DECOMMISSIONING OFFSHORE OIL AND GAS PRODUCTION SYSTEMS WITH SMAA-ExpTODIM

ABSTRACT This study addresses the application of the Stochastic Multicriteria Acceptability Analysis (SMAA) technique, in combination with the Exponential TODIM method (ExpTODIM), by taking into consideration proposition made by Petrobras to the Brazilian National Agency for Petroleum, regarding the decommissioning of both Marlim and Voador production fields. The new approach called SMAA-ExpTODIM takes into consideration different perspectives of participants involved in decision making regarding decommissioning projects and incorporates them to its results. Besides incorporating decision makers’ uncertainties and ignorance zones, this new approach explicitly considers the decision making based on the different perspectives of the Proponent and of the Regulator. The application of the SMAA-ExpTODIM approach increased robustness by adopting different probability functions for stochastic variables, for the process of formulating and modeling the decommissioning issue. This was undertaken to represent profiles associated with aversion or propensity to risks faced by institutional decision makers. For each decision maker profile, different preference structures or comfort levels are created with a choice between decision alternatives.


INTRODUCTION
Decommissioning is understood as the set of activities associated with the definitive interruption of the operation of offshore oil and gas (O&G) production facilities, including the permanent abandonment and razing of wells, the removal of facilities, the proper disposal of materials, waste and tailings, and the environmental recovery of the affected region.The demand for decommissioning services is booming around the world.In the Brazilian market, the National Agency The general objective of this work is to establish an approach capable of incorporating the uncertainties of the DM zones of ignorance and the approximations of the alternatives evaluations of a complex decommissioning problem, which involves institutional DM with different incentive instruments.In other words, it seeks to establish what Aissi and Roy (2010) call "a priori robustness": an MCDA (Multiple Criteria Decision Analysis) capable of resisting criteria assessments through vague approximations and/or zones of ignorance.To this end, the combined use of the stochastic multicriteria acceptance analysis (SMAA) technique with the ExpTODIM method (Multi-criteria Interactive Decision Making in its exponential formulation) is adopted, giving rise to the SMAA-ExpTODIM approach.The new approach is then applied in the alternatives selection for the decommissioning of subsea systems from Marlim and Voador production fields.
The decision problem is evaluated from different perspectives of the main institutional DM in order to interpret zones of ignorance and profiles of risk aversion or appetite.The stochastic representation is revealed in factors internal to the MCDA proposed in the evaluation and im-portance of criteria weight, amplification factors, and significance of the decision problem.Extra simulations are generated by creating external factors representing points of view of conservative, neutral, and bold magnitudes of propensity, and aversion to risks representing the different perspectives of evaluation of alternatives between the Proponent (Petrobras) and Regulator (ANP, IBAMA, and the Brazilian Navy).

Offshore decommissioning
The decommissioning of offshore production systems is the study subject of several authors.Ekins, Vanner and Firebrace (2006) perform comparative assessments in decommissioning scenarios of offshore exploration and production structures, exploring non-financial risks versus returns.Bull and Love (2019) carry out a historical survey of alternatives and decommissioning strategies practiced in the Gulf of Mexico involving abandoning structures for coral formation.The development and study of the decommissioning of offshore systems is also a topic that has been gaining relevance among companies in the O&G sector (Petrobras, 2021;Repsol, 2017;Shell, 2017Shell, , 2020)).
Being the last stage in the life cycle of an O&G exploration and production project, decommissioning must be initiated when the economic efficiency of the reservoir is lost.Kaiser (2019) states that there are two ways to extend the economic life of an asset -reduce operating costs and/or increase revenue.Whether due to external factors, such as supply, demand, price, or internal factors, as obsolescence or wear of equipment, technology, or decline in the reservoir's production factor, all can interfere with the anticipation or amendment of the economic limit of an offshore production asset.
For OGUK (2020), the full impact of the COVID-19 pandemic on commodity price volatility and demand is yet to be seen.In Brazil, throughout 2020 more than 60 O&G production platforms had their activities interrupted.In contrast, the high volatility in oil prices is due to both the resumption of world economic activity and the strong environmental pressure to reduce greenhouse gas emissions.
Different decommissioning options can be applied to the different components of an offshore production asset.The main components considered during the decommissioning process include production wells, surface facilities, and subsea facilities (Eke et al., 2020).
In the field of developing alternatives to decommissioning, Fowler et al. (2014) summarizes the options in a decision tree of total removal, partial removal, and abandonment.The decommissioning options list can be modified to suit the specific scenario, without affecting subsequent steps in the decision process (Fowler et al., 2014).Martins et al. (2020b) present a more detailed survey of alternatives, segregating the options between surface structure and subsea structure, ranging from the creation of wind generation units or oceanographic study stations to flexible and rigid subsea pipeline removal options.
The alternatives for decommissioning are wide, and new solutions or reuse technologies may emerge over time.Each alternative can be characterized by its own impact on the environment, costs, socioeconomic, and safety aspects, in view of the growing importance of aspects such as sustainability and environmental protection (Martins, Moraes, et al., 2020).

