Private Partner Prioritization for Public–Private Partnership Contracts in a Brazilian Water Company Using a Multi-Criteria Decision Aid Method

Abstract

Public–private partnerships (PPPs) are long-term contracts between government entities and private companies, and are increasingly being adopted in developing countries due to the large need for investments in sectors such as water and sewerage and also in order to benefit from the experience and to have access to the resources and technology of the private sector. Prioritizing the private party of the contract becomes a complex decision due to the characteristics of PPP contracts, and a standard of evaluation has not been adopted yet, the decision usually being made by evaluating the price. Thus, this research aims to propose a set of criteria to be incorporated into the decision problem that involves technical aspects. It then seeks to rank alternatives by using a multi-criteria decision aid method, FITradeoff, which supports the decision-maker (DM) in prioritization and provides transparency and security to the process.

1. Introduction

Public–private partnerships (PPPs) are joint arrangements between the public and private sectors that are entered into in order to achieve an objective, and this entails sharing risks, resources, responsibilities, liabilities, and authority [1]. PPP contracts enable government entities to access high-level expertise, modern technologies, innovative financing, and modern design, and to maintain the public infrastructure, thereby enhancing service provision to users due to being able to draw on the expertise of the private sector [2,3].

According to Li and Wang [4], who researched PPP failure rates from 2014 to 2020 in China, the cities of Gansu, Heilongjiang and Hainan presented failure rates of 57.69%, 33.33%, and 30.43%, respectively. Considering that China is the world’s second-largest economy and PPPs are widely applied there, this investigation leads to conclusions that should be taken into account for other developing countries.

The main factors that can lead to failure of PPP contracts are risk allocation, level of government support provided, the project’s economy and social utility, the actual demand, and the characteristics of the environment in which it operates, and in practice, its success depends on the tenders and contracts to be designed and operationalized [4,5].

The main characteristics of PPPs are that they are long-term contracts that can last for 20 to 30 years. During the contract, payments are made from the public to the private sector, and the infrastructure created is either the property of the public partner or is transferred to it at the end of the contract [6].

PPPs that involve new assets are denoted greenfield projects, and the private companies are responsible for financing, building, and managing new public assets. Also, PPPs can be used so that a public entity can transfer to a private party the responsibility of upgrading and managing existing assets—these are known as brownfield projects. For both cases, the key aspect is defining what is required rather than how it should be done. There are several types of PPP models, which include multiple project phases or functions regarding the responsibilities of the private party, namely, design (engineering work), build or rehabilitate, finance, maintain, and operate. Combinations of PPP arrangements include: design–build (DB), design–build–operate (DBO), build–operate–transfer (BOT), build–own–operate–transfer (BOOT), and build–own–operate (BOO). For each of these, there is a certain level of risk involved [2]. DB and DBO models integrate project design and project construction phases [7]. In BOT contracts, the private sector provides the financing and construction of the facilities, operates the infrastructure over a fixed period of time, and then transfers the facilities to the public sector when the contract ends. BOO execution relates to complete privatization, and BOOT is similar to BOO, including the transfer back to the public sector after the concession period [8].

According to Brazilian Federal Law 11.079, a PPP is an administrative contract of concession, which can be sponsored or administrative. An administrative concession relates to a service provided for which the public administration pays, and a sponsored concession involves collecting fees from service users (user pays) and also payments from the government (government pays). The payment mechanism, either way, should be defined by the private partner’s performance [9].

Despite the abovementioned advantages of PPP arrangements, the benefits of providing services such as raising investments and constructing and managing infrastructure via private sector participation also depend on effective PPP contracting and procurement by the government. Infrastructure projects usually involve construction companies. Thus, the choice of the contractor has a major impact on costs and quality, and if the contractor’s performance is weak, this can lead to delayed completion, increased costs, poor construction quality, and legal disputes [10].

Private and public sector interaction and linkage are essential for the successful implementation of PPP projects, since a deteriorating relationship can result in controversy, misunderstanding, conflict, and dispute. Thus, private partner selection represents the most important factor prior to starting a PPP project [11].

Practicing managers usually avoid highly mathematical models to make decisions with regard to private partner selection, because such models require mastery of technical details and coming up against difficulties. Therefore, it is common for these decisions to be made intuitively, which can be unreliable for solving complex problems such as selecting a private partner for a long-term contract [12].

This study sets out to contribute to the literature by providing a framework for the problem of the private partner prioritization of a PPP contract. It proposes criteria to be considered to attend to the sector and the needs of government, and it also proposes a methodology that supports the DMs of water and sewerage companies. These companies increasingly need to engage on infrastructure PPPs in Brazil due to the need to invest heavily to provide better services for their users. The framework proposed aids in the evaluation of technical aspects and of the price of the components in the procurement processes by applying a multi-criteria decision aid method (MCDM). To achieve evaluation of the technical aspects, criteria adopted in the literature were analyzed and then input into the model in order to propose a standard process for selecting a private partner and to reduce the cognitive effort of the committee responsible for the evaluation. By acting in this way, the prioritization process can rely on more transparency and credibility [13,14].

The methodology stems from what is being used nowadays, a global value obtained from a weighted sum to a technical evaluation, and instead of being performed differently according to the evaluation committee, it is performed using the FITradeoff method. The results of our research also indicate the most relevant criteria to be adopted by the evaluators of the private partner prioritization problem for a PPP contract. In addition, an application is simulated of a practical case currently in development. This is for a government entity that provides water treatment and supply, and the simulation is undertaken in order to analyze and validate the proposed research idea.

The main objective of the project was to propose a model for prioritizing private partners for a PPP contract based on a set of criteria to be adopted as a standard for water production/distribution companies and being able to obtain a ranking that will lead to the company that will be hired. Therefore, the research aimed to answer the following research questions (RQs).

RQ1:

How do water and sewerage PPP tenders currently take place in Brazil?

RQ2:

What aspects should be considered for the technical evaluation of a private partner in a PPP contract?

RQ3:

What criteria should be taken into consideration for PPP contracts for companies that provide water and sewerage services, considering the long duration of 20 to 30 years of such contracts, and how to measure them?

