Formwork material selection and optimization by a comprehensive integrated subjective–objective criteria weighting MCDM model

Formwork is a crucial temporary structure that supports and shapes fresh concrete along the position and alignment until it strengthens [1]. It also supports workers, building materials, and equipment by accommodating full, partial, and incremental loads. It can be sideways, uplifted, overturned, and slide steadily [2]. Based on the material, it can be plywood, steel, aluminum, plastic, and other materials [3]. It also categorized as a vertical, climbing, slab, shoring, scaffolding, and so on in terms of functionality [4]. The quality of the concrete's dusting, discoloration, and stains are influenced by each formwork type and craftsmanship. Additionally, it impacts the distortion of concrete surfaces due to inadequate support and reuse [2]. Thus, maintaining the quality of the concrete [1] necessitated choosing the appropriate formwork material for the optimum form, characteristics, and strength [4, 5]. For optimizing the speed, skilled, experienced labor, and reuse [6] by supporting the concrete's pressures at the height pour, rate, height of discharge, temperature, kind of cement, admixtures, and plan dimensions [2] appropriate formwork is needed.

Additionally, formwork makes up 10% of the building's total cost and 40 to 60% of the concrete frame primarily due to labor costs [2, 7]. Concrete structural collapses and failures account for one-fourth of construction failures; of these, more than half are due to formwork failure, which can be caused by inadequate bracing, unstable support or mudsills, inadequate shoring and reshoring, poor formwork structural design, improper construction techniques during construction, and insufficient concrete strength to sustain the applied load after construction [2]. In addition, choosing the right formwork material shall be based on several sustainable development competing and compromise criteria to lower the building sector's global resource consumption, emissions, and waste by 40%, 33%, and 40%, respectively [7]. This illustrates the necessity of optimizing [2] and selecting formwork [1] with consideration for cost, safety, ease of construction, and environmental friendliness [8], as well as operations, cycling, and project progress [9], all of which have a direct impact on the project's overall performance [1, 10].

The selection of formwork materials under a variety of criteria requires the successful use of MCDM techniques, which have been in use since 1990s, to complete the project on time, with quality, within budget, and without incident [10]. It has been the subject of various research in the past [11], as well as selection based on life cycle cost, energy demand, and environmental impact [12]. It excludes, however, the general requirements for formwork selection, such as quality and surface finish, safety, behavior, project duration, and structural dimension; the formwork's load-carrying capacity; its lifespan and weight; its future value creation; its impact on the environment when land is being stored; and its societal effects, such as the creation of jobs, social acceptance, social benefits, and the extent of technological maturity, efficiency, resource density, and production.

Earlier, the MCDM method used fuzzy logic [13], AHP [14], Integrated Rough AHP-EDAS [10], TOPSIS [15], MCDM with life cycle assessment and economic analysis [7], simple TOPSIS with SAW methods [16], mean score analysis of structural questioners [6, 8], and the hybrid MCDM method [17] to select formwork. Each of them employed a MCDM technique assumption and shortcoming of the combined MCDM techniques. In terms of objective scaling, parameter handling, and economic significance analysis, they have distinct advantages and disadvantages [18, 19]. It is also difficult to choose one [20, 21] because every multi-criteria approach has an inconsistent answer that yields different findings using different procedures [20, 22]. The acceptability of the MCDM result was limited due to the method's unique scope and performance [21], a hierarchical structure, arbitrary and inconsistent decision-making [18, 23], and inaccurate alternative prioritization. For a longer time, this tendency makes the MCDM methods' information-gathering and real-life problem-iteration strategies useless [18, 23]. Therefore, to control accuracy and performance [24], it needs careful selection of multi-criteria analysis [21].

