Selecting Rooftop Solar Photovoltaic Modules by Measuring Their Attractiveness by a Categorical-Based Evaluation Technique (MACBETH): The Case of Lithuania

Abstract

The paper examines the challenges related to solar photovoltaic (PV) development with a pivotal focus on the impacts of the dynamics of the relevant markets and technological advancements in the solar industry. In this regard, household investments into rooftop solar PV modules as one of the available incentives are investigated based on a conducted experiment in Lithuania for selecting rooftop solar PV systems for the prosumer by measuring the attractiveness of solar PV modules by a categorical-based evaluation technique (MACBETH). While a variety of multiple-criteria decision-making (MCDM) methods used by scholars have their specifics in terms of application and the divergence of results, the findings of the conducted experiment reveal MACBETH’s utility when based upon qualitative judgments about the differences in the attractiveness of offers, quantifying their relative value and accordingly ranking the latter. The findings also confirm MACBETH’s potential to be used not only to solve operational and tactical tasks but also for strategic objectives of private and public organizations aiming at competitive and sustainable development in short- and long-term contexts.

1. Introduction

In the context of the Taxonomy Regulation [1], the Fit 55 package [2] subject to the Green Deal [3], and the recent REPowerEU Plan [4], power generation technologies are subject to scrutiny. The sense of use and development perspectives (as to the short and long run) of fossil-fuel- (coal, natural gas, and oil; FF) based technologies is subject to tightening requirements [1,2,3,4] for curbing emissions, rising commodity prices [5], and the need (moreover, its urgency) to ensure sustainable power generation and supply for security and sustainability of economy [5]. Furthermore, a shortage of stocks or a lack of respective natural resources makes the use of FF-based solutions costly because of the recent dynamics of commodity prices [4,5]. Switching to more polluting but less expensive alternatives such as shale oil and coal is, in the light of the Green Deal [3] and the Paris Agreement [6], a temporary trade-off. For instance, Lithuania, Poland, and Estonia switched provisionally to coal and shale oil for heating (for the winter of 2022, at least) as an exception provided to European Union (EU) members of the European Commission (EC) due to the implications of the war in Ukraine. In this regard, to maintain the competitive performance of an organization or economy (or its sector in question), the possession of power generation capacity must be mandatory. In addition, if there are no traditional fossil energy resources to extract and use, the needed power generation capacity must be built based on renewable energy sources (RES), namely as follows: solar, wind, geothermal, ocean energy, hydropower, bioenergy, and nuclear power. Although nuclear power is not renewable, it is low-carbon and recyclable, and thus it is counted as an RES for this paper. Indeed, RES-based power generation is promoted and supported [1,2,3], yet the speed and the scale of the transition to the latter have appeared to be deficient when the power supply is reduced or cut instantly or shortly (e.g., due to implications of the war in Ukraine), whereas alternative power generation capacity is inadequate or not available.

Given the context, nevertheless, both FF- and RES-based solutions have their drawbacks. The required combination of the latter for secure and sustainable power generation needs to be rationally matched. Grouping RES measures or combining RES with conventional FF solutions is a complex task and thus inevitably involves multiple-criteria decision-making (MCDM). Due to the variety of FF- and RES-based solutions as well as MCDM methods, the author narrows the object of research to the challenges of the selection of rooftop solar photovoltaic (PV) modules by the self-consumer—the household (as the target of the research in this paper) striving to meet its electricity consumption demand. The latter is also called by scholars [7] a prosumer—a consumer generating electricity on their own, and storing and selling part of it. This emphasis is also reasoned by the observation that no substantial scientific research over the past decade was found subject to the challenges of selecting rooftop solar PV modules. In addition, selection is burdened by a vast number of manufacturers, producing a variety of modules specific in terms of scale and scope of application characteristics [8,9,10]. In addition, no research was found regarding the application of MCDM methods for selecting the latter. Furthermore, solar power can be used for electricity, heating, cooling, and fueling; due to the scale and scope of these, each could be a subject for separate research. Subsequently, the author focuses namely on selecting rooftop solar PV modules by measuring attractiveness by a categorical-based evaluation technique (MACBETH) [11,12]. The author’s choice of MACBETH is grounded in the fact that scientific research on MACBETH, as a method for the selection of rooftop solar PV modules as well as of other FF- and RES-based technologies, is, at best, limited and fragmentary; although examining at least 700 works of scholars across Elsevier journals, the author could not identify any. Moreover, MACBETH is based on qualitative judgments [11,12,13,14,15,16] only, and therefore this feature makes the latter a reasonable option, especially when decisions are subject to prompt finding, collecting, and processing relevant data which are naturally fuzzy [17]. Indeed, in this regard, a variety of MCDM methods are available [16,18]. For instance, the following MCDM methods were observed as consistently used by scholars concerning the solar PV theme:

• (i). AHP/ANP (analytic hierarchy/network process) [19,20,21,22,23,24];

• (ii). TOPSIS (technique for order of preference by similarity to ideal solution) [25,26,27,28];

• (iii). COPRAS (complex proportional assessment) [29,30];

• (iv). VIKOR (a multicriteria optimization and compromise solution (from Serbian: VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR))) [26,31];

• (v). MULTIMOORA (multi-objective optimization by ratio analysis) [30,32,33,34,35,36];

• (vi). DEA (data envelopment analysis) [37,38,39,40,41];

• (vii). SAW (Simple Additive Weighting) [29,30,42];

• (viii). PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation) [42,43];

• (ix). SMART (Simple Multi-Attribute Rating Technique) [27,29,30,44,45];

• (x). ELECTRE (MCDM method for elimination and choice translating reality (from French: ÉLimination Et Choix Traduisant la Réalité)) [27,29,43].

Moreover, these methods are seen to be used in combination in numerous cases, e.g., [16,28,31,35,46,47,48], where the specifics of each MCDM method may stipulate divergent or constrained solutions for the comparable task. Consequently, to choose the appropriate one (or their mix), a household needs to be duly qualified as well as acquainted with the peculiarities and drawbacks of applying every method. In this context, the author of this article attempts to apply the MACBETH method to support households deciding to rationally select rooftop solar PV modules using the primary data received from a conducted experiment in Lithuania. The paper aims to contribute to reaching the intended results (the desired level of effectiveness) with justified efforts (the desired level of efficiency) for the prosumer.

The article is composed as follows. The second part explores the literature on the range of solar PV modules available to the target group of the largest global producers as well as their market dynamics over the last decade. The third presents findings on the application of MCDM methods concerning solar power generation, and the selection of rooftop solar PV modules. As a result of the advantages and drawbacks observed by the application of MCDM methods, Part 4 introduces a methodology based on MACBETH for the selection of rooftop solar PV modules and subsequently analyses the results of the MACBETH application. Consequently, Part 5 discusses the outcomes of MACBETH use, aiming at improving the efficiency and effectiveness of the selection process for the target group. The final part provides conclusions and future research outlines.