RQ4:

Why use multi-criteria decision support methods (MCDM) to prioritize private partners in the provision of water and sewerage services?

The article is structured as follows. Section 2 presents the methodology of the research, including concepts of PPP structuring, private partner selection, a Brazilian perspective of the criteria to be applied to evaluate candidates in PPPs, and a brief literature review of private partner selection. Section 3 presents the case study applied to a public water company and the managerial implications of the subject studied, and Section 4 draws some conclusions and makes suggestions for future lines of research.

2. Materials and Methods

2.1. PPP Structuring

The structuring of PPP project models occurs due to the need for the public authority to carry out projects for reasons such as the need for large-scale investments in various sectors and the efficiency of the private sector in terms of contracting and execution.

The first step consists of defining the project that will be carried out through the PPP contracting modality, which will depend on prioritizing government projects. Developing a PPP model demands some steps and definitions from different perspectives. These perspectives can be divided into three areas: legal, engineering, and financial approaches.

The legal approach refers to various aspects of the tendering process that range from the documents needed to inform the stakeholders and potential investors of the project, drawing up the invitation to tender, and entering into a contract.

The technical and engineering approach is related to the diagnosis of the current situation of the construction works, structures, and operational areas that will be affected by the project in order to obtain relevant data to undertake financial and demand studies.

From the data obtained from the technical and engineering step, mainly the demand studies, the financial approach tackles the study of the economic and financial viability of the project proposed, which is a requirement laid down in Brazilian Federal Law 11.079 and represents important data from the potential investors [9].

2.2. Private Partner Selection

Deciding which supplier to select in procurement processes is considered one of the most significant decisions in procurement [15]. Organizations, especially in the public sector, struggle with the pressure to explain their choice of suppliers [16]. Public organizations have their selection processes regulated and guided by specific laws and other forms of accountability. EU public procurement directives request transparency, equal treatment, objectivity, non-discrimination, calculation methods to be published, criteria for accepting a tender, and their relative importance in a proposal [15].

Selecting a concessionaire represents an important element for the public partner in PPP projects, as it is this partner that is responsible for guaranteeing adequate contract performance and may face political, social, and financial problems associated with an unsuccessful PPP [17]. In order to tackle making these decisions, it is important to establish how to measure the performance of the concessionaire by setting criteria and defining the method to be used to evaluate these attributes, for which the complexity of the problem needs to be considered.

The five major critical success factors of a PPP project identified by Zhang [18] are as follows: favorable investment environment of the project location; economic viability of the project; reliable concessionaire with strong technical strength; sound financial package of the concessionaire in project financing; appropriate risk allocation; and supported by reliable contract arrangements. Thus, 40% of the success factors are dependent on the concessionaire aspects and thus on selecting the concessionaire.

Li et al. [19] presents first-level indicators to evaluate the components for water environment treatment PPP projects, which include financial capability, technology capability, management capability, credit reputation, and technology solutions. These first-level indicators are then divided into second-level ones that represent detailed evaluations, made by conducting a literature review and using the Delphi method.

Tavana et al. [12] propose sustainable private partner selection that considers economic, environmental, technological, and social aspects. These aspects are detailed in criteria taken from the literature and suggested by experts.

Chen et al. [10] describe a set of criteria comprising technical criteria, tenderer’s competence, tender price, and health, safety, and environment considerations to be used for constructor–contractor selection. These criteria are broken into subcriteria obtained from the literature. Of the ten criteria presented, one is quantitative and the rest are qualitative.

Olanrewaju et al. [20] present a platform for the process of decision-making on choosing contractors based on selection criteria including aspects such as financial capability, health and safety records, previous performance, and past working experience, and they use a multi-regression model to aggregate these components.

Zhang et al. [21] present a framework for selecting concessionaires based on Hong Kong’s experiences in BOT arrangement for tunnels. The BOT concessionaire integrates diverse functions such as finance, design, construction, and operation, which are integrated, while in traditional projects, these functions are fragmented. The concessionaire has to deal with several participants in the project: the public client, investors, main contractor, main designer, insurers, suppliers of material and equipment, operators, maintenance staff, and intermediate/end product/service purchasers.

Zhang [17] presented a best-value concessionaire selection (BVCS) methodology, which is based on a fuzzy logic system. The procedure requires a clear definition of the government’s best-value objectives, an appropriate trade-off of the objectives, and a methodology—best-value source selection—to choose the right source to attend to the objectives defined.

2.3. Defining the Criteria

The literature adopts aspects divided into categories, which are financial, technical, managerial, and health, safety, and environmental. These categories are then divided into a large set of criteria, which leads to a complex evaluation process, since it may not be easy to obtain all the information nor can it all be considered at once for each candidate of the tendering process. Moreover, this is a phase that consumes a lot of time to complete. Thus, this research seeks to offer an affordable set of criteria and a direct way to measure them in order to support the DM to select the most adequate candidate considering the complexities of selecting the private partner for a PPP project.

According to Keeney and Raiffa [22], the decision criteria should attend to the properties of the criteria being complete, which indicates that it is sufficient to describe the goals expected by the DM; operational, which is related to the criteria being clearly understood by every actor involved in the problem; and non-redundant, which means that there is no criterion in the set that measures the same attribute of another criterion.

The criteria obtained by conducting the literature review were analyzed regarding the abovementioned properties and by evaluating how they can be measured. During the process, some redundancies were identified and some modifications were made to their description in order to define a way of quantifying them.

2.3.1. Financial

The financial perspective represents the information regarding the candidates and is also the aspect considered in the proposals. The company’s financial aspects are indexes of the service acceptance by the user and their payments: timely payments; the assets owned by the service provider; the asset-liability ratio; and the net profit growth rate [12].

The financial aspect of the proposal consists of the financing plan of the project, which can be evaluated by considering the charge to the public party of the contract and the grant that the public party is going to receive.

2.3.2. Technical

The technical aspects for infrastructure selection processes mainly concern the experience of the company from different points of view. Aspects such as the service provider’s project engineering design ability and project process design ability can be evaluated by counting the number of engineering projects developed, which can be proved through certificates, and the number of constructed and operating plants. The number of unfinished and delayed works is also an important aspect to be considered. This represents the company’s ability to fulfill its construction programs [10].