Prior studies typically employed a single or hybrid MCDM technique and omitted the major formwork selection criteria. The selection of formwork shall therefore consider the following key factors: quality and surface finish; safety; behavior; project duration [8, 9, 25]; structural dimension [8]; load caring capacity [8, 25]; lifespan [4, 25]; weight [4, 8, 25] and cycle time [4, 8, 25, 26]; future value creation [4, 25, 27]; environmental impact on land storage [4, 25, 27]; job creation [2, 4, 25, 27]; social acceptance [4, 27]; organization behavior; social benefit [4, 25, 27]; technological maturity [2, 4, 25]; efficiency [2, 4, 25]; resource density [2, 4, 25, 27]; and production [4, 25, 27]. So, these criteria shall combine with cost [4, 8, 25]; maintenance [27] and environmental impact of pollutant emission [4, 25]; effect on the ecosystem [4, 25] and climate condition [9, 25]. In addition, to address MCDM techniques selection, this study utilize all highly uncorrelated MCDM methods and weighting to balance the drawbacks of a single MCDM approach with the benefits of the other through robust Monte Carlo simulation randomization [28, 29] the formwork performance score at 95% confidence.

Thus, this study main select the optimum formwork by creating a comprehensive integrated subjective–objective criterion weighting MCDM model. It developed connecting and randomly distributing the uncorrelated MCDM performance score and criteria weight for any possible formwork selection criterion. An LFN questioner was initially developed and condensed utilizing the Delphi and Interview techniques to achieve this aim. Second, decision maker performance was ranked and assessed. Thirdly, the formwork system will be chosen using all uncorrelated major MCDM techniques. Fourth, the formwork options in the Monte Carlo Simulation are ranked using a 95% performance score. Finally, the study will be validated and rationalized by a comparative, environmental and cost analysis.

The selection of materials is crucial that requires a suitable decision-making instrument [18]. The instrument needs a systematic and formal procedure of problem identification, performance derivation, alternative evaluation, and identification [23, 30]. By breaking down complicated situations, the choice will be normative, prescriptive, and descriptive [19, 20, 22, 23]. Therefore, making decisions involves finding the best outcome for a variety of factors at various points in time [31]. Everybody in the relief industry makes decisions [32] based on a single criterion or multiple criteria [23]. The single criteria decision-making problem is addressed by programming and nonlinear optimization [33]. The multicriteria problem is addressed by multicriteria decision making or multicriteria decision analysis [23, 34]. It can be multiple attribute decision making (MADM) and multiple objective decision making (MODM), which is a set of techniques for choosing amongst competing criteria [35, 36] for both qualitative and quantitative data [22, 37].

To establish attribute weights and alternative priorities, decision makers utilize the weighted aggregate information from MCDM [30]. Through the division of the issue into significant and manageable components [21], it permits a complex problem analysis [20]. For numerically valuing and mathematically ranking the MCDM problem [21], the alternatives, criteria, and weights shall all be precisely described. Since, the MCDM method calculation, mathematical tools [37], and the notion of criteria weights [38] are the basis for the ranking. It primarily utilized energy, environment, and sustainability [37] through subjective decision-maker participants [39] and objective data analysis [18]. The MADM considers ratings for discrete preference variables and a small number of predator-mined alternatives [22]. The MODM allows for the best selection of design and planning issues with a set of goals interactions of an unlimited range of alternatives. The main difference is, MADM approach continuous alternatives that optimize multi-objective problems, while MODM address discrete alternatives [23]. To accomplish the goal of this study, a new model will be created as indicated.

2.1 Random number criteria weighting model for formwork selection

Weighting the criterion is a crucial [40] that mainly influence MCDM analysis [41] and the outcome of decision-making [42]. In addition, the distinct theoretical rules, interpretations, and ramifications are misinterpreted and disregarded by the decision-makers [40]. It can be objective, subjective, and integrated criteria weighting [41]. The subjective assessment is determined by the subjective technique [43] like Bayesian [44], pairwise comparison, Swing, Delphi, TRADE-OFF, direct rating, point allocation, and SWARA [42]. However, due to unique advantages and disadvantages the stated methods need to be combined. For example, utility function integration is required for Swing weighing [42] through Bayesian [44]. The integration of Delphi with pairwise comparison, TRADE-OFF, SMART, and Bayesian removes the bias of expert groups [45, 46]. Point distribution, direct rating, ranking, and ratio weight also required integration due to imprecise ordering and restricted applicability [42].