MCDA in offshore decommissioning
The main purpose of using MCDA methods is to provide elements to answer questions raised by a stakeholder in a decision process (Roy, 2016).DM seek help from an MCDA precisely because they have difficulty understanding which options will best meet their long-term aspirations (Belton & Stewart, 2002).
The decommissioning process is controversial, as each alternative involves different levels of costs, benefits, and risks for different groups of stakeholders and for the environment (Schroeder & Love, 2004).ANP resolution No. 817 mentions five aspects that must be considered in the preparation of the Installations Decommissioning Program, they are: Technical, Environmental, Social, Economic, and Safety.None of the criteria in isolation should be considered decisive for the definition of the alternative (ANP, 2020).These same aspects have already been considered in other evaluations and choices of alternatives to the decommissioning of an O&G production unit, both in technical reports (Repsol, 2017;Shell, 2017) and in scientific studies (Eke et al., 2020;Ekins et al., 2006;Fowler et al., 2014;Henrion et al., 2015;Martins, Bahiense et al., 2020).

Multicriteria interactive decision making with the exponential value function: the ExpTODIM method
The authors of the TODIM method (Gomes & Lima, 1991, 1992) propose the conception of Prospect Theory (Kahneman & Tversky, 1979), using a conditional function for the process of comparison by pairs of alternatives, in each evaluated criterion (Leoneti & Gomes, 2021a).Let (A 1 , A 2 , ..., A m ) be the set of m alternative solutions to the decision problem at hand and (c 1 , c 2 , ..., c n ) the set of n criteria; Gomes and Rangel (2009) highlight that experts should be asked to estimate, for each of the criteria, the contribution of each alternative to the objective associated with the criterion.Thus, an evaluation matrix (m x n) is composed, which still needs to be normalized.Leoneti and Gomes (2021a) evaluated several normalization techniques, having obtained the best results through linear maximization.Equation ( 1) is adopted when the evaluation criterion of the alternative is of the Benefit type, that is, the higher the value, the better for the decision objective.
Conversely, the evaluations must be normalized through equation ( 2) if the criterion is of the Cost type, thus obtaining the normalized matrix of alternative versus criteria.
Pesquisa Operacional, Vol.43, 2023: e267436 The conditional function (ϕ c ), equation (4), uses an additive multi-attribute utility function to determine the dominance between the alternatives.Thus, let δ (A i , A j ), equation (3), be the measure of dominance of alternative A i over alternative A j : Where the exponential formulation of the TODIM method (ExpTODIM) is the one that best demonstrated adherence to the rational choice theory presented by Prospect Theory (Leoneti & Gomes, 2021a).In ExpTODIM, the additive multi-attribute conditional function (ϕ c ) is represented by equation ( 4): In (4) λ represents the amplitude parameter that adjusts to the different behavioral profiles of the DM in levels of loss aversion.λ is normally between 1.5 and 2.5 (Novemsky & Kahneman, 2005).ρ ∈ N* and indicates how significant the result of the decision is for the DM (Leoneti & Gomes, 2021a).The authors suggest the adoption of a scale of favorability (Likert scale), with ρ assuming values between 1 and 5.The values assumed by ρ represent how sensitive the DM is to the decision problem.Values close to 1 reveal a bold DM with less sensitivity to losses, while values close to 5 should reflect a more conservative and risk-averse stance.Fig. 1 shows the curves for the values assumed by ρ in ExpTodim with λ = 2.25.
Once the partial dominance matrices of each criterion are obtained, it is possible through the sum of the elements of the different matrices to arrive at the final dominance matrix.This final matrix, obtained through equation ( 5), is the normalized measure of the global utility of each alternative.
The global measures obtained through (5) allow the complete ordering of all alternatives.Sensitivity analyzes must be performed on λ , as well as on the weights of the criteria, on the choice of reference criterion, and on the performance evaluations of each alternative (Gomes & Rangel, 2009).