By evaluating human resources, which is the talent reserve of the service provider, a quantification of this could be the number of employees of the candidate private partner. This was not considered in this study, because “human resources” refers to measuring the results of operational aspects evaluated.

Since it is important to consider building and operating experience for a BOT project, some operational aspects can be also taken into account, such as indexes of the quality of the service provided. For water projects i.e., aspects of water quality, the availability of water to the consumer can be considered. Also, the aspect of quality can consider certifications of the company in standards such as ISO.

The development and use of new technologies are important, because they can present positive results for the technical aspects in the dimensions of project design, building, and operations. This aspect can be measured, if there is an innovation sector in the company, by how much the company invests in innovation and the prizes awarded.

Key mechanical equipment is an operational aspect to be evaluated, although it becomes redundant, since this research aims to measure the construction or operational capacity, which has already been considered in a number of constructed and operating plants.

2.3.3. Managerial

The managerial aspects considered in Li et al. [19] present some criteria that can be redundant given other perspectives from finances and technical matters. Capital management capability is an aspect that is evaluated by finances, and the operation management capability is measured by evaluating the quality of the service provided from the operational perspective, which can also embrace the quality management capacity. Schedule management capability is also considered in the technical perspective of completing construction programs. Standardization is already evaluated in the technical perspective of quality from certifications.

Neither contract management capability, subcontractor management capability, nor risk management capability were considered, because their effects are represented in the technical results.

2.3.4. Credit Reputation

Credit reputation embraces some aspects that can be related to the company in the managerial perspective, e.g., the credit rating provided by financial institutions, position for special population and social reputation. The company’s position for special populations can be measured by quantifying the contribution of social actions to the local community of the operation sites. The company’s social reputation can be evaluated by the complaints of their clients and the historical litigation situation. This is an important aspect to be evaluated that may be an indicator of how the company deals with the legal issues from its contracts, and can be measured by the quantity of ongoing and resolved legal actions [12].

2.3.5. Health, Safety, and Environment

Zhang [18] presents the criteria of the perspective of health, safety, and the environment, which are very specifically to be quantified and evaluated for each candidate, such as past performances, qualifications of the team, and protection of flora and fauna. This research will consider the licenses obtained from environmental agencies and ISO14000 certification, since these certificates establish the measures needed that are related to the environment.

2.4. Evaluation of the Alternatives

The selection mechanisms for private partners in a PPP should take into consideration the alternatives in the disputes, which may comprise the set of alternatives for the problem under analysis. Depending on the criteria that will be defined, there may be limitations in relation to the participants.

The requirements for proof of experience may be satisfied by presenting certificates, and depending on the definition of these quantities and types, companies may participate individually or in consortia of companies in order to meet the prequalification requirements of the tender.

Companies that operate in the sector of interest and have participated in similar projects can be considered in the evaluation of alternatives to verify their adherence to the definition of the criteria that will be required; however, the set of alternatives will only be defined after the bidding process has begun.

The publication of the invitation to tender defines the moment when the companies can submit their tenders containing the material for technical and price analysis. From the moment that such documents are delivered, the set of alternatives that will compose the decision-making model of the private partner in a tendering process for contracting a public–private partnership will be formed.

2.5. Trends of PPPs

The trends that are evaluated in this section are related to the criteria usually adopted from the analysis of different PPP applications resulting from research developed by gathering information from the World Bank database and Brazilian sanitation companies and after a brief review of the literature on PPP usages in other countries.

Figures collected from the World Bank database using a customized query of the PPP projects from the countries that represent 80% of the registered data considering different primary sectors—water and sewerage (W&S), energy, information and communication technology (ICT), and municipal solid waste (MSW)—are presented in

Table 1. PPPs worldwide.

Country	W&S	Energy	ICT	MSW	Transport	Total
China	622	646	4	216	357	1845
Brazil	164	1167	34	32	320	1717
India	23	512	7	48	548	1138
Mexico	44	161	3	9	118	335
Turkey		215	1	7	41	264
Colombia	46	94	3	1	70	214
Russian Federation	24	101	21	8	34	188
Peru	10	106	6		46	168
Thailand	19	118		6	9	152
Vietnam	7	126	1	3	15	152
Philippines	13	96	1	4	28	142
Argentina	6	90			35	131
Ukraine	3	120	2	1	4	130
Indonesia	26	71	3	1	23	124
Bulgaria	1	73	1	36	7	118
South Africa	5	91	3	4	12	115

.

China, Brazil, and India represent 54.53% of the projects, mostly in the energy sector, followed by transport and water and sanitation. China and Brazil are classified as upper-middle income and India as lower-middle income by the World Bank.

In international practices for selecting a concessionaire, open competitive tendering is a trend [21]. This process consists of the following stages: request for prequalification, prequalification, invitation to tender, tender evaluation and shortlisting, negotiations with shortlisted tenderers and selection of best tender, and award of concession.

A concessionaire is commonly formed by a consortium formed for a particular project and usually has no track record. The main difference between selecting a concessionaire and selecting a contractor is that the former has more commitments due to its response to, besides the construction questions, the finance, design, long-term contract of operation and maintenance, and transfer of the project facilities to the client at the end of the concession period. The concessionaire’s competence depends on the constituent companies, its ability to design competitive financial and technical packages, and the partnering skills of the proposed project participants.

There are competitive tender evaluation methods cited by Zhang et al. [21], such as the simple scoring method, the NPV method, sensitivity analysis, multiattribute analysis, and the Kepner-Tregoe decision analysis technique.

2.6. Water and Sewerage in Brazil

Most PPP projects in Brazil, as presented in

Table 2. PPPs in Brazil for water and sewerage.