To these subjective criteria, the objective criterion weighting that quantitative analysis of non-subjective data [39] will be applied. It may be MEREC, LOPCOW, SD, CRITIC, ENTROPY or SVP [47]. To promote objectivity, ENTROPY measured the degree of diversity [48] and the uncertainty of a system [47, 49] using probability theory [50]. Thus, it can be combined with CRITIC and Criterion Impact Loss to incorporate the link of conflicting criteria [47, 49]. However, to acknowledge the criteria’s roles [42] with standard deviation [49] and variance value of criteria [42, 47], the integration shall include SD and SVP. In addition, MEREC and LOPCOW used to adept criteria weighting of interrelated criteria by minimize disparities of significant criteria [31, 41] and merges distinct spanning information [47] through exceling interdependencies criteria [51, 52].

The integration of criteria weighting is needed due to the behavior of substantive weights were used to ascertain the relative relevance of criteria, while objective increased each criterion's capacity to evaluate alternatives [53] in a more accurate and valuable way [47]. This led the researchers to develop integrated criteria weighting like Cubic Effect-Based Measurement [47], IDOCRIW [47, 54], multiplication synthesis, etc. [42] to solve a practical problem [49]. Since, the real world needs integration [49] of the critical [40], significant [41], and unequal assumptions [50] of criteria weighting. However, the above integration integrates a few methods that need to increase the accuracy and reliability of criteria analysis [55]. So, the researcher shall develop criteria weights that integrate weighting through randomized at 95% confidence to counterbalance subjective limitations and biases by objective weighting strength and value.

2.2 Comprehensive integrated MCDM models

Researchers used two or more MCDM approaches with other theories to address the shortcomings of one approach when the MCDM problem called for more features than standard MCDM [18]. The most popular approach [20] to make up for the shortcomings of one MCDM method by utilizing another [34] is integrated MCDM. For example, WASPAS combines a WSM and a WPM. Even if the outcome is irrational and not accurate for the challenge of fuzzy logic techniques [56], it is employed for high-accuracy ranking [56, 57]. To handle high uncertainty and unknown functions, the Integrated Approach of Grey-AHP and Grey-TOPSIS is a hybrid MCDM that combines MCDM with grey systems theory. It will address the shortcomings of the discrete character of the data and the fuzzy collection of models [23]. In addition, Integrated Prospect Theory and PROMETHEE [27] and Integrated mathematical MCDM model of fuzzy-AHP, objective weight MCDM, linear programming, and linear Monte Carlo simulation [18] are example real-world problems driven MCDM integration.

Similarly, the integrated approach of fuzzy-FMEA and VIKOR is used to accommodate the subjective inputs of industrial experts to prioritize the risk; limit outcome bias and ambiguity [23]. Hybrid fuzzy-MCDM method that integrated combination weight with Delphi, fuzzy-ANP, entropy, and fuzzy-PROMETHEE to handle multiple, uncertain, and conflicting factors [58]. Integrated DEMATEL-ANP MCDM was used to determine the criteria interrelationships and the overall risk index [23]. The above method can be applied to address uncertainty and veganism in human decisions [23, 27], with the addition of data shortages [18, 23] and the mathematical complexity of low data [18]. However, the shortcoming of integrated MCDM is not solved all in all, and the specific component of integrated MCDM is based on the interest of the researcher in the specific study.

For instance, integrated prospect theory and PROMETHEE address uncertainty, subjectivity, and vague challenges but do not address the MCDM problems of mathematical complexity and data shortage [18, 27]. The integrated mathematical MCDM model solves objective and subjective decision-making of uncertainty, mathematical complexity, and law information with known properties [18] that are limited to the theories of fuzzy-AHP, CRITIC, entropy, statistic theory, Monte-Carlo-simulation, and linear programming. In addition, the ranking of concrete grade is done by the average of the three MCDMs. A Hybrid Multi-Criteria Decision-Making aggregation method and GIS integrated TOPSIS, TODIM, WASPAS, COPRAS, ARAS, and MULTIMOORA [59]. However, in this method, the critical element of MCDM is limited to SWARA, and the MCDM ranking is limited to Correlation Coefficient and Standard Deviation aggregation. It did not include mathematical complexity or a data shortage. So, the researcher proposed a comprehensive integrated subjective–objective criterion weighting MCDM model that combined the uncorrelated MCDM methods by a powerful Monte Carlo simulation under LFN to solve the deviation of different techniques of utility functions and parameters to address specific MCDM methods inconsistency. In addition, it summarized the data through Delphi and interview method.