2. Literature Review on Critical Aspects of Solar PV Development

The global market for solar PV modules has shown exponential growth since 2006. While growing from a cumulative 1.3 Gigawatts of solar PV capacity installed in 2000 to 6.6 Gigawatts in 2006, the installed cumulative capacity of solar PV worldwide grew to 940 Gigawatts in 2021 [49]. Maturation and advancements of technologies (as a result of a learning curve) have led to a decline in the cost of electricity produced by solar modules by 88% since 2010, making solar energy generation even less expensive than the equivalent of generated power of gas- or coal-based solutions, according to International Renewable Energy Agency (IRENA) data [50]. If EUR 1 is invested into solar PV modules, it generates a fourfold amount of power in comparison to the amount of electricity generated in 2010. Due to improving profitability, solar power generation capacity reached almost 10%, by the end of 2021, of the total power generation capacity worldwide [51]. Concerning the European Union (EU), annually generated solar power increased from more than 66 Gigawatts per annum in 2012 to more than 157 Gigawatts per annum in 2021 [52]. The observed growth of the capacity installations since 2006 and then its acceleration, especially since 2010, is not only affected by stricter regulations for curbing emissions of greenhouse gases [1,2,3]. The launch of the EU Emissions Trading System (EU ETS) in 2005 and subsequently established EU ETS-like schemes worldwide (25 operating systems could be counted as of the start of 2022 [53]) has also contributed to solar power generation market growth. Furthermore, the application of monetary and fiscal stimulatory measures of up to 30% of the solar-capacity-equivalent investment amount (i.e., tax reductions, financial subsidies, and partial reimbursements of interest rates) [50,54,55] is another set of enhancing factors. Hereby, the EUR 660 million “NextGenerationEU” facility [56] launched in June 2021 for subsidies exclusively for households’ solar PV installations in the EU is unparalleled and is also contributing considerably to the rise in solar PV generation capacity [50,55]. In addition, another contingency to be considered vital to solar PV capacity development in the EU and worldwide is the growing power demand. This impacts electricity prices due to unsustainable power supply [4] and hence also the dynamics of commodity prices [5,10], particularly since the autumn of 2021 (Figure 1).

In this context, more than 350 producers of monocrystalline rooftop solar PV modules (as the one of most efficient solutions still nowadays) [57] can also be found worldwide. Each of these offers a wide spectrum of modules to choose from as per the specifics of the needs of the households (while each manufacturer also has a range of offerings for utilities and commercial use). If, for the purpose of this article, we focus on the 10 leading manufacturers in terms of actual shipments of rooftop solar PV modules [9,10] from 2019 to 2021, one will note at least one type of solar PV technology per manufacturer in use to produce at least two types of solar PV module per type of technology with at least four variants per type of solar PV module (Table 1).

Furthermore, the power generation efficiency rate of solar PV modules sold worldwide nowadays varies by the type of technology used to manufacture the module, from 15% for polycrystalline to 23% for n-type interdigitated back-contact monocrystalline silicon cells [53]. In addition, recently laboratory-tested all-perovskite tandem solar cells with 27.5% [58] and even 32.3% [59] power generation efficiency rates may be the next benchmarks to prove as commercially viable solutions in terms of added value for both the customer and the manufacturer. In this regard, the household will need to explore at least three variants per type of solar PV module of at least one type of manufacturing technology (as per Table 1) in seeking the effectiveness of power generation. For a comprehensive analysis, households may in principle compare even nine variants of eight different types of solar PV modules per each of the specific technologies. Subsequently, to obtain the efficient sustainable performance of solar PV modules, the household will also need to choose a solar PV inverter to convert the direct current generated by solar PV modules into alternating current. In this respect, the range of the latter to choose from is also vast. For instance, as per the estimated 10 largest manufacturers by shipment of solar PV inverters worldwide [57], there can be counted four types of solar PV inverter with up to 10 variants per each type in terms of power equivalent to match the wattage to be generated by solar PV modules.

In addition to the preceding insights into the solar PV market landscape, the regulations over metering schemes for generated power must also be considered. Their necessity, for instance, is addressed by the EU Clean Energy Package [56], but with no unified specific rules. In addition, the relevance of the availability of grid capacity is addressed so as not to hinder the evolution of prosumers. In this regard, scholars identify four types of metering regimes applied in the EU since 2013 by 19 member states [56]. Consequently, regulatory divergence can be a contingency factor for households willing to become prosumers, whereas if the net metering scheme can be seen as stimulating solar capacity installations, the net billing regime can cause the opposite effect. Hereby to be noticed, e.g., over the last decade as for the data on commodities [5,10], the equivalent electricity generated during the daytime and (or) summertime, ceteris paribus, was considerably cheaper (except for prices in 2022, due to the impact of Russian aggression on Ukraine) than that generated during nighttime and (or) wintertime. In this respect, the net billing scheme is less advantageous than net metering due to greater exposure to fluctuations in commodity prices. For example, in Poland, under the net metering scheme launched in 2016, Polish solar capacity installed by households has grown exponentially from 100 Megawatts in 2017 to 3715 Megawatts in 2021 [51]. However, since the switch to the net billing regime in 2022, solar PV capacity installations by households have been slowing down in Poland due to the anticipated risk of reduction in profitability of investments into rooftop solar photovoltaic (PV) modules for the purpose of self-consumption [60,61].

Bearing in mind the context above, when selecting solar photovoltaic (PV) modules, the household must consider the risk of changes in the regulatory framework as the evolution of relevant markets within the investment payback period planned. In this regard, the author will address the methods to reasonably select solar photovoltaic (PV) modules in the subsequent part.

3. Review of MCDM Methods Regarding Selecting Solar PV Modules for Prosumers

Exploring scientific sources subject to the solar PV theme, numerous applications of various MCDM methods are observed in use by scholars. For instance, Dahooie et al. (2022) mentioned 28 studies of scholars applying different MCDM methods. In 12 of these, AHP was used as a sole technique, while in the other 7 research cases, AHP was applied in concert with TOPSIS, VIKOR, ELECTRE, and DEA. The use of DEA, ELECTRE, and VIKOR in this regard was observed in two and three cases, respectively, and the use of other MCDM methods was rare in the rest of the works. Ayough et al. (2022) noted 12 cases related to solar PV topics, of which 5 are also subject to AHP along with TOPSIS, VIKOR, or (and) DEA. As the next example, Deveci et al. (2021) pointed out 55 studies concerning the solar PV theme, of which 28 articles are subject to the application of AHP, including 7 cases of its combination with TOPSIS and VIKOR, while other cases were characterized using geographic information system (GIS) and other programming solutions. Concluding per the latter cases, the dominance of AHP applications accompanied by TOPSIS, VIKOR, ELECTRE, DEA, and GIS is seen. In this respect, nevertheless, the author also finds that most of the works in question focus on the selection of the locations of solar PV farms and (or) power plants—no studies were found explicitly about the selection of solar PV modules.

For the robustness of the latter findings, the author also delved into 700 works in Elsevier journals concerning the solutions for the selection of solar PV modules. As a result, in principle, most of the same MCDM methods were used (Table 2) as per the studies mentioned above. While the application of AHP (together with other methods) is also noticed in most cases, the author, however, finds only three articles (Table 2) where scholars investigate the challenges of selection of solar PV modules using, respectively, AHP, TOPSIS, and the combination of the Characteristic Objects Method (COMET) and TOPSIS.

Based on the above-mentioned sources, MCDM methods are mainly used for weighting criteria, ranking alternatives, and giving different outcomes while coping with similar or even identical tasks. In this regard, distinct characteristics and application specifics of the methods imply that each may have its advantages and drawbacks. For instance, AHP is rather technically simple in its application. As to its weakness, weighting criterion may influence the final score, whereas weighting is subject to the preference of the decision-maker, and hence the results may vary. Furthermore, irregularities are possible in ranking and judging variables because of pairwise comparison. Moreover, adding or removing an alternative may cause rank-reversal problems [22,24,43]. Regarding TOPSIS, concerns can be related to the lack of a Euclidean Distance focus toward the correlation of the attributes. Furthermore, TOPSIS does not consider the importance of the distances from both positive and negative ideal solutions [26,27,28]. In this respect, VIKOR also needs prerequisites for weighting and checking judgment consistency as well as dealing with qualitative values [26,31].