Administrative Concession
Project	State	Judgment Criterion
Cariacica Sanitary Sewage [23]	Espírito Santo	Lowest price
Desalination Plant [24]	Ceará	Lowest price
Mato Grosso do Sul Sanitary Sewage [25]	Mato Grosso do	Lowest price
	Sul
Vila Velha Sanitary Sewage [26]	Espírito Santo	Lowest price
São Lourenço Water Production System [27]	São Paulo	Lowest price
Jaguaribe Ocean Disposal System [28]	Bahia	Lowest price
Rio Manso Water Production System [29]	Minas Gerais	Lowest price
Alto Tietê Water Production System [30]	São Paulo	Lowest price
Serra Sanitary Sewage [31]	Espírito Santo	Lowest price
CORSAN Sanitation [32]	Rio Grande do	Lowest price
	Sul
High Part of Maceió Sanitary Sewage [33]	Alagoas	Lowest price
Divinópolis Sanitary Sewage [34]	Minas Gerais	Lowest price
Piracicaba Sanitary Sewage [35]	São Paulo	Price and technique
Rio Claro Sanitary Sewage [36]	São Paulo	Price and technique
Guaratinguetá Sanitary Sewage [37]	São Paulo	Price and technique
RMR and Goiana Sanitary Sewage [38]	Pernambuco	Price and technique
Atibaia Sanitary Sewage [39]	São Paulo	Price and technique
Rio das Ostras Sanitary Sewage [40]	Rio de Janeiro	Price and technique
Agreste Adductor System [41]	Alagoas	Price and technique
Mauá Water Supplier System [42]	São Paulo	Price and technique
Guarulhos Sanitary Sewage [43]	São Paulo	Price and technique
Sponsored Concession
Project	State	Judgment Criteria
Paraty Water and Sewage [44]	Rio de Janeiro	Price and technique
Macaé Sanitary Sewage [45]	Rio de Janeiro	Price and technique

, consider the lowest-price criterion of judgment to choose a private partner from a competitive tender. To choose the criteria of technique and price usually means that for companies, this represents spending more time in analyzing the tenders and setting up a committee consisting of at least three professionals to examine the proposals received. Also, after this examination has been conducted, the result can be the subject of appeal from the bidders that did not win the tendering process. That represents for the public party more time to sign the contract with the winner and more resources to be allocated in order to prepare to respond to the appeals. This is unlikely to occur with the lowest-price criterion of judgment, since it is an attribute that does not leave space for subjectivity.

After adopting the lowest-price criterion, public companies usually consider habilitation requests to evaluate the technical part of the competitors, such as certifications from previous projects performed by the professionals and by the company to reduce the risks of contracting without having made a technical evaluation directly.

The habilitation phase usually occurs after the partner selection to reduce the human resources effort. Thus, selection occurs based only on the price criterion. If the candidate with the lowest price meets all the habilitation requests, then the selection process has finished. Otherwise, the second-ranked candidate is evaluated, and this process continues until there is a candidate that satisfies all the requisites. Habilitation plays the role of a filter, since the process does not consider other criteria in order to make the choice. Therefore, the competitor that can present an intermediate price and better technical performance may not even be considered.

The trade-off between the technical aspects and price can be considered by selecting technical and price judgment criteria. The technical aspect brings more complexity to the process, but since selecting the right partner is the most critical step in a PPP partnership, it should be considered [18]. This can be why the lowest price usually is adopted in PPP procurement processes, as shown in Table 2, which leads to a gap in this research: the lack of a standardized set of criteria and MCDM to aggregate to reach the technique and price evaluation of the private partners in the procurement process.

Defining the technical evaluation means to define more attributes related to aspects beyond price and may include aspects that relate to the candidate’s capacity to perform its part of the PPP project adequately, respecting the contract and being able to meet the schedule, and performance indicators. For public services especially, which bring services and benefits that directly impact the population, such as transport, energy, water, and sanitation, it is an important task to choose a private partner that is committed. This selection should not be performed based only on the criterion of price.

The prioritization process based on technique and price occurs by a weighted sum, where the weights are defined in a public notice for each element considered, frequently adopted as 0.4 for technique and 0.6 for price. The technical analysis must be detailed in the public notice, and depends on the judgment of the evaluation committee, which can usually bring subjectivity to the prioritization process.

2.7. MCDM/A

The choice of an MCDM/A method to deal with a particular problem depends on considering the aspects of the DM’s preference structure, characteristics of the decision problem itself, contextual features of the decision problem, such as organizational aspects, and the time available to achieve the decision [46].

As to the DM’s preference structure, this concerns defining it as a compensatory or non-compensatory rationality. The compensation occurs when an action denoted a is strictly preferred to action b and both have the same performances on all but one criterion i, in which b is significantly worse; and improving one or more performances of b in other criteria than i defines an action, c, that is indifferent to a. These improvements compensate the bad performance of b on the i-th criterion [47].

The problematics of the decision problem must also be addressed in order to define which MCDM/A may be chosen. In tendering processes, the ranking problematic is adopted because it provides the possibility of establishing a list of winners, and if the first one chooses not to sign the contract, the second candidate may be called. Therefore, for the ranking problematic and compensatory rationality, some methods remain to be analyzed.

The additive models for a unique criterion of synthesis, MAVT (multi-attribute value theory) and MAUT (multi-attribute utility theory), include the scope of compensatory rationality, and solving an MCDM/A problem in this context requires scaling constants to be obtained for each criterion, which are required to obtain the global value of the alternatives considered that are to be evaluated. The global value, here denoted v($a_i$), is considered for a consequence vector x_i = {$a_{i1},a_{i2},\dots ,a_{in}$} for an alternative i and is obtained through a weighted sum in (1):

$$v\left(a_i\right)={\sum }_{j=1}^n{k}_j{v}_j\left(a_{ij}\right),$$

(1)

where x_ij is the consequence of alternative i for criterion j, v_j(x_ij) is the value of the consequence criterion j for alternative I, and k_j is the scaling constant for criterion j, where j > 0.

Also, the scaling constants are usually normalized as follows in (2):

$${\sum }_{j=1}^n{k}_j=1,$$

(2)

The alternative with the highest global value is considered the best one for the problem. The main concern of the unique criterion of synthesis is related to the achievement of the scaling constants for the model, which represents the trade-off between the performance of an alternative in a criterion to make the compensation needed to keep the same global score as another preferred alternative.