2.4
The stochastic analysis of multicriteria acceptance: the SMAA technique SMAA is a multicriteria decision support technique for multiple DM in discrete problems.In it, DM do not need to express preferences explicitly or implicitly.SMAA has been developed in MCDA problems where criteria assessment measures are uncertain or imprecise and, for some reason, the DM preferences are unknown (Tervonen & Lahdelma, 2007).
In SMAA, the values of imprecise or uncertain criteria are represented by probability distribution functions from which the method calculates the confidence factors that describe the reliability and robustness of the analysis (Lahdelma & Salminen, 2001).Decision making is performed in a real-life context that may not exactly match the model on which the MCDA is based.It is still judged in terms of a value system that will seem relevant (and not necessarily stable) to a future that may not be well defined; as a result, this value system may not exactly match the one used to create and explore the model (Aissi & Roy, 2010).
Uncertainty means that in a given situation the DM does not have quantitative and qualitatively adequate information to describe, prescribe, or predict deterministically and numerically a system, its behavior, or other characteristics.Durbach and Stewart (2012) use the term uncertainty mainly for that arising from an unknown action, which depends on future events.This is sometimes called external uncertainty because it refers to uncertainty about environmental conditions that are beyond the DM control.Internal uncertainty is related to the process of structuring and analyzing the problem.Inaccuracies in human judgments, whether of preference or weight of importance between criteria, should ideally be resolved as much as possible by better structuring the decision problem (Stewart & Durbach, 2016).
SMAA is particularly applicable in decision problems with imprecise, uncertain, or incomplete information (Tervonen & Lahdelma, 2007).The choice of the SMAA technique is due, as high-lighted by Lahdelma, Hokkanen and Salminen (1998), to support multi-objective decision making for several DM.When considering the points of view of decision-makers, both Proponents and Regulators, the SMAA proves to be particularly appropriate.Ultimately, the method also allows the analysis of n-dimensional multi-objective problems with stochastic criterion values (Lahdelma et al., 1998).