2.3 Formwork selection through comprehensive integrated MCDM model

The comprehensive integrated subjective–objective criteria weighting MCDM model used formwork selection because of the counter-balancing of one method by another method through systematically bonding uncorrelated MCDM. It addresses the previous study drawback. For instance, SAW used for simple problems [23, 57] of unreal and illogical output [23] and that need to be integrated with TOPSIS. These two methods can be combined with AHP to address complex real-life problems [20, 23] and ANP to accurately predict the dependent variable of intangible criteria [23]. However, TOPSIS is sensitive and inconsistent due to the uncorrelation of attributes and monotonically variation of criteria assumptions [20, 23] and lack of guidelines to define criteria weights [60]. This challenge a pair-wise comparison judgment of AHP [61]. And ANP is inconsistence and complex for uncertain things. Similarly, if the model needs to address uncertain and vague conditions of incomparable alternatives [20, 21, 23] for compromise solution [62] it need ELECTRE, PROMETHEE and VIKOR.

But ELECTRE is limited to criteria result-relationship interpretation [23], too long computational process [20], and the threshold values used are arbitrary [60], and PROMETHEE is unclear weighting [58] and the result evaluation process is complicated and hard to explain [60]. VIKOR marginalizes the quality of the solution without considering the causal relationships [63]. Similarly, adding DEMATEL solve the causality problems but it is unsuitable for ranking and the result is vague. To increase the accuracy by increasing features in the MCDM model, the fuzzy family analysis the interaction between criteria under ambiguous conditions with low information of subjectivity of human opinions in the real world [23]. However, fuzzy family results are dependent on the criteria selected for evaluation and the effect of one attribute on the other that does not fit the real world [23, 64]. Hence, the results of LINMAP address the qualitative and quantitative criteria by the scale of uncertain and fuzzy information in a set of pre-specified incentives in multidimensional attribute space and COPRAS rank the imprecision impute by eliminating the bias of the decision maker [23, 65]. However, LINMAP has no formal guidelines for weighing, which complicates the preference information and makes it hard to explain for non-specialists, and COPRAS is difficult to develop, the data is completely reliable, and the factors are subjective [23].

MOORA is used in discriminatory decision making but the weighting is difficult, and ARAS used utility function analysis of decision although qualitative initial measurements, comparative preference, and verbal decision-making analysis are not effective, the solution is unstandardized [23]. CoCoSo calculates the utility values of different perspectives but it used for complete and clear problem without considering subjective and objective weights [30, 32] CODAS used for the evaluation of large complex information and data [34] without considering the influence on the inconsistent actual situation [66]. The integrated interpretative structural modeling method analyzes complex problems by incorporating experts’ opinions of vague, poorly articulated mental models of systems [67]. Even though it requires experts with long experience and is applied to a small number of variables. SWARA select a real-life problems of stakeholder policy, even if it used expert opinion the criteria weighting. TODIMU handle uncertain and risk decision problem in decision-making of risk aversion or risk seeking of gain or loss function of subjective, sensitive, and complex problems [62, 68]. However, it does not handle the uncertainty of independent criteria and closed transparency with a finite number of alternatives and criteria performances [69].