2.8. FITradeoff Method

Incomplete or partial information can occur when a DM does not have a precisely defined preference structure or inexactly evaluates the consequences [48]. The FITradeoff method, proposed by de Almeida et al. [49], improves the application of the traditional trade-off due to the easier elicitation questions, requiring less information from the DM.

The FITradeoff method allows the elicitation of scaling constants to occur more fluidly, as it enables the DM to work with comparisons of consequences by strict preference statements, while in the traditional trade-off method, indifference relationships between consequences are required, and this is one of the advantages of the method [50]. Nonetheless, the proposed method was not able to deal with the problematic ranking, making its choice as the best alternative instead of a ranking.

Frej et al. [48] extended the concept of flexible and interactive trade-off elicitation to the ranking problematic. The ranking problematic includes allocating alternatives in ascending order of preference based on a preference model. Pairwise dominance relations were included to achieve a partial or complete order at each interaction with the DM. For each pair of alternatives, an LPP model is run in order to find dominance relations. At each step, for each pair of alternatives (A_i, A_k), the LPP runs (3)–(8):

$$\max D\left(A_i,A_k\right)=\sum _{j=1}^m{w}_j{v}_j\left(A_i\right)-\sum _{j=1}^m{w}_j{v}_j\left(A_k\right)$$

(3)

s.t.

$$w_1>w_2>\cdots >w_m|\sum _{j=1}^m{w}_j=1$$

(4)

$$w_j{v}_j\left({x\prime }_j\right)>w_{j+1} j=1 to m-1$$

(5)

$$w_j{v}_j\left({x″}_j\right)<w_{j+1} j=1 to m-1$$

(6)

$$\sum _{j=1}^m{w}_j{v}_j\left(A_i\right)>\sum _{j=1}^m{w}_j{v}_j\left(A_k\right)$$

(7)

$$w_j\ge 0,j=1\dots m$$

(8)

The method consists of two steps: building the ranking visualization diagram of alternatives and building a ranking of the alternatives based on the ranking visualization diagram of the previous step.

The FITradeoff decision support system was developed to implement the FITradeoff method. It is available online at www.fitrade-off.org (accessed on 16 June 2024) and is a useful tool to guide the DM through making his/her decision in the context of MCDM/A.

2.9. Other Potential MCDM/A Methods

The choice of the MCDM/A method relies on the problematic of the defined decision problem. In this research, the decision problem is obtaining a ranking of alternatives, represented by the private companies, and the top rank should be the company to be contracted by the public part to perform the water or sewerage service through a PPP contract. Thus, the ranking problematic is addressed.

There are several MCDM/A methods that can be used in this case, depending on the DM’s rationality, that can be compensatory or non-compensatory. Compensatory methods allow trade-offs between criteria and a bad performance in one criterion can be counterbalanced by a better score in other criteria, while non-compensatory methods do not take these trade-offs into consideration [51]. Considering a compensatory rationality and ranking problematic, to allow comparison with FITradeoff, methods such as TOPSIS (technique for order of preference by similarity to ideal solution), AHP (analytic hierarchy process), and WSM (weighted sum method) can be considered.

TOPSIS brings the definition of positive ideal solution (PIS) and negative ideal solution (NIS) and uses Euclidean distance to evaluate the alternative’s distance to the PIS [52]. The alternative closest to the PIS and farthest from the NIS represents the optimal solution. The alternatives are evaluated through indicators, and a ranking from best to worst is obtained.

AHP is a recognized and widely applied MCDM/A based on a decision-making process that sets a hierarchy of criteria and subcriteria, makes pairwise comparisons to define the weights of each criterion, and derives a composite score for each potential alternative [53]. DM’s judgments are the inputs of this method, and the outputs are each factor’s weight and a ranking with decreasing importance [54]. WSM is an aggregation technique based on summing weighted alternative’s scores in each criterion. Its advantages are that it is simple and easily applied, but the criterion’s weight definition lacks a methodology, and this approach is very sensitive to this choice.

Additive models, which consider the trade-offs to obtain the scale constants, take a lot of effort from the DM to define parameter evaluation, since they need to establish an exact level of satisfaction with a criterion that they are ready to exchange for a better level of satisfaction with another one [55]. FITradeoff elicitation is able to make this process more fluid for the DM, reducing the time spent and also cognitive effort, and the fact that it can work based only on preference relationships adds to its benefits.

3. Results and Discussion

3.1. The Problem

The decision problem related to the PPP structuring tackled in this research is the prioritization of the private partner to be contracted by the public party—the water company. Contracts signed by the public parties in Brazil have certain rules that pertain to the tendering processes. According to Federal Law 8.666 of 1993, which regulates the tendering rules, for engineering services and works above the value of BRL 1,500,000, a situation in which the PPPs are included, the modality must be competitive [56].

A competitive modality is defined by the abovementioned law as the tendering process of any interested party that in the phase of preliminary habilitation proves to have the minimal requisites of qualification requested in the public notice to execute the object defined in the tendering process.

Federal Law 13.303 of 2016 presents a different sorting phase, a so-called phase reversal, where habilitation stays in its latest position. The tendering steps are preparation, disclosure, proposal presentations, judgment, proposal effectiveness verification, negotiation, habilitation, appeal, object award, and homologation [57].

Regarding the judgment of the proposals presented, there is the decision problem of selecting the best one for the object and company. According to Brazil [56], this choice can be made by identifying the lowest price presented amongst the candidate companies, the best technique, or a combination of technique and price.

Evaluation through “best technique” and “technique and price” requires preestablished criteria to be defined in the public notice and becomes a more complex process compared to the “lowest price”, since the latter is a direct evaluation.

The first step of the framework of the PPP modeling related to the decision-making process, therefore, is to define the set of criteria that is going to be used to evaluate the different proposals. This step is performed with the group responsible for structuring the PPP.

3.2. DMs and Other Actors

The DMs of the prioritization of the private partner for a PPP project form a committee, usually from among the company’s employees that are linked to the object of the process.

For sanitation decision problems, this committee may rely on professionals of different specialties in engineering, since the object includes water or sewerage infrastructures and their operation.