THE SMAA-EXPTODIM APPROACH
In this article, the SMAA technique is incorporated into the ExpTODIM method, obtaining what Aissi and Roy (2010) call "a priori robustness".For Aissi and Roy ( 2010) robustness most often involves a concern that must be considered before formulating the problem.In ExpTODIM there are four input parameters that can be simulated in the robustness evaluation, the alternative evaluation input data (c i ), the importance weights of each criterion (w c ), the amplitude parameter (λ ), and the factor of significance (ρ).
The choice of the exponential formulation of the TODIM method, the ExpTODIM (Leoneti & Gomes, 2021a), is supported by incorporating the parameters of loss aversion amplitude, λ , and the significance of decision making, ρ.These parameters reinforce the possibility of adapting the MCDA to both a risk aversion or propensity profile of the decision-maker, regarding the confrontation of losses or gains, as well as the sensitivity of the DM in relation to the decision problem.These characteristics are fundamental in the representation of the different decision-makers, Proponent and Regulator, with bold, neutral, and conservative profiles, enabling the building of strategies to approach and solve the problem in an a priori robust way.
To combine the SMAA technique with the ExpTODIM method, one must simplify the Exp-TODIM method to a value function where u(i,x,q) = ExpTODIM (i,x,w,λ ,ρ), q = [w, λ , ρ], where i ∈ M, M ={1,2,...,m}, x is the deterministic matrix [m x n] alternative x criteria, w is the deterministic weight corresponding to the criterion, λ is the parameter of amplitude that fits the behavioral levels of the DM in loss aversion, and ρ ∈ N* indicates how significant the decision problem is for the DM.When considering the ExpTODIM parameters λ and ρ, the following indicators are incorporated: CAF (Central Amplification Factor) and CSF (Central Signification Factor).
Let f (x) (x ij ) be the PDF (probability density function) of the uncertain or imprecise evaluation of the stochastic variable x ij (∀ i ∈ M e j ∈ N).From the lack of knowledge, total or partial, of the preferences and attitudes of the DM to the joint probability f (Q) (q), the sample space Q is represented through equation ( 6).
Where W ∈ R+ represents the sample space of the importance of weights, Λ ∈ R | 1.5 ≤ λ ≥ 2.5 represents the sample space of the amplitude parameter, and P ∈ N* | ρ ≤ 5 the sample space of the DM sensitivity in relation to the decision problem.
The probability density function f (Q) (q) is given by equation ( 7).
The absence of knowledge of the DM preference in the definition of importance weights between criteria allows us to consider that w assumes a uniform distribution in the W space, equation ( 8).
Similarly, in a total or partial absence of knowledge of the loss aversion or propensity profile, as well as the importance that the decision problem has for the DM, uniform distributions are assumed for λ , equation ( 9), and ρ, equation ( 10), in their respective sample spaces: After obtaining adequate distributions for criteria measures and preference parameters, it is necessary to derive the general utility of each alternative through stochastic simulation by simultaneous sampling of criteria measures, the criteria evaluation weights, the amplitude factor λ , and the significance factor ρ.
Tervonen and Lahdelma ( 2007) present the ranking of alternatives as an integer from the best classification (= 1) to the worst classification (= m) through equation ( 11).
Where γ (true) = 1, γ (false) = 0, and u(i,x,q) is the utility value function ξ i of alternative i, equation ( 9), obtained from the evaluation of each alternative through stochastic simulation by simultaneous sampling of criteria measures (f x (x)), criteria weights (w), amplitude factor (λ ), and significance (ρ) of the decision problem for the DM ρ.
Lahdelma, Hokkanen and Salminen (1998) point out that, in group decision making, DMs often have different opinions about which weights should be used for each criterion.Even a single DM may be unable or unwilling to specify weights.Thus, in SMAA-ExpTODIM, for each alternative i, the favorable preference order Q i r (x) is determined.That is, the set of weight vectors, equation ( 12), makes the general utility of alternative i greater than or equal to the utility of any other.
From this point, the SMAA-ExpTODIM performance indexes can be defined.RAI is obtained by equation ( 13), a ratio between the expected volume of Q i r (x) and the volume of the feasible Pesquisa Operacional, Vol.43, 2023: e267436 RAI i r (x) measures the variety of different preference parameters that give A i the ranking r.RAI assumes values between 0 and 1, with 0 being the index value of the alternative that never obtains maximum ranking for r = 1.At the other extreme, the value 1 indicates that the alternative leads the ranking for any preference parameter (Tervonen & Lahdelma, 2007;Zhang et al., 2017).
Based on the RAI obtained, one can analyze the robustness of each alternative for a given post.
Robust alternatives are those with a high acceptance rate for the best ratings (Zhang et al., 2017).
The next indicator, CWV, is the center of gravity of the weight vector that favors the first order of alternative A i .In SMAA-ExpTODIM it is defined by equation ( 14).
By definition, CWV will only exist for alternatives that have an acceptability index RAI i 1 greater than 0. Analogously, the indicators CAF and CSF can be represented through equations ( 15) and ( 16).
Analogously, the indicators CAF i c and CSF i c will only exist for alternatives that have an acceptability index RAI i 1 > 0. The fifth indicator CF, equation ( 17), describes the probability of alternative A i obtaining the first ranking in the ranking for a given vector of criteria weights (w), amplitude factor (λ ), and significance of the decision problem for the DM (ρ).
As it originates on bases derived from CWV, CAF and CSF, CF i c is only calculated for alternatives that have an acceptability index RAI i 1 ̸ = 0. Confidence factors assess the measurement accuracy of criteria to robustly distinguish alternatives.
The last indicator of the SMAA-ExpTODIM is PWI, whose definition refers to the probability that the alternative A i is preferred over A j .The indicator can be represented in equation ( 18).
It is important to note that approximations due to simplifications, imperfect determinations, or arbitrary choices are not uncertain, nor are they zones of ignorance, but rather mean imperfect knowledge about the complexity of phenomena or value systems concerning the decision problem (Aissi & Roy, 2010).
Figure 2 presents the reference framework for the application of the SMAA-ExpTODIM.
The application of SMAA-ExpTODIM takes place through The Decision Tools Suite® software, a Microsoft Excel® supplement that performs Monte Carlo simulations.Practical applications of SMAA methods use a number of iterations, normally between 10 4 and 10 6 (Tervonen & Lahdelma, 2007).In the present study, we chose to perform simulations with 10 4 iterations.Technical meetings are held with senior engineers and consultants working in the area of offshore decommissioning of O&G systems in order to identify uncertainties, their maximum and minimum limits, zones of ignorance, complexity of the decision problem, and define and typify the evaluation criteria alternatives for the decommissioning of the subsea systems of the Marlim and Voador fields.The technical meetings have pre-established agendas and seek consensus in the definition of stochastic parameters and types of criteria for the decision problem, both from the perspective of the Proponent and the Regulator.
The objective is to evaluate the real problem of selecting one of the five alternatives for the decommissioning of subsea systems (flexible lines, rigid pipelines, and equipment) of the platforms that will be decommissioned in the Marlim and Voador fields.