This show the difficulty of choosing the most effective MCDM methodology since different MCDM methods yield varied results and use incorrect techniques that lower the results quality [21]. According to the choice of an acceptable uncorrelated approach to validate the result, this shows how to combine MCDM to solve a problem. Furthermore, criterion weightage drives the decision-making process in MCDM problems more so than MCDM methodologies [70, 71]. Therefore, in this study, the researcher takes all MCDM methods’ unique features, benefits, advantages, and limitations to counterbalance each other. The challenge of one problem shall be minimized by the strength of another MCDM model through Monte Carlo simulation random numbers generation of the performance score of each MCDM. The model includes and compromises the specific strength and decreases the shortcomings of the uncorrelated MCDM method under consideration of the statistical properties of the corresponding performance value at 95% confidence as shown in Fig. 1. Finally, linear programming shall be integrated if the MCDM problem requires maximizing benefit by minimizing cost in solving uncertain problems.

Graphical representation of the assumption of how the model developed (developed by author)

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2.4 Data analysis and modelling in formwork selection

When there is information to choose the formwork, the opinion of professionals becomes the only source [56]. In the introduction, it has stated different MCDM methods to select formwork. In addition, single and extended MCDM methods like TOPSIS, fuzzy extended AHP, fuzzy-VIKOR [7], and Integrated TOPSIS-AHP-SAW were used in material selection [72]. However, this study fills the research gap of formwork selection using the most common criteria using an integrated Delphi, interview, statistical theory, Monte Carlo simulation, and uncorrelated MCDM models and criteria weighting under an LFN. To address these, the investigator initially determined the common formwork selection criteria, and to overcome the shortcomings of single MCDM approaches, the researcher then created a hybrid MCDM model using the Monte Carlo criteria weight and performance score of all key highly uncorrelated MCDM methods. This model combines Delphi, interviews, major MCDM, Monte Carlo simulation, and statistics theory to pick key content and, in conjunction with formwork selection, fill the gap left by prior research. It demonstrates to the researcher how to combine the outcomes of the main MCDM techniques with one another in an uncertain setting with known certainty. Because of its treatment of the benefits, drawbacks, and areas of application of the main MCDM techniques, it is also regarded as the final integration of all MCDM techniques.

Furthermore, this model can be developed because a variety of industries use one or a combination of MCDM methods for material choice [13, 18, 73]. This said that, subject to certain limits, material selection will be carried out using single, extended, and hybrid MCDM. Thus, choosing formwork is a difficult process that affects concrete grade [18], as well as quality, time, safety, and cost [26]. Thus, the strength of this model is to counter balance shortcoming of MCDM method through the powerful Monte Carlo simulation. Additionally, it eliminates the difficulty of choosing a MCDM technique for a given problem [60], such as formwork selection, by minimizing and providing material selection in place of the complex AI method that necessitated additional parameters and complex processing [16]. Furthermore, in cases of uncertainty, ambiguity, data limitation, and mathematical complexity of formwork selection by specific MCDM techniques under LFN, the robust Monte-Carlo simulation combined with statistical properties of all data will be used. Therefore, the researcher believes that integrating uncorrelated MCDM and criteria weight with Monte-Carlo simulation under a fuzzy environment called the Comprehensive integrated subjective–objective criteria weighting MMCD Model for Construction Material Selection and Optimization will tackle the most important and critical MCDM problem.

3.1 Research procedure and method

To achieve its goal of creating a combined correlation analysis, Monte Carlo, and MCDM model for crucial engineering decision-making-in this case, the choice of the most cost-effective formwork system-the procedures and methods are summed up as follows. Finding information from the literature study, assessing the overall effectiveness of MCDM ways to identify the uncorrelated MCDM techniques, and creating objectives to provide a step-by-step guide to achieve the goal are the first common formwork material selection criterion. The critical literature review highlights the processes, practices, and shortcomings of the primary MCDM techniques. Additionally, it demonstrates how to include the existing model into the recommendation and formwork system selection for the subsequent decision-making process. In the second step, a structured questioner using Delphi and an interview technique collected subjective data for the formwork selection system. To collect objective data, however, a review of the literature was employed.