For the application proposed in this research, there will be one DM, who is a professional with 20 years of experience in the company, a civil engineer who has worked in different areas such as engineering projects as operation manager and has developed the business plan and financial and economic studies of the company. They have implemented another PPP that already is contracted by the company, and nowadays they act as a specialist for the company because of their wide knowledge of the different processes and existing and planned infrastructure.

3.3. Objectives and Criterion Definition

Defining the criteria is one of the most important phases of this research, since in the literature, there is a lack of studies that apply the defined criteria in the ranking problem of prioritization of a private partner of PPPs. Some studies present only the criteria, but not how they can be measured, which brings a gap when they are applied.

In this phase of the research, a literature review was performed in order to obtain the most relevant criteria to be adopted to evaluate a private partner for a PPP project, and some criteria were also collected from papers about constructors’ selection problems. Some of the criteria obtained were identified as not relevant or redundant and were not considered. Then, for the remaining criteria, some were categorized as habilitation criteria, which include criteria that are prerequisites for the alternative. In this case, this will the company or consortium to be evaluated during the qualification step.

The qualification step includes the stage in which the alternative is evaluated through the technical and financial aspects. Thus, it is the phase where the FITradeoff DSS is applied.

Table 3. Criteria for private partner prioritization of PPPs.

Criteria	Description	Measurement
Human resources (HR) [12]	The talent reserve of the service provider determines the innovation ability of service providers.	Experience of the technical team
Water environment treatment project process design ability (OA) [10]	Investigates the service provider’s water environment treatment process and level, process design means, personnel, and other aspects of the service provider’s ability.	Quantity of work performed in the area under study/quantity of units in operation by the company in the area under study/quality of operation (evolution in meeting index targets)
Water environment treatment project engineering design ability (PA) [10]	According to the requirements of water environment control project construction, comprehensive analysis, and demonstration, the ability to prepare construction engineering design documents.	Quantity of projects developed in the area under study (proven through certificates)
Development and use of new technologies for water environment treatment (TE) [10]	Ability to apply scientific research techniques to projects to produce benefits.	Existence of an innovation sector in the company/investment in innovation
Quality management capability (QC) [20]	The service provider is willing to strictly abide by the construction specifications for the quality control of the building during the construction process.	Certifications in quality standards such as ISO or other reference standards in the area of civil construction
Credit rating (CR) [12]	Credit rating is an important indicator reflecting the credit information of the service providers.	Credit rating (rated by financial institutions)
Social activities (SP) [12]	An important indicator that reflects the social responsibility, corporate culture, and humanistic care of the service provider	Number of local development programs
Social reputation (SR) [12]	Whether the service provider has reputational problems, such as default.	Customer complaint rates
Historical litigation situation (LS) [12]	Reflects the credibility level of the service provider and their ability to resolve disputes.	Number of open court cases/number of finalized cases

presents the criteria that were identified and analyzed to define a description and how to quantify them in order to input the MCDM/A method chosen—in this case, FITradeoff. Some criteria identified by Li et al. can be evaluated by analyzing the business plan and EVTEA proposed by the winner of the process, acceptance of which is related to the EVTEA developed by the public sector by comparison and evaluation [19].

Also, some of the technical, financial, and economic aspects are pre-defined in the public notice and represents the habilitation criterion. Those are defined as follows.

Technical qualifications:

• Registration with the engineering and agronomy regional council.
• Proof of technical–operational capacity: by holding certificates or attestations, proving technical experience with similar characteristics to the object of the contract, including installation, operation and maintenance, and contract management of PPPs.

Financial and economical qualifications:

• Negative certificate of bankruptcy, judicial or extrajudicial recovery.
• Financial statements for the last fiscal year.
• General liquidity, current liquidity, and general solvency ratio greater than or equal to 1.
• Proof of a minimum net worth of 10% of the value of the price proposal, corresponding to 12 months of the monthly government payment.

Due to the previous evaluation of the companies’ experience in the habilitation phase, the criteria OA, PA, and CR are not considered in the MCDM/A problem. TE, QC and SR, the remaining criteria to be considered in the evaluation by the DM, were not considered relevant either. Through these considerations, the analyst and the DM noticed the absence of the companies’ experience in managing PPPs measured by the number of contracts of PPPs and concessions.

Therefore, the criteria considered in the MCDM/A problem and its classification related to the types of criteria and objective—minimizing or maximizing—are presented in

Table 4. Criteria adopted in the research.

Criterion	Measure	Type	Objective
Human resources (HR)	Experience of the technical team	Natural	Max
Social reputation (SR)	Percentage obtained through the number of complaints responded to and the number of total complaints	Natural	Max
Historical litigation situation (LS)	Number of judicial processes	Natural	Min
Operating PPPs or concessions (PC)	Number of PPPs or concessions in the project’s area of interest	Natural	Max
Price (GP)	Proposal price provided by each participant regarding the government pays (in BRL millions)	Natural	Min

.

3.4. Alternatives and Problematics

The alternatives to the private partner prioritization of a PPP bidding process are the companies interested in the proposed project. They are invited to participate via the publication of the official notice and are aware of the conditions of the prioritization, such as the criteria judgment, the qualification requests, the financial and economic viability, the scope of the project, and the risk matrix. The proposed problem involves alternatives that can be companies or a consortium of companies that decide to work together to attend to the criteria defined in the public notice.

For infrastructure projects, the feasibility of the project was sounded out in the market considering the potential participants before the tendering process started in order to prepare for meetings to present the project and evaluate the attractiveness of the project.

In recent years, the Brazilian Federal Government has set about standardizing indexes of the availability of water until 2033. Therefore, other PPPs have been entered into to do this, and consequently some companies of interest to this project can be identified.

In this phase, a survey is conducted to obtain the potential alternatives to be considered in the study, referring to companies that have participated in tendering processes in the area of sanitation. Considering the winners of the tenders held from 2020 to 2021 in the water and sewerage sectors, and considering several modalities of tendering and the value of services for areas with high populations—ranging from BRL 1.4 million to BRL 7 million—the set of alternatives could be formed by companies from the Brazilian northeast.