The Marlim and Voador fields
The PDI (Petrobras, 2021) proposes to the regulatory institutions ANP, IBAMA, and the Brazilian Navy the decommissioning of ten production platforms, including the subsea wells and asso-Pesquisa Operacional, Vol.43, 2023: e267436 ciated systems.Located approximately 111 kilometers off the coast of the state of Rio de Janeiro, the decommissioning of the facilities in the Marlim and Voador fields will allow the revitalization of the fields through the subsequent installation of two FPSO type units to replace the platforms and their production systems (subsea wells and lines/equipment) that are being decommissioned.
In this study, we chose to use the evaluation data of five alternatives for decommissioning flowlines.The choice is due to the greater complexity of the subject, mainly due to the large number and variety of flexible lines installed, as well as the extension of the Marlim and Voador fields, and the diversity of existing environmental scenarios, with the recurrent presence of sensitive environments (Petrobras, 2021).In summary, the PDI presents the following alternatives: • A 1 : Full removal of flowlines after temporary deposition of risers on the seabed.
• A 2 : Removal of all risers at the time of pull out and later, full removal of flowline sections.
• A 3 : Platforms in "more environmentally sensitive areas": removal of risers at the time of pull out and permanent in situ flowlines.For platforms in "less environmentally sensitive areas": full removal of flexible lines after temporary deposition of risers on the seabed.
• A 4 : Removal of all risers at the time of pull out and definitive in situ permanence of all flowlines, regardless of region.
• A 5 : Deposition of risers on the seabed and definitive in situ permanence of all flowlines.