Thirdly, statistic theory, Monte Carlo simulation linked MCDM, and linear programming were used in conjunction with the optimal combination of individual criteria weight and MCDM techniques to optimize the uncertain data in the data gathering of high-rise structures. Fourth, the main MCDM method, data analysis, and discussion were critically examined to select the optimal MCDM and criteria weight that matched the study's goal. To determine the relative ranking of different formwork systems and to propose a workable dynamic critical decision-making approach for critical decision-making, the data was also examined. To convince stakeholders of the study's real benefits and support the model and its outcomes in the construction industry, the fifth step involved validating the selection and combination of multiple MCDM models using cost analysis, comparison analysis, and previous research. Finally, the new MCDM model that connected uncorrelated MCDM, cost analysis, and discussion of crucial building materials would be selected, completed, and sent to stakeholders.

3.2 Data collection, sampling and analysis

In this study, the researcher used Delphi technique to gather and refine group opinions without in-person meetings [47, 63]. However, the expert opinions were compiled with consensus using a combination of Delphi and Interview [89] with iterations [13, 14] involving 10–18 respondents [47]. The Delphi technique's divergence choice is summarized by iteration [51, 63] and the remaining steps were carried out using direct phone interviews to compile the group's verdicts [14]. To merge the expert and formwork selection, the researcher utilized the Delphi and Interview method under LFN. Additionally, the secondary data used in the analysis was gathered from prior research [15]. The researcher converted language data into consistency-AHP analysis data for use in the major uncorrelated MCDM technique to counteract the limitations of data collecting by all MCDM approaches.

In conversion of linguistic data, the linguistic fuzzy questioner outcome (> 79%) to compare and modify the related consistency AHP however if the it is between 65 and 80%, utilize the next best consistency-AHP value. The second rule is that when deciding on the intermediate consistency-AHP value the decision-maker must base their choice on the actual circumstances. A pairwise comparison consistency check validates this method. In general, the Comprehensive integrated subjective–objective criteria weighting MMCD model was summarized as followed in decision of construction industry MCDM problems. After gathering information, the algorithm was improved to choose materials weighing less than 70%. To address the limitations of the MCDM method, the study conducts a critical literature review and develops a formwork selection model that incorporates interviews, Delphi, and LFN questioners. The performance of the uncorrelated MCDM approach is assessed using goal-setting, alternative-setting, and randomization. A helpful tool for discovering delicate decision-making issues in ambiguous scenarios, it employs a 95% confidence level random number approach that is confirmed by LFN analysis and linear programming for uncertain conditions.

An expert panel of engineers, economists, lawyer, supplier and government official was invited to choose a decision-making of formwork selection as shown in the following set. DM = {Eng₁, Eng₂, Eng₃, Eng₄, LE₅, EC₆, SE₇, GO₈}. The first four are staff of contractors, consultants, clients, and banks; LE₅, EC₆ SE₇ and GO₈ are economists, legal expertise, supplier and government officials, respectively. First, 16 questioners were dispersed under LFN. The researcher reviewed the questionnaire replies on the spread over of the original responses and delivered a summary of the distribution of the initial response to the respondents, so they may update their opinions if they agreed. To shorten the number of iterations in the Delphi method's process for obtaining an opinion summary, the researcher got in touch with the second questioner directly regarding the divergence in response.

4.1 Formwork selection criteria

Formwork selection criteria are stated Table 1 and Fig. 2 as follows through a critical literature review to be used for formwork selection, the critical review referencing is stated in the introduction.

Hierarchical structure for formwork selection

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4.2 Quantification of formwork selection criteria and criteria matrix

Quantification of formwork systems based on sequence, reusing formwork panels, and generic formwork properties [26]. For example, a measure of maturity will be the amount of time saved when assembling and disassembling formwork. Aluminum formwork enables structural work to be completed in 4 days, as opposed to 12 days for typical timber formwork, which can take up to 12 days per floor [14]. Safety is defined as the sum of 1/safety factor, load carrying capacity, and deflection [74], since safety is established using the safety factor of the formwork material. Steel, plastic, plywood, timber, and aluminum have safety factors of 1.65 [75], compared to an average of 2, 4, 5, and 8 [74], 2 [76], 1.3 [77], and 1.5–3 [78]. The load carrying capacities of plastic, steel, aluminum, and eucalyptus wood are 75 [79], 55 [80], 46.8 [81], and 14.72 [82] KN/m², respectively. Because of ambiguous data, plywood formwork has the same load carrying capacity as timber. Furthermore, while the formwork system's reuse is unknown [7], the researcher uses plywood, steel, aluminum, plastic, and wood formwork that has been reused roughly 7 [7], 100 [83], 120–250 [74], 100 [74], and 7 [7] times, respectively. The relative deflection of the material by the moment of elasticity is used to analyze the deflection [84].