Therefore, the set of alternatives A = {A1, A2, A3} is established, which will be evaluated according to the j criteria obtained in Table 4.

The private partner prioritization of a PPP process is a ranking problem, since all the candidates that submit tenders should be ranked using a global value associated with the judgment criteria adopted. These results are published in reporting mechanisms such as journals and official diaries to meet the principles of transparency and publicizing governmental processes.

Ranking is important due to the possibility of the first candidate not wishing to sign the contract during the tendering process, which usually lasts for about six months. Then, the second candidate is invited to sign the contract, and if it does not wish to, this process continues until a company signs the contract.

In addition, from the published ranking, the competitors are able to access its evaluations and file appeals in case they think that some mistake may have been made.

In order to make the methodology clearer, Figure 1 presents the theoretical framework for the project, from understanding the research gap to the answers to the research questions.

3.5. MCDM/A Application

The number of operating PPPs and concessions was obtained by consulting information available on the companies’ websites. Information on the experience of the technical team could not be found. Thus, this will not be considered in this application.

The situation of historical litigation was measured by examining consumers’ complaints registered on the internet and was gathered by accessing the website https://www.jusbrasil.com.br/, accessed on 15 February 2023. The social reputation was obtained via a Brazilian platform located on the website https://www.reclameaqui.com.br/, accessed on 15 February 2023, since some companies were not registered in https://consumidor.gov.br/, accessed on 15 February 2023.

The experience of human resources could not be obtained in the case of this application due to its specificity, but in a real case, the companies are required to present those documents in order to participate in the prioritization process.

The government pays, related to the price criteria, since there is just an illustrative example, was established randomly in order to include this criterion in the simulation.

By gathering information about the alternatives, the matrix of consequences can be compiled, and it is presented in

Table 5. Matrix of consequences.

	Max	Min	Max	Min
Criteria/ Alternatives	Social Reputation (SR) (%)	Historical Litigation Situation (LS)	Operating PPPs or Concessions (PC)	Price (GP) (Millions of R$)
A1	80.0	295	49	2.5
A2	26.9	101	14	2.0
A3	99.2	241	18	4.0

. This information was presented to the DM and inserted into the FITradeoff DSS.

The first step of the process is ordering the ranking of the scaling constants of the criteria, which can occur by pairwise comparisons, as presented in Figure 2, or by overall evaluation. The DM chose to start with the pairwise comparison, and the final order found is presented in (9).

$$k_{GP}>k_{PC}>k_{LS}>k_{SR}$$

(9)

After this step, the DSS reported that there were two rankings, and the DM was asked to continue the process by eliciting by composition or switching to a holistic evaluation. The DM opted for elicitation by composition to continue (Figure 3). Elicitation by composition compares two alternatives: the first comparison is one alternative with an intermediate consequence of criterion GP, and the other with the best consequence of criterion SR, which are the first and the latest in the ranking obtained of the scaling constants. The DM chose the first consequence, and thus accepted the intermediate consequence of criterion GP, and therefore the equation presented in (10) was inserted in the model.

$$k_{GP}\times 0.5>k_{SR}$$

(10)

The DSS continued asking questions of the DM, comparing the alternatives with intermediate results in order to insert more constraints into the model, and after five questions were answered, a ranking consisting of the three alternatives was obtained. This step is presented in

Table 6. Application report for comparison between Consequences A and B, whereas Consequence A is better than Consequence B in all cycles.

Cycle	Consequence A	Consequence B	Answer	Number of Levels
0			Ordering…	2
1	3000 of price (GP)	99.2 of social reputation (SR)	Consequence A	2
2	3000 of price (GP)	49 of operating PPPs or concessions (PC)	Consequence A	2
3	31,500 of operating PPPs or concessions (PC)	101 of historical litigation situation (LS)	Consequence A	2
4	198,000 of historical litigation situation (LS)	99.2 of social reputation (SR)	Consequence A	2
5	3500 of price (GP)	49 of operating PPPs or concessions (PC)	Consequence A	3

. Thus, the winner of the process would be Alternative 2.

The aim of the research is to provide a novel manner to support DMs in order to select the private partner of a PPP project. The winner alternative, A2 (Figure 4), is also the one with the lowest price (government pays). In a prioritization based only on this criterion, coincidentally, the choice would be the same, but as can be seen in the matrix of consequences of the problem, there are a wider number of aspects of interest to be considered in choosing a private partner of a PPP.

Also, the boundaries of the scaling constants—shown in Figure 5—corroborate the idea of the price being the most relevant aspect considered in trade-offs amongst other criteria related to the technical aspects. Thus, there is a concordance of the current price and technical evaluation already adopted and the proposed model of this research.

In the simulation case, the DM agreed who had won the process, since the lowest price was chosen, which would bring more security to the government party and the committee. It would also be comfortable to defend an alternative with a higher price but better technical evaluation, considering that the decision was reached by a methodology based on MCDM.

However, the range of scaling constants can be the subject of inquiries from the other participants in the process, which can be considered a limitation of this research, and this is something to be evaluated in further research. In addition, the application considered only one DM in a context in which usually at least three professionals are involved.

Ulutas et al. [58] utilized the MCDM to select the ideal supplier, avoiding supply chain disruptions. In their study, resilience criteria (RESC) were selected as the main criteria that affected the supplier selection. The subcriteria of RESC were risk awareness, restorative capacity, strategic stock, capacity to invest in bumpers, and flexibility.

Shen [59] combined a centralized and a decentralized decision models with game theory to analyze a supply chain network with regard to impacts of the COVID-19 pandemic in economic recovery. This combination of methods pointed to stimulation of manufacturer quality production and to reduction in retailer promotional costs.

Stević et al. [60] proposed a novel MCDM to prioritize a sustainable supplier for health industries through an alternative ranking. Despite the fact that W&S PPPs represent a different decision problem, amongst the criteria considered, price, human resources and social reputation are present in both studies. To evaluate health industry suppliers, social reputation was the criterion that had the most influence, while in this research, it was the criterion that was last in the order provided by the DM. Nevertheless, the price criterion for both cases had major influence.