Application of SMAA-ExpTODIM in decision modeling
In the present study, the application of the SMAA-ExpTODIM is conducted during the selection of alternatives, the conceptual phase of a project.Therefore, records of the evaluations, criteria, and alternatives analyzed must be available to the DM, Proponent and Regulator, until the decision is taken.Keeney and Raiffa (1993) state that in an objective there are three characteristics: a decision context, an object, and a preference direction.The context and object of decision are described in the PDI (Petrobras, 2021).Steps 1 and 2 of the SMAA-ExpTODIM implementation reference framework, Fig. 2, are already covered in the Conceptual PDI of Marlim and Voador, as well as the identification of alternatives, step 3. To identify the evaluation criteria of the alternatives, the table of quantities of operations and materials that will be applied in the decommissioning of flexible lines is selected (Petrobras, 2021).The table of quantities of operations and materials is related to the aspects presented in section 2.2.The environmental aspect is included in criteria 1, 2, 9 and 10.Safety is included in criteria 3, 4, 5, 11 and 12.The Technical, Cost and Social aspects are included, respectively, in criteria 7, 8 and 13, see Table 1.
For Figueira et al. (2009) a family of coherent criteria should be defined in order to reduce dependencies between criteria as much as possible.Thus, meetings were held with specialists in offshore decommissioning operations aiming to verify correlation and interdependence between criteria.It was identified that the items "quantities of risers and flowlines collected" and "quantities of risers and flowlines that will remain in situ" evaluate alternatives to decommissioning in an inverse, but redundant way in the same parameter, one being a Benefit type formulation and the other a Cost-type formulation.Similar characteristics are observed in the amounts of metallic materials and polymers.Another eliminated redundancy was the total operating time, given that it represents a significant portion of the cost composition of the alternatives.
After eliminating the redundancies, the group of specialists identified that one of the five criteria provided for in ANP resolution No. 817, the social criterion, was not covered.Through the collection of expert opinions, it was concluded that it was appropriate to insert the sub-criterion "employment generation", aggregating all relevant social aspects that could be evaluated at the time of proposing the PDI.
After making the adjustments to the evaluation criteria, the remaining items can be adopted in SMAA-ExpTODIM.Finally, Table 1 consolidates the quantitative evaluation criteria of the alternatives considered in the SMAA-ExpTODIM calculations.From the perspective of Petrobras evaluation, the Proponent's view, criteria C 1 to C 12 are modeled as Cost-type criteria, that is, the lower the value, the better for the decision objective.Costtype criteria must be normalized through equation (2).Still from the Proponent perspective, only criterion C 13 is of the Benefit type and must be normalized as defined in equation ( 1).The Conceptual PDI shows the preference for an alternative that results in less environmental interference, less impact on the underwater life developed in the region, as well as a lower emission of greenhouse gases with less release of consumed energy.Furthermore, reading the PDI in conjunction with the strategic plan (Petrobras, 2020b) shows the recognition of the value of lower exposure of human life to operational risks and the preservation of natural and financial resources.
In contrast, when evaluating the approach to the decision problem from the Regulator's perspective, it is assumed that only criteria C 4 , C 6 , C 8 , C 9 , C 11 , and C 12 are of the Cost type.The point of view is reinforced by the opinion of the experts consulted in the elimination of redundancy in the criteria.The other criteria, C 1 , C 2 , C 3 , C 5 , C 7 , C 10 and C 13 , are of the Benefit type.
The fourth step of the frame of reference, Fig. 2, provides for the identification of the uncertainties involved in the evaluation of the criteria (4.1), in the importance of the weights (4.2), in the loss aversion amplitude factor (4.3), and in the level of significance of the decision problem (4.4).
For the criteria evaluation uncertainties, step 4.1, the ranges of estimation variation by project maturity level of the AACE (Association for the Advancement of Cost Engineering) guideline 18R-97 are adopted (Dysert, 2016).In the variation of importance of the evaluation weights of the criteria, step 4.2 of the reference frame Fig. 2, normal PDF are adopted with a standard deviation of 10 % of the nominal weight attributed to each criterion.Fig. 3 exemplifies the stochastic function attributed to the criteria of the Security category.To define the amplitude factor, step 4.3 of the frame of reference, Fig. 2, continuous values between 1.5 and 2.5 are assigned (Novemsky & Kahneman, 2005) through a PERT function.
Step 4.4 of the reference framework provides for the definition of uncertainties about the DM sensitivity to the problem.The possibility is assumed for the DM to assume one of the bold, neutral, or conservative profiles.For each profile a discrete PDF is assigned, with different pertinence for each value of the parameter ρ, according to Table 2.

Monte Carlo simulation in SMAA-ExpTODIM
The start of steps 5.1, 5.2, 5.3, and 5.4, Fig. 2, takes place with the definition of how many K iterations the Monte Carlo method will perform the SMAA-ExpTODIM calculations.The number of 10 4 iterations was selected for the Monte Carlo simulations using @Risk, a Microsoft Excel® supplement, a component of The DecisionTools Suite® software.
At each k iteration, the following steps are executed: 5.1.drawing of a sample from the evaluation matrix of alternatives (x i k ).
5.2.drawing of a sample from the possible arrangement of w k weights for evaluating the criteria.
5.3.drawing of a value for the amplitude factor λ .
5.4.drawing of a value from the PDF of the DM sensitivity ρ, Table 2.
6. calculation of the global utility function of each alternative in ExpTODIM, ξ i k equation (5).
The above steps are repeated until the k iteration reaches the defined K value.