Compared to TOPSIS and VIKOR, COPRAS can be considered more exposed to data variation and divergent in terms of ranks [29,30]. Regarding DEA, concerns can be subject to the fuzziness of the data and their availability before the use of the method, and hence its application results will depend on the sufficiency and reliability of data [39,40].

In this respect, MULTIMOORA is more robust with no need for normalization if not processing negative data [32,35]. In comparison to the latter, SAW also needs positive and maximizing inputs for values of criteria, but the results of the application may not necessarily reflect the real business circumstances [29,30,42]. Concerning PROMETHEE, this can be seen as simple to use [42,43]. However, it does not include solutions either for weighting or assigning values, meaning that complementary techniques will have to be involved accordingly.

In terms of the number of iterations and outranking, PROMETHEE has similarities to ELECTRE. Nevertheless, the latter can be seen as not clear in terms of process and its outcomes; also, outranking may impact the parameters of the alternatives in addition to the results being difficult to validate [27,43]. In this regard, the SMART method is also considered procedurally complicated but relatively easy to use, as long as enough data are available to the decision-makers [29,30,32].

In addition to the findings above, the author found no works (as per the explored Elsevier articles) involving the use of MACBETH for the selection of solar PV modules for households or other market players, investigating neither site selection challenges for solar objects nor other solar PV themes. Nonetheless, at least 192 scientific articles can be found in the Scopus database [13], although with no drawbacks explicitly observed concerning the MACBETH application. While a variety of MCDM methods reviewed have shortcomings as stated above, MACBETH relies on a humble question–answer procedure constructing numerical scales of intervals, tolerating differences of attractiveness between elements of a certain set to be cardinally measured [11,12,13,14,15,16]. The latter also uses linear programming, and thus there is no need for additional solutions to define the weighting coefficients for criteria. As a result, the consistency of judgments is also checked under the method application procedure. Considering the above-mentioned context, MACBETH can be a reasonable choice of MCDM method for selecting rooftop solar PV modules for prosumers. Consequently, the methodology to solve this task using MACBETH shall be detailed in the next part.

4. Methodology and Its Application

The uniqueness of MACBETH in principle, while considering the findings of the previous part, is subject to the characteristic of the method which allows justifying the decision of a choice not only for the organization but also for an individual (let it be the prosumer in this article) based upon qualitative judgments about the differences of values of options, especially when there is a vast number of the latter (i.e., Table 3).

To aid in carrying out the task of selecting rooftop solar PV solutions for households, the following experiment was conducted in Lithuania. In practice, following the procedure of application of MACBETH [11,12] to form a finite set O = {o₁, o₂, …, o_n} of n offers (where O $=n\ge 2$), the author, formally acting as a household, contacted 24 Lithuanian solar energy association members, marketing themselves as contractors of rooftop solar PV systems for households, with the request to provide offers for delivery and installation of a rooftop solar PV system of 10 kW electricity generation capacity in the location of 54.299110, 25.377370 (Lat/Lon). As a result, the 22 proposals received (92% of all contractors inquired) are accordingly specified in terms of 11 criteria in Table 3 using the data provided in the offers in a random sequence (they are not yet based on any ranking in terms of the criteria at this stage). Concerning the set of selected criteria, first, this is supported by El-Bayeh et al. [25], Wang et al. [41], Deveci et al. [63], and also the findings of Solangi et al. [64]. Hereby, the author notes that the spectrum of criteria chosen has a pivotal focus on justifying the decision in terms of economic utility for the prosumer.

Furthermore, the 11 criteria the author employs for the finite set of offers (Table 3) are consistent with the observed regularity of an average number of criteria used by the scholars (e.g., see references in Table 2). In addition, to support the latter statement, using data from the work of Dahooie et al. [34] and Deveci et al. [65], the author investigated 45 scientific works referred thereto and concludes that 11.68 is the average number of criteria used by the scholars. Secondly, the concept of Blue Ocean [65] is also considered, where criteria are aimed at lowering costs while focusing on the most beneficial solution for the prosumer. Thirdly, the criteria chosen are also coherent with the fundamentals of the utility theory as well as the cost–benefit analysis concept. In this respect, the criteria given in Table 3 are also the reflection of data that contractors provided in their offers while aiming to reveal their advantage in utility for the household. Consequently, while the specifications of manufacturers of solar PV modules that the received offers are based on set performance efficiency levels, the timeline and the quality of installation works are nonetheless crucial. In this respect, the criterion “Time until solar PV system is installed and operational (days)” is to be noted. The declared lengthy waiting periods (from 60 days to even 210 days; Table 3) by contractors before the solar PV modules are installed on the rooftop of the household are due to the labor shortage the contractors are facing caused by unprecedented demand among households for rooftop solar PV systems. The latter is in principle triggered by the number of calls for financial aid (an amount of 322 EUR/kW of installed electricity generation capacity) for solar PV module installations for households from the government of Lithuania during the last two years in the context of the “NextGenerationEU” facility [56]. Subsequently, the specifics of weather conditions of the region Lithuania belongs to must be considered.

During the winter in Lithuania, the generation of electricity by rooftop solar PV systems is in essence insignificant. For instance, for the location of 54.299110,25.377370 (Lat/Lon), subject to the experiment in question, the EC Photovoltaic Geographical Information System (PVGIS) [66] indicates energy output (of 10 kW electricity generation capacity) between 131 kWh in December and 395 kWh in February (with the roof oriented to the south, with no shadows and a slope of 21° degrees, and also assuming the estimated system to have an average loss of 14% (due to, e.g., snow, dust, and system degradation over its warranty period)). Hence it is critical to have a solar PV system installed and operational as soon as possible between March and October (when average amounts of generation of electricity vary from 731 kWh in March to an estimated peak of 1350 kWh in June and then 511 kWh in October (with an estimated 194 kWh for November, according to data from PVGIS) to get prosumers’ investments paid back as soon as possible. Moreover, as in the example of Poland and other findings in Part 2 of this paper, the metering scheme for generated power determined by the government is also vital for the length of payback period.

Next in the application of MACBETH, the individual household, H, focusing on finite set O (Table 3) pairwise compares offers o₁, o₂, …, o₂₂ using semantic judgments concerning the difference of attractiveness between the latter. As the result of the comparison, H may decide that offer o_i is more attractive than offer o_j (i.e., o_iPo_j) if associating the offers in question in terms of values v(o_i) and v(o_j), so H concludes that v(o_i) > v(o_j). Furthermore, if v(o_i) = v(o_j), H may decide that offer o_i is as attractive as offer o_j (i.e., o_i I o_j). Hereby, pairwise comparison is carried out using the scale of semantic categories (Table 4) predetermined [11,12] subject to differences in the attractiveness of values of offers in terms of the criterion in question (moreover, the same principle can also be used to rank criteria). Accordingly, H judges verbally the difference in attractiveness between each pair of offers (o_i, o_j) ∈ O by choosing one of the semantic categories of Table 4.