A kilogram of aluminum is produced when 40–60% alumina from bauxite [85] and it produce 212.12 kg/m² aluminum formwork. A ton of metal formwork requires 1.4 tons of ore [86], which equates to 891.25 kg of metal per square meter of column. However, the quantity of raw materials required to make wood, plywood, and plastic is estimated differently in numerous researches. For every m² of concrete column, this study calculates that 2.5, 4, and 1.35 tons of plywood, plastic, and timber are required produce 310.02, 214.16, and 358.09 kg of plywood, plastic, and timber formwork, respectively. Further, the purposes of this investigation, the quantitative variation of formwork system across various structural and architectural design is negligible. Then, the greenhouse gas and the energy consumption for a kilogram of aluminum production is of 14.77 kg-CO₂eq and 144.612 MJ [87]. Similarly, to produce TF, P_oF, SF and PF, 55, 76, 262.9 and 194 kg-CO₂eq of greenhouse gas and 5262, 8432, 29,522, and 23,022 MJ energy consumed [7]. The amount of kg-SO₂eq for one ton of aluminum production is the average of 36.99 [88] and 21.46 [89]. In production of TF, PoF, SF and PF, the kg-SO₂eq produced is 54.07, 85.88, 11.13 and 26.05 corresponding [7]. Similarly, the amount of NO₂ or NO_x is 1.94 kg-NO_xeq [89]. It also released in the production of TF, PoF, SF and PF as 38.17, 92.24, 8.30, and 6.48 kg-NO_xeq respectively [7].

The mean dichlorobenzene released in production of aluminum is 18.76 kg-DCBeq [90] but in the production of TF, PoF, SF and PF is 6.57, 2.97, 9.97 and 14.65 respectively [7]. The total emitted Kg-CO₂eq, kg-SO₂eq, kg-NO_xeq and kg-DCBeq per square meter is stated on Table 6. Crude oil and natural gas are the raw materials utilized in the production of polypropylene; in this study, only the 1.57 trillion barrels of crude oil reserve [91], and the 200–250 kg of polypropylene per ton are considered. The planet has 27 billion tons of iron [92], 30 billion tons of bauxite reserves [93], and 4.06 billion hectares of forest [94]. The present study examines the potential production of plywood and lumber on 50% of the forest area using 50–80 feet tall and 0.5 m² pine trees, which are estimated to yield 200–250 kg of timber [95]. The behavior of plastic, metal, aluminum formwork will be reduced construction time; however timber formwork will be reduced by 1/3 behavior of formwork [78]. So, the researcher takes the point of view of subjective respondent of Structural Dimension-S₁₅, Storage land-S₄₁, Job creation-S₅₁, Social acceptance-S₅₂, Social benefit-S₅₃ and Production-S₆₄ for objective valuation.

All the quantification on Table 7 was conducted and summarized using the above data as follow; quality and surface finish-S₁₁ are the product of lifespan and cost per cycle, Safety-S₁₂ is loading capacity, Behavior-S₁₃ is the cost of erecting and dismantling per floor, Project Duration-S₁₄ is the number of full formwork required for 2B + G + 22 floor, Load caring capacity-S₂₁ (KN/m²), Lifespan-S₂₂, (No of cycle), Weight-S₂₃, Kg/m³ of concrete, Cycle time-S₂₄ is recycling, Life Cycle Cost-S₃₁ is the life cycle cost per floor, Payback period-S₃₂ is cost reimbursement per life cycle, Future Value creation-S₃₃ reused (%), Pollutant emission-S₄₂ is the sum of kg-CO₂eq, kg-SO₂eq and kg-NO_xeq per floor by assuming the same effect, Effect on the Ecosystem-S₄₃ is the embodied energy in MJ, Climate condition-S₄₄ is kg-DCBeq, Construction speed-S₆₁ is labor cost per floor in m², Efficiency-S₆₂ (Kg of raw material per m² of vertical formwork) and Resource density-S₆₃ is the resource availability.