Robustness measures in SMAA-ExpTODIM
After performing the iterations of the Monte Carlo method, step 8 is implemented with calculation of the RAI, CWV, CAF, CSF, CF, and PWI indicators for each alternative, to finally choose the most robust alternative.
We chose to evaluate the decision problem from two perspectives, the point of view of the PDI Proponent (Petrobras, 2021) and the Regulatory bodies ANP, IBAMA, and the Brazilian Navy.Different risk propensity profiles on the part of the DM are also added to the PDF of parameter ρ, Table 2.
Equation ( 13) is applied in order to obtain the ordering acceptability index RAI i r (x).Table 3 consolidates the acceptability results in all the ranking positions of the alternatives, for the bold, neutral and conservative risk profiles, as well as for the perspectives of the Regulatory and Proponent bodies of the decision problem.
From the RAI it is possible to get to the other indicators.It is through equation ( 14) that the central weight vector CWV i c (x) is calculated, a weight vector that favors the positioning of the respective alternative in the first position of the order, from the perspective of evaluating the decision problem.Finally, the SMAA-ExpTODIM is finalized, obtaining the winning index of the PWI pairwise comparison, equation ( 18).
The different pertinences of the PDF of the parameter ρ, Table 2, represent the way in which the individual DM faces the decision problem, in a conservative, neutral, or bold way, according to the perspectives of the Proponent or Regulator.
Finally, step 9 of the SMAA-ExpTODIM frame of reference is conducted, Fig. 2. The appreciation of the values obtained for the RAI of the alternatives, Table 3, as well as the confidence factors, allows for greater acceptability and confidence for alternatives A 4 and A 5 , both from the perspective of the Proponent and the Regulator.

RESULTS AND DISCUSSION
The PDI (Petrobras, 2021) adopts comparative analysis of alternatives, a method of aggregating points in which the chosen alternative is that with the highest score.In the comparative evaluation, there is no difference in weight importance between criteria, and it presents evaluation only from the perspective of the Proponent.Table 4 summarizes the rankings obtained by applying the proposed MCDA SMAA-ExpTODIM, and the comparative assessment of the PDI (Petrobras, 2021).
From Table 4, it is possible to observe greater relevance of alternatives 4 and 5 in the first and second position of the orders obtained in the SMAA-ExpTODIM, with alternative 4 being preferred from the perspective of the Regulator DM, while alternative 5 represents the interest of the Proponent DM.In contrast, alternatives 1 and 2 are the most strongly dominated, as they occupy the last positions in all SMAA-ExpTODIM simulated scenarios.
Pesquisa Operacional, Vol.43, 2023: e267436 In addition to risk propensity or risk aversion profiles, the SMAA-ExpTODIM is robust in allowing it to consider, in its stochastic modeling of the problem, the zones of uncertainty in the evaluation of alternatives, as well as the incompleteness of understanding the weights of the criteria.
From the RAI, Table 3, it is still possible to verify that from the Regulator's point of view, all the alternatives, in some of the 10 4 iterations, occupied the top of the ranking.In contrast, from the point of view of the Proponent and in all risk profiles, alternative 5 is preferred in all iterations.It is possible to verify, still from Table 3, that the adjustments of the probability distributions to the risk profiles, from bold, neutral, and to the conservative, reinforce the ordering of alternatives.This reveals an increase in robustness and comfort to the DM from the Regulator's perspective, for example, in opting for the ordering A 4 ≻A 5 ≻A 3 ≻A 2 ≻A 1 .
The SMAA-ExpTODIM proved to be adequate in terms of creating a priori robust decision solutions due to its flexibility and greater scope in representing the areas of uncertainty, ignorance, and complexity of the decision problem.