For instance, H may state that offer o_i is more attractive than o_j and the difference in attractiveness is strong, meaning that (o_i, o_j) ∈ SC₄. As the result of such pairwise comparison, all the pairs of offers (o_i, o_j) will belong accordingly to the same SC of semantic differences in attractiveness, whereas differences in values v(o_i) − v(o_j) will be subject to the same interval. Subsequently, the asymmetric subsets of the positive real numbers to subset classes of ordered pairs (o_i, o_j) (i.e., o_iPo_j) are related, whereas two adjacent intervals correspond to two following categories of differences of attractiveness [11,12], namely as follows:

o_iP^ko_j: s_k < v(o_i) − v(o_j) < s_k+1 (1)

where P^(k)—the value preference; s_k and s_k+1—the thresholds of value function (v). Hereby, H needs to make sure their judgments are consistent, namely [12,16]:

∀ o_i, o_j ∈ O: v(o_i) > v(o_j) ⇔ o_iPo_j(2)

∀ k, k* ∈ {1,2,3,4,5,6}, ∀ o_i, o_j, o_p, o_q ∈ O with (o_i, o_j) ∈ SC_k and (o_p, o_q) ∈ SC_k^*: k ≥ k* + 1 ⇒ v(o_i) − v(o_j) ≥ v(o_p) − v(o_q)(3)

If offer o_i is strictly more attractive than offer o_j (i.e., o_iPo_j), then v(o_i) > v(o_j). Respectively, when offer o_i is as attractive as offer o_j (i.e., o_iIo_j), then v(o_i) = v(o_j), meaning (o_i, o_j) ∈ SC₀. As the result of having preferences of values consistent, linear programming is used to minimize v(n) and for the scale of attractiveness [67], as follows:

Minv(n), S.T.: ∀ o_i, o_j ∈ O: o_iPo_j ⇒ v(o_i) ≥ v(o_j) + 1; ∀ o_i, o_j ∈ O: o_iIo_j ⇒ v(o_i) = v(o_j); ∀ (o_i, o_j), (o_p, o_q) ∈ O(4)

If the difference in attractiveness between offers o_i and o_j is greater than that between offers o_p and o_q, then: v(o_i) − v(o_j) ≥ v(o_p) − v(o_q) + 1 + δ(o_i, o_j, o_p, o_q); v(o_i⁻) = 0, where o_n belongs to the set O so as to ∀ o_i, o_j, o_p, o_q, … ∈ O: o_n(P ∪ I) o_i, o_j, o_p, o_q, …, and o_i⁻ belongs to the set O so as to ∀ o_i, o_j, o_p, o_q, … ∈ O: o_i, o_j, o_p, o_q, …(P ∪ I) o_i⁻; δ(o_i, o_j, o_p, o_q) is the minimal number of categories of difference in attractiveness between offers o_i and o_j and the difference in attractiveness between o_p and o_q. As a result, n is the most attractive offer of set O (i.e., o_n (P ∪ I) o_i, o_j, o_p, o_q, …), and o_i^- is the least attractive offer in the set O (i.e., o_i, o_j, o_p, o_q, …(P ∪ I) o_i⁻).

In this context, H proceeds with ranking the criteria (Table 3). Assuming the latter to be equally important, H pairwise compares the criteria and makes their value judgments using the semantic scale presented above (Table 4). This procedure was technically facilitated by M-MACBETH software [12]. The obtained results of pairwise comparisons of offers o₁, o₂, …, o₂₂ per criterion c₁, c₂, c₃, …, c_n (Table 3) are summarized in Appendix A. Consequently, the latter can serve as the basis for the prosumer to decide on the most attractive offer as well as the ones which could be subject to additional negotiations with the contractors and reconsideration of pairwise judgments if the offers in question were improved.

In this regard, the versatility of the MACBETH method allows correspondingly to set up the management process from selecting, negotiating, and consequently deciding on the potentially most effective and efficient offer and proceeding with commencing installation works. For instance, judging the merits of compensation for non-produced electricity (c₁₀), the advantages of offer o₁₃ (Appendix A, Table A1a,b) could be between several cents and several hundred euros assuming that the rooftop solar PV system is not operational from several days to several months (in the case of a conservative scenario) due to defects in the solar PV system components or installation works. Whereas the latter are subject to contractors’ responsibility, the warranties for the product (c₃), inverter (c₅), installation construction (c₇), and installation works (c₈) are to be enforced. Consequently, having in mind a cost difference of more than EUR 2000 between the best offers, namely o₁₃ and o₃ (Figure 2a), the formal advantage of offer o₁₃ in terms of criterion c₁₀ could be considered as marketing-related rather than significantly tangible added value generating for the prosumer.

Furthermore, the utility of one maintenance inspection (c₁₁) in a five year-period as per offer o₁₃ (Table 3; Appendix A, Table A1a,b) can be questioned as well, whereas according to practical observations (as well as individual interviews with the providers of such services), inspections are advised to take place once in three years, ceteris paribus. Otherwise, the prosumer should call for an inspection if it is visually obvious that the solar PV modules are dirty to the extent that the overall system does not function (electricity is not generated). The regularity of such cases would indicate that the territory in question is at risk of pollution, and hence the respective state environment protection authorities are to be contacted. As the result, the prosumer may need to have inspections once per year (or as soon as needed due to the fact of physical dirtiness of modules). The cost of such inspections may vary up to a few hundred euros (as in the case of Lithuania), assuming the distance is up to 50 km from the service provider to the place of a prosumer.

Regarding the latter aspects, the formal advantage of offer o₁₃ in terms of criterion c₁₁ could be, as in the case of c₁₀, considered as not resulting in any significantly tangible added value to the prosumer.

Having in mind the above context, the attractiveness of the offers could be reviewed disregarding criteria c₁₁ and c₁₀ (even though offer o₁₃ has a formal advantage over the other offers in question). As the result of such a second scenario (when nine criteria are used) of the pairwise comparison of the offers, it can be concluded that offer o₃ is the most attractive and substantially outpaces other offers (Figure 2b; Appendix A, Table A2a,b).

In this respect, the cost difference if comparing the outperforming offer o₃ with its closest rivals (Figure 2b) is also critical to note, due to the risk of a change of metering regulation. The latter is adjusted annually by the National Energy Regulatory Council, an independent national regulatory authority in charge of regulating the activities of entities in the field of energy and conducting the supervision of the state energy sector in Lithuania. Hence, the greater the cost difference, the shorter the payback period of the investments will be, even when the net metering regime is changed to net billing (as in the case of Poland, as mentioned in Part 2). Moreover, in this regard, there is an insignificant difference (Table 3; Appendix A, Table A1a,b and Table A2a,b) among the offers in terms of product efficiency level (c₁) and performance efficiency level warranty (c₄); the more costly offers will have lower economic benefit in the case of net billing as well as in the case of increasing inter-bank interest rates if the borrowed funds are used for the investments in question.

If we assume, following the insights from both scenarios examined, the third scenario where the household is not cost-sensitive and is focused on gaining most of the economic value, resulting, in principle, due to technological advantages stated by the contractors, offer o₂₁ is to be considered as most attractive (Table 5; Appendix A, Table A3a,b). In this scenario, the household is expected to be resilient to the impacts of the possible changes related to fiscal and (or) monetary regulatory measures.

Based upon the comparison of the results of the three scenarios investigated (Table 5), it can be stated that the household should consider offer o₃ aiming at most economic benefit, while the choice of offer o₂₁ should be considered as not resilient to the possible negative impacts related to fiscal or (and) monetary regulatory measures as well as price fluctuations of energy-related commodities.