Chai et al. [61] used a fuzzy MCDM to recommend a sustainable supplier with a ranking problematic. Price and social reputation were also considered criteria, similar to the proposed application of this research. Price remained being considered the criterion of most influence on the DM’s structure choice.

Behera and Beura [62] applied a combination of MCDMs (analytic hierarchy process (AHP) and method based on removal) to select a coal supplier for a power plant. Again, price and social reputation were the criteria used to evaluate the alternatives for both projects (power plant and the abovementioned W&S). For this selection decision problem, price was considered to be in third place, while social reputation was the criterion of most influence on the process, indicating that price is not always the most important criterion to be taken in consideration for supplier selection.

Fossile et al. [63] applied FITradeoff to select renewable energy sources for Brazilian ports, considering as alternatives wind, photovoltaic, and wave energies. From the selected criteria and the linear programming model run, photovoltaic and wave energy were identified as potentially optimal. When the DM answered the elicitation question, wave energy was then excluded from the set of alternatives and photovoltaic energy was defined as the best alternative. This application represented a selection problematic, while the FITradeoff application for prioritizing private partners for PPPs of W&S should be considered a ranking problematic, since the results must be a ranking of alternatives, due to the possibility of the first alternative withdrawing the contract. Then, the second alternative can be called and so on.

Ferreira et al. [64] also applied FITradeoff to evaluate companies in terms of technological maturity for Industry 4.0, adopting strategy and innovation, technology and processes, sustainability, and people and leadership as criteria. From the obtained results, the companies were able to be sorted with different levels of maturity accordingly to their ability to the achievement of Industry 4.0-level of strategic management.

de Oliveira et al. [65] proposed a multidimensional framework to sort Brazilian cities regarding the concept of sustainable and smart cities through a combination of European Telecommunications Standards Institute (ETSI) and FITradeoff using availability, reputation, and currency dimensions. Among the conclusions, the authors identified that the northeast capitals of Brazil obtained critical values of technology access and economy issues, justifying that in a developing country, regions with lower performance in economic and technological development exist. The technological aspect represents an important issue of PPPs, since private partners can bring great contributions to government projects and should be considered in companies’ evaluations besides price.

Kara et al. [66] proposed a green-based supplier selection, combining multiple regression analysis and fuzzy multi-criteria decision-making (F-MCDM). The authors identified that just five criteria were necessary to define: green dynamic capacity, green purchasing, eco-design, investment recovery, and green product innovation. This research also foresaw alignments with current law. This represents that the Brazilian legislation for PPP contracts must be considered to substantiate the model to prioritize PPP private partners of W&S services.

3.6. Limitation of the Study

The proposed research aims to support decisions about ranking private partners that participate in tendering processes for PPPs for water- and sewerage-related services, and it was designed and applied for just one DM. Technique and price evaluation brings complexity to the analysis, which was addressed partly in this study through the criteria definition and through application of FITradeoff, but this kind of decision can involve a group of DMs, mostly to bring more security and transparency to the results obtained.

This represents a limitation of the research, which can be extended to a group decision-making (GDM) problem. Multi-criteria group decision-making (MCDMG) can be described as a decision approach that can gather professionals of different fields, thus approaching problems from different perspectives, improving the rationality and accuracy of the final decision result [67].

For future research, there are several applications of MCDM combined with machine learning techniques to solve MCDM problems in the era of big data, such as those presented by Ma and Li [68] and Bhol et al. [69], to create powerful decision-making solutions. Machine learning technologies can also be applied to determine parameters, integrate solutions in MCDM, and construct a knowledge base [70].

4. Conclusions

The process of selecting the private partner in a PPP contract is somewhat complex, especially in view of the fact that it is a long-term contract—between 20 and 30 years. Factors other than price—government pays—must be taken into consideration, which is often not the case in Brazil, as evidenced in this research. The second point would be how to aggregate the scores for the price analysis with the technical analysis, where there is no standard either, since the public entity is responsible for defining these “weights” and the aggregation is performed using methods such as weighted sum.

From the research gap, result-oriented points were identified, as follows.

• Among the multi-criteria decision aid methods presented in the literature, FITradeoff was chosen because it presents the advantages of making the elicitation process easier for the DM, since it reduces cognitive effort and reduces the time spent on decision-making processes.
• Despite its advantages, the method is more suitable for one DM, and a group-decision method should be applied to extend the proposed model for cases in which more than one DM participates.
• The criteria investigated are related to financial, technical, credit reputation, managerial, health, safety, and environmental aspects. Besides that, legislation and government prospects are limiting factors.
• The chosen criteria were: human resources, social reputation, historical litigation situation, operating PPPs or concessions, and price.
• The tools provided from the FITradeoff application to evaluate the potential private partners, defined as alternatives, were: the application report to compare the criteria; Hasse diagram to define the ranking of alternatives and the recommended choice, and the graph of boundaries to clarify the boundaries of each criterion.
• Thus, the answers to research questions (ARQs) were obtained:

  o

  ARQ1—the procurement processes of W&S PPPs occur mostly by adopting the judgment criterion of price, but this does not take into consideration the complexity of the decision in context, most importantly in a developing country.

  o

  ARQ2—the aspects that should be considered are: financial, technical, credit reputation, managerial, health, safety, and environmental.

  o

  ARQ3—the chosen criteria for the application were: human resources, social reputation, historical litigation situation, operating PPPs or concessions, and price.

  o

  ARQ4—the alternatives were evaluated from the comprehensive perspective of MCDM, and FITradeoff application provided the ranking of private partners, which led to the procurement winner, considering the set of criteria proposed in this research.

The criteria suggested in this research may serve as a basis for procurement processes in defining the criteria to be adopted in both the qualification and habilitation phases in different PPP sectors. As suggestions for future work, several PPP contracts based on the criteria defined by this article should be investigated, pointing out factors such as execution time, amount invested, and percentage of execution in comparison to old PPPs. In addition to MCDM, the use of machine learning can facilitate this data combination. These comparisons take some time, due to the temporal definition of PPPs and the termination of contracts.

Furthermore, the FITradeoff model may serve as a basis for decision-making for those in charge in the public sector for selecting the private partner of PPP projects considering a diverse set of criteria.