CONCLUSION
The combination of the SMAA technique and the ExpTODIM method, designated in this work as SMAA-ExpTODIM, reveals an expressive range of a priori robustness, allowing the solution of complex problems with consistency.It was capable of covering the antagonistic perspectives of Proponent and Regulatory institutions in ordering the choice of alternatives to the decommissioning of O&G production assets.
Through the SMAA-ExpTODIM approach, the choice of alternative to the decommissioning of the subsea systems of the Marlim and Voador fields takes place in a broad and comprehensive way, considering the areas of uncertainty and adjustments to the position of the Proponent and Regulator DM.The stochastic aspect of SMAA-ExpTODIM allows creating risk appetite profiles, considering different PDF for bold, neutral, and conservative individuals.There is also the differentiation of the Cost and Benefit criteria in the evaluation of alternatives.These characteristics reveal the ability to present a robust choice of alternative to a priori decommissioning, that is, from the beginning of the construction of the decision model.For the composition of the ordering acceptability indices, RAI i r (x) revealed the robust stochastic ordering of the SMAA-ExpTODIM.
Incorporating the SMAA stochastic measures in ExpTODIM follows the path identified by Leoneti and Gomes (2021a) of optimizing the parameters of the new ϕ function, considering that the results provided proved to be very consistent in terms of adherence to the agents' preference, with high levels of robustness of the results with a minimal range of variations.
The application of the SMAA-ExpTODIM revealed a range of robust choices when approaching the decision problem from the antagonistic perspectives of the Proponent and Regulator entities.However, in an effective policy exercise one must consider not only the measurable and contrastable dimensions of the simple parts of the system, which even if complicated, can be technically simulated.Future applications of SMAA-ExpTODIM may consider broader dimensions of the problem, that is, power relations, hidden interests, social participation, cultural restrictions, or other factors capable of becoming relevant variables.
Real-life decision-making situations often preclude assessing how well the underlying assumptions of a decision model are satisfied.In the light of Game Theory, Araújo and Leoneti (2020) deal with new perspectives on how difficult it is for a regulatory agency to equate the different interests of the actors involved in choosing a regulatory regime (concession, sharing, partnerships, or contracting of services) to the O&G exploration and production market.In decommissioning projects, social, operational safety, and environmental factors outweigh technical and economic issues.Therefore, there is room to explore studies in future approaches that analyze the interactions of regulatory bodies in O&G decommissioning projects from the perspective of Game Theory.
In the present study, the stochastic parameters of the SMAA-ExpTODIM application were obtained from the contribution of specialist engineers and consultants working in O&G decommissioning projects.Future research with access to technical experts or DM from regulatory bodies can validate, or even adjust, the probability distributions proposed here.
In decommissioning projects that require public hearings, or where negotiations between the proposing company and the regulatory body are accessible, it is possible to model the interactions between those involved through the proposition of Leoneti and Gomes (2021b).The authors refine the additive multi-attribute utility function (ϕ) by adjusting the pairwise comparison in iterations of the group decision.Therefore, it is possible to seek the development of a more robust model or adjustments of smaller dispersion in the parameters of the SMAA-ExpTODIM.
Future applications of the SMAA-ExpTODIM approach in decommissioning projects may seek to understand the a priori interaction of other stakeholders (NGOs, community leaders, unions, fishermen's cooperatives, research institutes, etc.) in the decision-making process of an offshore decommissioning project, in order to improve the modeling and importance of criteria to explain the particularities and preferences of each one.
There is also the possibility of conducting documentary research in historical, legislative, and administrative archives of regulatory institutions, or even in files of judicial proceedings.These records can produce a map of the social actors relevant to the offshore decommissioning decision problem.

Figure 1 -
Figure 1 -Comparison of different values for the parameter ρ for the ExpTODIM function.

Figure 2 -
Figure 2 -Reference framework for the application of the SMAA-ExpTODIM.

Figure 3 -
Figure 3 -Probability density function of the Security category criteria.
equation (16), are then calculated.Concomitantly, through equation (17) the confidence factors CF i c of the alternatives are obtained, a probability measure of the alternative A i occupying the first classification for the vectors CWV i c (x), CAF i c (x), and CSF i c (x).
Fig. 4 presents the RAI i r (x) of the alternatives in all ranking positions, revealing the preferential stochastic ranking of the Regulatory DM with conservative profile A 4 ≻A 5 ≻A 3 ≻A 2 ≻A 1 .In contrast, evaluating the RAI i r (x) results of Table 3, from the point of view of the Proponent, only alternative 5 occupies the top of the ranking.For the bold, neutral, or conservative risk profile, in none of the 10 4 iterations, no alternative threatened the preferential stochastic ordering A 5 ≻A 4 ≻A 3 ≻A 1 ≻A 2 .

Figure 4 -
Figure 4 -RAI for Regulator and Proponent of conservative profile.

Table 1 -
Evaluation criteria for alternatives to the decommissioning of flexible lines in the Marlim and Voador fields.

Table 2 -
PDF for DM sensitivity.

Table 3 -
Acceptability index for the planning of alternatives to the decommissioning of the Marlim and Voador fields.

Table 4 -
Ranking of alternatives to the decommissioning of flexible lines in the Marlim and Voador fields.