Consequently, regarding all scenarios, the period until the solar PV system is installed and operational (since the date the contract is signed) is vital for achieving the estimated economic benefit, particularly in countries such as Lithuania, as per the case investigated, where the generation of electricity of solar energy between November and February is insignificant compared to generation estimations during the summer period.

5. Discussion

The findings of the application of MACBETH in the experiment conducted (Part 4) lead to the following considerations. Firstly, the results of the application of the method in question reveal the rationality of its use when households manage projects subject to the selection, delivery, and installation of rooftop solar PV systems. The application procedure allows the household to make judgments and reconsider (if needed) the criteria, as well as data updated by the contractors as the result of the actions of clarifying and negotiating the offers. In this respect, the MACBETH application results also reveal the possibility to apply the method in question for measuring and assessing the competitiveness of the market players based on the comparison of offers. For instance, following the concept of Blue Ocean [65], the results of the conducted experiment allow one to draw canvas of value curves (Figure 3) of, as in the example, the three most attractive offers per each scenario (Appendix A, Table A1a, Table A2a and Table A3a).

The canvas of value curves (Figure 3) in principle represent the competitiveness of the strategy of the organization per type of services in question. Value differences per criterion correspondingly indicate the extent of competitiveness. Consequently, judgments made applying MACBETH can be used to define the sources of divergence and to consider how sustainable the latter is, letting the organization concerned outperform the other market players not only in the short run but also in the long run. The resulting findings may allow the organization to timely determine the actual and possible future status of competitiveness of its strategy. In this regard, the household (besides judging the most attractive offer) as well as other market players in private and public sectors seeking to implement the investments in question, may also shape their holistic view on the sustainability of the respective economic sector.

Following the context, the adaptability and simplicity of the application of MACBETH (including its potential to be used with other analytic techniques) can also be subject to consideration by state regulatory authorities. Striving to accelerate the transition of the economic sectors towards RES-based and other more sustainable solutions for energy generation, MACBETH can facilitate the public procurement processes as well as the distribution of subsidies for private and public organizations including the state and municipal authorities seeking to become prosumers.

6. Conclusions

The ongoing transformation of economies towards RES-based power generation solutions contributes to sustaining the rising need for electricity consumption and tackling the challenges of climate change. However, the transition must be accelerated to ensure sustainable economic growth, notably under critical geo-strategic developments of the markets. In this respect, stimulating household investments into rooftop solar photovoltaic modules as one of the incentives of the RES spectrum also plays a significant role due to the abundance and low cost of solar energy, and its direct conversion to electricity. While a variety of MCDM methods are used by scholars to investigate and solve tasks related to developing solar plants on different scales, only a few examples were found subject to the selection of rooftop solar photovoltaic modules for households. Furthermore, the specifics of the application of MCDM methods and also their potential to rely upon not only quantitative but also qualitative data may require profound efforts while bringing different results. Consequently, the findings of the conducted experiment in selecting rooftop solar PV solutions for households in Lithuania by measuring attractiveness by a categorical-based evaluation technique (MACBETH) reveal its utility, especially in processing the data, which can be qualitative, quantitative, or a combination of both. Based upon qualitative judgments about the differences in attractiveness, 22 offers were compared and assessed quantifying the relative value of the offers and accordingly ranking the latter. The revealed versatility of the method in question allows consistently selecting, negotiating, and accordingly deciding on the potentially most effective and efficient one. The findings also confirm MACBETH’s potential to be applied not only to solving operational and (or) tactical tasks but also to the strategic objectives of private and public organizations aiming at the competitive and sustainable development in the short and long run. In this context, future research could be subject to combining FF- and RES-based solutions for specifics of different economy sectors by applying the MACBETH approach for reasoning decisions considering the constantly changing business landscape, regulatory systems, and geo-strategic shifts.

Data Availability Statement

Data available on request.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. (a) Cumulative installed solar PV capacity and average installed cost for solar photovoltaics, worldwide, for the 2010–2021 period (source: author, based on [49,50]); (b) average annual WTI and Brent crude oil (global), Nord Pool electricity (Europe), and natural gas prices (Europe and U.S.), for the 2010–2022 period (source: author, based on [5,10]).

Figure 2. The position of offers in terms of cost and an overall score of attractiveness.

Figure 3. The canvas of value curves of the three most attractive offers per each of the scenarios.

Figure 3. The canvas of value curves of the three most attractive offers per each of the scenarios.

Table 1

The 10 leading manufacturers (in actual shipments in 2019–2021) worldwide.

No.	Manufacturer of Solar PV Modules, Country of Headquarters	No. of Types ofSolar PV Technology	No. of Types of Solar PV Module per Type of Technology	No. of Variants of SolarPV Module per Type
1	Canadian Solar, Inc., Canada	3	At least 1; max 5	At least 5; max 7
2	Hanwha Group, Plc., S. Korea	2	At least1; max 2	At least 6; max 8
3	First Solar, Inc., United States	1	2	At least 6; max 8
4	Ja Solar Technology Co., Ltd., China	1	2	At least 5; max 6
5	Jinko Solar Holding Co., Ltd., China	3	At least 4; max 6	5
6	Trina Solar Co., Ltd., China	2	5	At least 8; max 9
7	Chint Solar Co., Ltd., China	2	At least 2; max 4	4
8	LONGi Green Energy Technology Co., Ltd., China	2	5	3
9	Risen Energy Co., Ltd., China	2	At least 3; max 8	At least 5; max 6
10	Shunfeng International Clean Energy Ltd., China	3	3	5

Source: Author; the findings are based on the analysis offerings of entities in the table; entities listed in alphabetical order; the first 6 are also among 10 leading manufacturers worldwide in terms of actual shipments since 2012 [8,9,10].

Table 2

Summary of the search on the solar PV module selection using MCDM methods.

Ref.	Country	Case Study	Method
[19]	Turkey	Solar farm location selection	AHP
[20]	Indonesia	Solar PV business evaluation	AHP
[21]	Ghana	Site evaluation of solar PV	AHP, geographic information system (GIS)
[22]	Saudi Arabia	Solar PV plant site selection	AHP
[23]	China	Solar PV plant site selection	AHP, GIS
[24]	Not specified	Solar PV module selection	AHP
[25]	Not specified	Solar PV module selection	TOPSIS
[26]	India	Solar park risk evaluation	TOPSIS
[32]	Uganda	Ranking solar PV module manufacturing countries	VIKOR
[33]	Spain	Site selection for solar farm	ELECTRE, TOPSIS
[35]	Turkey	PM manufacturer evaluation	AHP, MULTIMOORA, Interval Valued Pythagorean Fuzzy (IVPF)
[41]	Vietnam	Solar energy versus fossil fuel	DEA, AHP, and TOPSIS
[62]	China	Solar power plant site selection	PROMETHEE
[45]	Not specified	Solar power plant site selection	PROMETHEE and Interactive Simple Additive Weighting (ISAW)
[43]	Brazil	Assessment of solar farms	AHP, TOPSIS
[42]	Switzerland	Evaluation of buildings for photovoltaic integration	ELECTRE
[46]	India	Selection of solar power plant site	Fuzzy Linguistic Modeling Aggregated with VIKOR
[28]	Iran	Solar PV plant site selection	Fuzzy-Boolean logic and AHP
[47]	Not specified	Solar PV module selection	The Characteristic Objects Method (COMET) and TOPSIS
[31]	China	Solar PV plant site selection	The fuzzy grey relational projection (FGRP)
[48]	Iran	Solar PV power station site selection	The combined fuzzy best-worst method (FBWM), GIS

Table 3

Summary of offers received from contractors of a rooftop solar PV system with a 10 kW electricity generation capacity.

