in the 3rd criterion (probability of the alternatives’ B/C > 1.15), i.e. 40 6 weight3 6 100. Specifically, diagram (8c) illustrates the alternatives’ total scores arising through (14) to (17), when the weight3 takes values from 0 to 100 and the other 1 2 criteria weights take equal values: weight ¼ weight ¼ 3 4 5 weight ¼ weight ¼ 100weight . Thus, it is shown in (8c) that 4 the project’s 3rd alternative will be preferred by a risk-seeking decision maker. (iv) However, if we assume that a decision maker is risk-seeking in a higher degree (considers higher profits than the B/ C > 1.15), then he will probably give higher weight values

in the 4th, or 5th criteria that is the probability of the alternatives’ B/C > 1.25 and B/C > 1.35, respectively, i.e. 40 6 weight4 6 100 or/and 40 6 weight5 6 100. According to diagrams (8d) and (8e) which present the alternatives total scores when the weight4, weight5 take values from 0 to 100 and the other criteria weight values are equal, then there is the project’s 2nd alternative that is selected and not the 3rd. The project’s alternatives that are preferred according to different risk preferences of a decision maker are illustrated in Table 8. As can be seen, decision makers with different attitude towards risk will probably give a weight value higher than 40 in one of the defined criteria and thus they will select a different project’s alternative. (v) The RBMCA approach takes into account the financial, technical, environmental and social risks that maybe posed in various alternatives of a WM project, through the probability distribution of all appropriate variables and the quantitative RA of the alternatives’ B/C ratios. Specifically, we consider that each variable present a different risk, as it may has a positive or negative impact on the project’s performance. For instance, if the personnel cost or/and the negative externalities get higher values than those initially estimated then the B/C ratio will be lower, otherwise if these variables get lower values then the B/C ratio will be higher. Moreover, by assigning probability distributions to each variable, is estimated the range of its values separately. In the RBMCA, we use all these variables as inputs and the alternatives’ B/C ratios as outputs in the MCS model, in order to estimate their overall impact on each project’s alternative that is presented by the CPDF of its B/C ratio. Therefore, all the financial, technical, environmental or social risks of a WM project’s alternatives can be included in the RBMCA.

Fig. 8. Sensitivity analysis of the project alternatives’ total scores in the criteria weight values.

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Criteria weight values 1

Risk-neutral Risk-averse Risk-seeking Risk-seeking Risk-seeking

2

3

4

5

weight

weight

weight

weight

weight

40 6 weight1 6 100 0 6 weight1 6 15 0 6 weight1 6 15 0 6 weight1 6 15 0 6 weight1 6 15

0 6 weight2 6 15 40 6 weight2 6 100 0 6 weight2 6 15 0 6 weight2 6 15 0 6 weight2 6 15

0 6 weight3 6 15 0 6 weight3 6 15 40 6 weight3 6 100 0 6 weight3 6 15 0 6 weight3 6 15

0 6 weight4 6 15 0 6 weight4 6 15 0 6 weight4 6 15 40 6 weight4 6 100 0 6 weight4 6 15

0 6 weight5 6 15 0 6 weight5 6 15 0 6 weight5 6 15 0 6 weight5 6 15 40 6 weight5 6 100

(3) However, implementation of the RBMCA system requires contribution of experts in the WM field, who will support the decision makers in the project’s technical issues and particularly in the variables’ probability distributions. Conclusively, crucial in the proposed system are:  The selection of the variables’ distributions and particularly the forecasted range of the variables’ values around their base case values; and  The selections of the evaluation criteria with their weight values. (4) Further research can be focused on cases where there is a group of decision makers with different risk preferences and to examine the evaluation criteria that are used in the RBMCA approach. 5. Conclusions CBA is one of the most widely used methods for the investment evaluation in the WM field, which uses the B/C ratio, in order to demonstrate that the project’s benefits are greater than the relative costs. Generally, the literature includes several methods for the evaluation of a WM project’s alternatives, either with the analytic hierarchy process (AHP), or other multi-criteria decision making methods. However, there is no specific system for the evaluation of a WM project’s alternatives according to specific criteria, which are based on the CPDFs of the alternatives’ B/C ratios and their respective weight values are selected according to the decision makers’ risk preferences. In this paper, a RBMCA system is presented as a novel approach, which includes the stages, that decision makers should follow, in order to evaluate a WM project’s alternatives and to select the optimum one. In summary, the following outcomes can be pointed out:  The proposed system takes into consideration the financial, technical, environmental and social risks that maybe posed in various alternatives of a given WM project, through the probability distribution of all appropriate variables and the quantitative RA of the alternatives’ B/C ratios.  In the RBMCA, the decision makers define evaluation criteria based on the CPDFs of the alternatives’ B/C ratios. Specifically, the project’s alternatives are evaluated according to: (i) The magnitude of the EVs of the alternatives’ B/C ratios, or/ and (ii) The probability of the alternatives’ B/C ratios to have higher values than specific B/C values, which are selected by decision makers.  The criteria weight values are selected by decision makers according to their risk preferences, i.e. whether they are riskneutral, risk-averse, or risk-seeking.  Preference to the multi-criteria against the one-criterion evaluation process is highlighted.

Preferred alternative (highest total score) 2nd alternative 3rd alternative 3rd alternative 2nd alternative 2nd alternative

In a case study presented, the RBMCA system is used for a waste incineration project with a waste throughput of 200,000 ton/year. Initially, four project’s alternatives are identified, which present different technical solutions and have different revenues, initial investment and operational costs. Through the proposed system, the variables of the project’s alternatives are used as inputs in a MCS model, so as the CPDFs of the alternatives’ B/C ratios are illustrated in a graph and the optimum alternative is selected according to specific evaluation criteria with specific weight values. Moreover, the sensitivity of the alternatives’ total scores in the criteria weight values is examined, while the correlation between the criteria weight values and the decision makers’ risk preferences is discussed. Conclusively, the RBMCA approach can be very useful tool for decision makers in the step three of the CBA (shown in Fig. 1), i.e. the study of the feasibility and of alternative options, as it can help them to evaluate a WM project’s alternatives, according to their risk preferences.

Acknowledgments We would like to thank the editors and especially the anonymous referees for their many helpful suggestions and insightful comments that have significantly improved the content and presentation of this paper.

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