	The Criterion (ci)	Product Efficiency Stated by theContractor (%)	Cost (€/10 kW)	Product Warranty (Years)	Product Performance Efficiency Warranty after 25 Years	Inverter Warranty (Years)	Time until Solar PV SystemInstalled and Operational (Days)	Installation Construction Warranty (Years)	Warranty of Installation Works (Years)	Waiting Time for Emergency Repairs Services Execution (Days)	Compensation for Non-ProducedElectricity (€/%/Day of Non-Generation/Average): Yes/No	Maintenance Inspection (Free of Charge): Yes/No
Offer no. (oi: Moduleand Inverter Names)		c 1	c 2	c 3	c 4	c 5	c 6	c 7	c 8	c 9	c 10	c 11
Offer 1 (o1) (Risen RSM40-8-400M, Foxess T10-G3, 10 kW)		20.8	9869.67	12	84.8	12	70	10	10	5	No	No
o2 (Trina Solar TSM-400DE09.08 (Vertex S); Sofar Solar 11KTLX-G3)		20.8	10,793.20	15	84.8	10	150	20	10	5	No	No
o3 (Canadian Solar CS6R-410MS; Sofar Solar 11KTLX-G3)		21	8062.16	25	84.8	10	70	10	10	5	No	No
o4 (Solet410MHS-54; SOFAR 8,8KTLX-G3-3PH)		20.97	9540.08	20	84.8	12	90	10	5	1	No	No
o5 (ZnShine410W; Sungrow)		20.25	10,750	16	83.33	10	90	10	10	10	No	No
o6 (Risen RSM144-7-450M; Sofar Solar 11KTLX-G3)		20.4	10,115.60	12	84.8	10	90	10	10	10	No	No
o7 (Trina Vertex S 400W DE09.08; Huawei-Sun 2000-10 kW KTL M1)		20.8	10,800	15	84.8	10	70	10	10	5	No	No
o8 (Risen RSM40-8-400M; Solis S5-GR3P10K0)		20.3	9015.98	15	84.8	10	77	10	10	5	No	No
o9 (Trinasolar TSM-DE09.08 400W; Foxess T10-G3, 10 kW)		20.8	9400	15	84.8	10	90	10	10	14	No	No
o10 (Solitek 365W; Huawei Sun 2000-10KTL-M1)		19.7	11,634.25	30	89.2	10	120	10	10	3	No	No
o11 (Risen RSM40-8-400M; Solplanet ASW10K-LT-G2)		20.8	9447	15	84.8	10	60	10	10	3	No	No
o12 (Canadian Solar CS3L-MS 380W; Huawei Sun 2000-10KTL-M1)		20.5	10,222.96	12	84.8	10	210	10	10	5	No	No
o13 (Canadian Solar CS6R-410MS; Huawei Sun 2000-10KTL-M1)		21	10,127.54	12	84.8	10	150	12	10	5	Yes (60%, a 10-year warranty)	Yes (1/5 years)
o14 (Hyundai HiE-S405Wp; Foxess T10-G3, 10 kW)		20.7	10,786.52	25	84.9	12	60	10	5	14	No	No
o15 (Hyundai HiE-S400VI; Huawei Sun 2000-8KTL-M1-1)		20.4	10,600	25	85	10	120	20	10	14	No	No
o16 (Hyundai HiE-S480VI; Growatt MOD 9000-TL3-X)		20.5	9821.43	25	85	10	90	10	10	10	No	No
o17 (Hyundai HiE-S400VI; Sungrow)		20.4	10,060.97	25	85	10	90	10	10	14	No	No
o18 (JASOLAR 410W; Huawei Sun 2000-8KTL-M1-1)		21	9959.35	12	84.8	10	90	10	10	5	No	No
o19 (Jinko Tiger Pro JKM445M-60HL-4V BF445W; FRONIUS Symo 10.0-3-M WLAN/LAN)		20.62	8954.25	12	84.9	7	90	10	10	7	No	No
o20 (Autarco S1.MHJ405; Autarco S2.LQ12000S-MII)		20.7	9765.75	12	84.8	5	140	25	10	14	No	No
o21 (Sunpower 6BLK 405W; Huawei Sun 2000-10KTL-M1)		20.6	12,140.94	25	87.2	10	120	15	10	3	No	No
o22 (Trina Solar Vertex S TSM-DE09.08 395 Wp; Delta RPI M10A)		20.5	9925.06	15	84.8	5	90	10	10	14	No	No

Table 4

Semantic scale [11,12].

Semantic Category (SC) of Attractiveness	CategoryIndicator (SCk)	Scale	Variant of Judgment Comparing Offers o1, o2, …, o22 per Criterion c1, c2, c3, …, cn (Table 3)
No (N)	SC 0	0	Indifference of judgments pairwise comparing offers o1, o2, …, o22 (i.e., o12 I o13) per criterion ci
Very weak (VW)	SC 1	1	Very weakly attractive oi over oj (i.e., oi P oj) pairwise comparing offers per criterion ci
Weak (W)	SC 2	2	Weakly attractive oi over oj (i.e., oi P oj) pairwise comparing offers per criterion ci
Moderate (M)	SC 3	3	Moderately attractive oi over oj (i.e., oi P oj) pairwise comparing offers per criterion ci
Strong (S)	SC 4	4	Strongly attractive oi over oj (i.e., oi P oj) pairwise comparing offers per criterion ci
Very strong (VS)	SC 5	5	Very strongly attractive oi over oj (i.e., oi P oj) pairwise comparing offers per criterion ci
Extreme (E)	SC 6	6	Extremely attractive oi over oj (i.e., oi P oj) pairwise comparing offers per criterion ci

Table 5

The comparison of scenarios’ final ranks and overall scores.

First Scenario			Second Scenario			Third Scenario
Rank	Option	Overall Score	Rank	Option	Overall Score	Rank	Option	Overall Score
1	o 13	60.24	1	o 3	70.40	1	o 21	71.88
2	o 3	57.60	2	o 11	64.05	2	o 3	66.70
3	o 11	52.41	3	o 21	63.90	3	o 10	63.82
4	o 21	52.28	4	o 1	61.46	4	o 11	62.50
5	o 1	50.28	5	o 4	59.64	5	o 1	61.05
6	o 4	48.80	6	o 10	58.77	6	o 2	60.38
7	o 10	48.08	7	o 2	57.10	7	o 7	59.45
8	o 2	46.72	8	o 16	56.36	8	o 15	58.10
9	o 16	46.11	9	o 7	56.11	9	o 4	57.72
10	o 7	45.91	10	o 15	55.57	10	o 16	55.13
11	o 15	45.46	11	o 18	55.18	11	o 18	54.36
12	o 18	45.15	12	o 8	52.89	12	o 13	51.39
13	o 8	43.28	13	o 13	51.40	13	o 17	50.91
14	o 9	42.00	14	o 9	51.34	14	o 14	48.87
15	o 17	41.97	15	o 17	51.30	15	o 9	48.01
16	o 19	41.34	16	o 19	50.52	16	o 8	47.37
17	o 14	38.48	17	o 14	47.04	17	o 19	44.52
18	o 20	38.06	18	o 20	46.51	18	o 20	43.87
19	o 6	35.23	19	o 6	43.06	19	o 6	41.82
20	o 12	32.86	20	o 12	40.16	20	o 12	38.94
21	o 22	31.80	21	o 22	38.87	21	o 5	37.83
22	o 5	30.59	22	o 5	37.38	22	o 22	35.83

Appendix A. The Pairwise Comparison Scores and Rankings

Table A1

(a) First scenario—the scores of pairwise comparisons of offers. (b) First scenario—rankings of offers per criterion.

(a)
Options	Overall	c1	c2	c3	c4	c5	c6	c7	c8	c9	c10	c11
o 1	52.28	91.94	64.71	0	30	100	93.76	0	100	72.73	0	0
o 2	46.72	91.94	30.88	30	30	57.14	31.25	70	100	72.73	0	0
o 3	57.6	100	100	80	30	57.14	93.75	0	100	72.73	0	0
o 4	48.8	96.77	75	60	30	100	75	0	0	100	0	0
o 5	30.59	3.23	33.82	40	0	57.14	75	0	100	27.27	0	0
o 6	35.23	45.16	52.94	0	30	57.14	75	0	100	27.27	0	0
o 7	45.91	91.94	29.41	30	30	57.14	93.75	0	100	72.73	0	0
o 8	43.28	1.61	97.06	30	30	57.14	87.5	0	100	72.73	0	0
o 9	42	91.94	77.94	30	30	57.14	75	0	100	0	0	0
o 10	48.08	0	18.38	100	100	57.14	62.5	0	100	90.91	0	0
o 11	52.41	91.94	76.47	30	30	57.14	100	0	100	90.91	0	0
o 12	32.86	51.61	50	0	30	57.14	0	0	100	72.73	0	0
o 13	60.24	100	51.47	0	30	57.14	31.25	20	100	72.73	100	100
o 14	38.48	70.97	32.35	80	40	100	100	0	0	0	0	0
o 15	45.46	45.16	35.29	80	50	57.14	62.5	70	100	0	0	0
o 16	46.11	51.61	66.18	80	50	57.14	75	0	100	27.27	0	0
o 17	41.97	45.16	54.41	80	50	57.14	75	0	100	0	0	0
o 18	45.15	100	61.76	0	30	57.14	75	0	100	72.73	0	0
o 19	41.34	58.06	98.53	0	40	28.57	75	0	100	54.55	0	0
o 20	38.06	70.97	67.65	0	30	0	50	100	100	0	0	0
o 21	52.28	64.52	0	80	80	57.14	62.5	40	100	90.91	0	0
o 22	31.8	51.61	63.24	30	30	0	75	0	100	0	0	0
[all upper]	100	100	100	100	100	100	100	100	100	100	100	100
[all lower]	0	0	0	0	0	0	0	0	0	0	0	0
Weights:		0.0909	0.0909	0.0909	0.0909	0.0909	0.0909	0.0909	0.0909	0.0909	0.0909	0.0909
(b)
		c1	c2	c3	c4	c5	c6	c7	c8	c9	c10	c11
		Upper—21%	o3	Best—30 years	o10	Best—12 years	Best—60 days	o20	Best—10 years	o4	Yes (>=60%)	Yes (1/5 years)
		o 3	Best—€8062	o 10	Best—89.2%	o 1	o 11	Best—25 years	o 1	Best—1 day	o 13	o 13
		o 13	o 19	o 3	o 21	o 4	o 14	o 2	o 2	o 10	o 1	o 1
		o 18	o 8	o 14	o 15	o 14	o 1	o 15	o 3	o 11	o 2	o 2
		o 4	o 9	o 15	o 16	o 2	o 3	o 21	o 5	o 21	o 3	o 3
		o 1	o 11	o 16	o 17	o 3	o 7	o 13	o 6	o 2	o 4	o 4
		o 2	o 4	o 17	o 14	o 5	o 8	o 1	o 7	o 1	o 5	o 5
		o 7	o 20	o 21	o 19	o 6	o 4	o 3	o 8	o 3	o 6	o 6
		o 9	o 16	o 4	o 1	o 7	o 5	o 4	o 9	o 7	o 7	o 7
		o 11	o 1	o 5	o 2	o 8	o 6	o 5	o 10	o 8	o 8	o 8
		o 20	o 22	o 2	o 3	o 9	o 9	o 6	o 11	o 12	o 9	o 9
		o 14	o 18	o 7	o 4	o 10	o 16	o 7	o 12	o 13	o 10	o 10
		o 21	o 17	o 8	o 6	o 11	o 17	o 8	o 13	o 18	o 11	o 11
		o 19	o 6	o 9	o 7	o 12	o 18	o 9	o 15	o 19	o 12	o 12
		o 12	o 13	o 11	o 8	o 13	o 19	o 10	o 16	o 5	o 14	o 14
		o 22	o 12	o 22	o 9	o 15	o 22	o 11	o 17	o 6	o 15	o 15
		o 16	o 15	o 1	o 11	o 16	o 10	o 12	o 18	o 16	o 16	o 16
		o 6	o 5	o 6	o 12	o 17	o 15	o 14	o 19	o 9	o 17	o 17
		o 15	o 14	o 12	o 13	o 18	o 21	o 16	o 20	o 14	o 18	o 18
		o 17	o 2	o 13	o 18	o 21	o 20	o 17	o 21	o 15	o 19	o 19
		o 5	o 7	o 18	o 20	o 19	o 2	o 18	o 22	o 17	o 20	o 20
		o 8	o 10	o 19	o 22	o 20	o 13	o 19	o 4	o 20	o 21	o 21
		Lower—19.7%	o 21	o 20	o 5	o 22	o 12	o 22	o 14	o 22	o 22	o 22
		o10	Worst—€12,140	Worst—12 years	Worst—83.3%	Worst—5 years	Worst—210 days	Worst—10 years	Worst—5 years	Worst—14 days	No	No

Table A2

(a) Second scenario—the scores of pairwise comparisons of offers. (b) Second scenario—rankings of offers per criterion.

(a)
Options	Overall	c1	c2	c3	c4	c5	c6	c7	c8	c9
o 1	61.46	91.94	64.71	0	30	100	93.75	0	100	72.73
o 2	57.1	91.94	30.88	30	30	57.14	31.25	70	100	72.73
o 3	70.4	100	100	80	30	57.14	93.75	0	100	72.73
o 4	59.64	96.77	75	60	30	100	75	0	0	100
o 5	37.38	3.23	33.82	40	0	57.14	75	0	100	27.27
o 6	43.06	45.16	52.94	0	30	57.14	75	0	100	27.27
o 7	56.11	91.94	29.41	30	30	57.14	93.75	0	100	72.73
o 8	52.89	1.61	97.06	30	30	57.14	87.5	0	100	72.73
o 9	51.34	91.94	77.94	30	30	57.14	75	0	100	0
o 10	58.77	0	18.38	100	100	57.14	62.5	0	100	90.91
o 11	64.05	91.94	76.47	30	30	57.14	100	0	100	90.91
o 12	40.16	51.61	50	0	30	57.14	0	0	100	72.73
o 13	51.4	100	51.47	0	30	57.14	31.25	20	100	72.73
o 14	47.04	70.97	32.35	80	40	100	100	0	0	0
o 15	55.57	45.16	35.29	80	50	57.14	62.5	70	100	0
o 16	56.36	51.61	66.18	80	50	57.14	75	0	100	27.27
o 17	51.3	45.16	54.41	80	50	57.14	75	0	100	0
o 18	55.18	100	61.76	0	30	57.14	75	0	100	72.73
o 19	50.52	58.06	98.53	0	40	28.57	75	0	100	54.55
o 20	46.51	70.97	67.65	0	30	0	50	100	100	0
o 21	63.9	64.52	0	80	80	57.14	62.5	40	100	90.91
o 22	38.87	51.61	63.24	30	30	0	75	0	100	0
[all upper]	100	100	100	100	100	100	100	100	100	100
[all lower]	0	0	0	0	0	0	0	0	0	0
Weights		0.1111	0.1111	0.1111	0.1111	0.1111	0.1111	0.1111	0.1111	0.1111
(b)
		c1	c2	c3	c4	c5	c6	c7	c8	c9
		Upper—21%	o3	Best—30 years	o10	Best—12 years	Best—60 days	o20	Best—10 years	o4
		o 3	Best—€8062	o 10	Best—89.2%	o 1	o 11	Best—25 years	o 1	Best—1 day
		o 13	o 19	o 3	o 21	o 4	o 14	o 2	o 2	o 10
		o 18	o 8	o 14	o 15	o 14	o 1	o 15	o 3	o 11
		o 4	o 9	o 15	o 16	o 2	o 3	o 21	o 5	o 21
		o 1	o 11	o 16	o 17	o 3	o 7	o 13	o 6	o 2
		o 2	o 4	o 17	o 14	o 5	o 8	o 1	o 7	o 1
		o 7	o 20	o 21	o 19	o 6	o 4	o 3	o 8	o 3
		o 9	o 16	o 4	o 1	o 7	o 5	o 4	o 9	o 7
		o 11	o 1	o 5	o 2	o 8	o 6	o 5	o 10	o 8
		o 20	o 22	o 2	o 3	o 9	o 9	o 6	o 11	o 12
		o 14	o 18	o 7	o 4	o 10	o 16	o 7	o 12	o 13
		o 21	o 17	o 8	o 6	o 11	o 17	o 8	o 13	o 18
		o 19	o 6	o 9	o 7	o 12	o 18	o 9	o 15	o 19
		o 12	o 13	o 11	o 8	o 13	o 19	o 10	o 16	o 5
		o 22	o 12	o 22	o 9	o 15	o 22	o 11	o 17	o 6
		o 16	o 15	o 1	o 11	o 16	o 10	o 12	o 18	o 16
		o 6	o 5	o 6	o 12	o 17	o 15	o 14	o 19	o 9
		o 15	o 14	o 12	o 13	o 18	o 21	o 16	o 20	o 14
		o 17	o 2	o 13	o 18	o 21	o 20	o 17	o 21	o 15
		o 5	o 7	o 18	o 20	o 19	o 2	o 18	o 22	o 17
		o 8	o 10	o 19	o 22	o 20	o 13	o 19	o 4	o 20
		Lower—19.7%	o 21	o 20	o 5	o 22	o 12	o 22	o 14	o 22
		o10	Worst—€12140	Worst—12 years	Worst—83.3%	Worst—5 years	Worst—210 days	Worst—10 years	Worst—5 years	Worst—14 days

Table A3

(a) Third scenario—the scores of pair-wise comparisons of offers. (b) Third scenario—rankings of offers per criterion.

(a)
Options	Overall	c1	c3	c4	c5	c6	c7	c8	c9
o 1	61.05	91.94	0	30	100	93.75	0	100	72.73
o 2	60.38	91.94	30	30	57.14	31.25	70	100	72.73
o 3	66.7	100	80	30	57.14	93.75	0	100	72.73
o 4	57.72	96.77	60	30	100	75	0	0	100
o 5	37.83	3.23	40	0	57.14	75	0	100	27.27
o 6	41.82	45.16	0	30	57.14	75	0	100	27.27
o 7	59.45	91.94	30	30	57.14	93.75	0	100	72.73
o 8	47.37	1.61	30	30	57.14	87.5	0	100	72.73
o 9	48.01	91.94	30	30	57.14	75	0	100	0
o 10	63.82	0	100	100	57.14	62.5	0	100	90.91
o 11	62.5	91.94	30	30	57.14	100	0	100	90.91
o 12	38.94	51.61	0	30	57.1	0	0	100	72.73
o 13	51.39	100	0	30	57.14	31.25	20	100	72.73
o 14	48.87	70.97	80	40	100	100	0	0	0
o 15	58.1	45.16	80	50	57.14	62.5	70	100	0
o 16	55.13	51.61	80	50	57.14	75	0	100	27.27
o 17	50.91	45.16	80	50	57.14	75	0	100	0
o 18	54.36	100	0	30	57.14	75	0	100	72.73
o 19	44.52	58.06	0	40	28.57	75	0	100	54.55
o 20	43.87	70.97	0	30	0	50	100	100	0
o 21	71.88	64.52	80	80	57.14	62.5	40	100	90.91
o 22	35.83	51.61	30	30	0	75	0	100	0
[all upper]	100	100	100	100	100	100	100	100	100
[all lower]	0	0	0	0	0	0	0	0	0
Weights		0.125	0.125	0.125	0.125	0.125	0.125	0.125	0.125
(b)
		c1	c3	c4	c5	c6	c7	c8	c9
		Upper—21%	Best—30 years	o10	Best—12 years	Best—60 days	o20	Best—10 years	o4
		o 3	o 10	Best—89.2%	o 1	o 11	Best—25 years	o 1	Best—1 day
		o 13	o 3	o 21	o 4	o 14	o 2	o 2	o 10
		o 18	o 14	o 15	o 14	o 1	o 15	o 3	o 11
		o 4	o 15	o 16	o 2	o 3	o 21	o 5	o 21
		o 1	o 16	o 17	o 3	o 7	o 13	o 6	o 2
		o 2	o 17	o 14	o 5	o 8	o 1	o 7	o 1
		o 7	o 21	o 19	o 6	o 4	o 3	o 8	o 3
		o 9	o 4	o 1	o 7	o 5	o 4	o 9	o 7
		o 11	o 5	o 2	o 8	o 6	o 5	o 10	o 8
		o 20	o 2	o 3	o 9	o 9	o 6	o 11	o 12
		o 14	o 7	o 4	o 10	o 16	o 7	o 12	o 13
		o 21	o 8	o 6	o 11	o 17	o 8	o 13	o 18
		o 19	o 9	o 7	o 12	o 18	o 9	o 15	o 19
		o 12	o 11	o 8	o 13	o 19	o 10	o 16	o 5
		o 22	o 22	o 9	o 15	o 22	o 11	o 17	o 6
		o 16	o 1	o 11	o 16	o 10	o 12	o 18	o 16
		o 6	o 6	o 12	o 17	o 15	o 14	o 19	o 9
		o 15	o 12	o 13	o 18	o 21	o 16	o 20	o 14
		o 17	o 13	o 18	o 21	o 20	o 17	o 21	o 15
		o 5	o 18	o 20	o 19	o 2	o 18	o 22	o 17
		o 8	o 19	o 22	o 20	o 13	o 19	o 4	o 20
		Lower—19.7%	o 20	o 5	o 22	o 12	o 22	o 14	o 22
		o10	Worst—12 years	Worst—83.3%	Worst—5 years	Worst—210 days	Worst—10 years	Worst—5 years	Worst—14 days

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