The quality and surface finish of AF is 1.72, 2.02, 20.19 and 26.60 time more than SF, PF, TF and P_oF per cycle. Project duration of TF and PoF is 14.29, 15.71 and 29.29 time more than PF, SF and AF respectively. PF, SF and AF is 20 time more recyclable than TF and P_oF. However, the safety, load carrying capacity, weight and construction speed of formwork varies within 1 to 4 ranges.

4.3 Cost and environmental impact analysis

For sustainable development of formwork selection, the cost and environmental impact shall be considered. The price covers production, transportation, erecting, and dismantling and recycling. For this study, nine high-rise buildings, ranging in size from 2B + G + 14 to 4B + G + 25 and quantity of 222.65 m³ C60 concrete designed. The cost analysis that follows is based on 2% withholding tax, 15% VAT, 10% surtax, and 5% custom charge. The costs of erecting and dismantling of TF is 1.3 more than PoF and 1.5 more than AF, SF and PF. Life cycle cost of timber formwork expressed as in per-cycle costs, after accounting for 13% insurance and fright factor, are 1.32, 1.38, 1.45 and 1.43 more than plywood, steel, aluminum, and plastic, respectively. Thus, the per cycle cost of formwork system ranked as AF > PF > SF > TF > P_oF from economical to costly. In addition, the payback period of TF is 2.58, 4.23, 9.64 and 18.89 time more than P_oF, SF, PF and AF respectively. However, the future value creation of SF is 1.11, 1.18, 5 and 5 time more than PF, AF, P_oF and TF. The cost, payback period and future value creation of formwork varies as the material change.

The environmental impact shall be analyzed by CO₂, NO₂, Fuel, power, water, raw material and production cost [18] for a specific cycle. Global Warming Potential (CO₂), Terrestrial acidification potential (SO₂), Human non-carcinogenic toxicity (DCB), Ozone formation and human health (NO_x) [7], natural resource depletion of formwork raw material, fuel and power [18]. For 222.65 m² of vertical wall, for a single cycle and assumption stated, plywood formwork 1.38, 4.54, 5.6 and 150.7-time Global Warming Potential than the corresponding TF, SF, PF and AF; 1.59, 2.71, 3.3 and 7.71-time Terrestrial acidification potential than the corresponding TF, AF, PF and SF; and 2.42, 5.60, 11.11 and 43.78 Ozone formation effect than the corresponding TF, PF, SF and AF. The production of Plywood formwork shall consume 1.6, 4.49, 5.23 and 1707.6 more energy than the corresponding TF, SF, PF and AF. Thus, Aluminum formwork is less Global Warming, Terrestrial acidification and Ozone formation.

However, TF is producing 2.21, 6.41, 10.26 and 10.36 more Human non-carcinogenic toxicity then the corresponding P_oF, PF, AF and SF. SF required 2.47, 2.87, 4.16 and 4.20 kg/ton of raw material than the corresponding PF, TF, P_oF and AF. PF has 2.88, 2.88, 108.45, and 195.20-time resource availability than the corresponding TF, PoF, SF and AF. All in all, it is not possible to specifically rank formwork material selection in the consideration of Pollutant emission, Effect on the Ecosystem, Climate condition, Efficiency, and Resource density like the previous environmental impact assessment of plastic, steel, plywood and timber formwork [7].

4.4 Summary of comprehensive integrated subjective–objective criteria weighting MCDM model

Two phases go into the development of this model.

4.4.1 Phase 1: criteria weighting and MCDM method selection

• Through rigorous assessment, the most effective weighting of subjective and objective factors is chosen.

• The representative criteria of the study were chosen using relative importance index.

• The criteria weighting was determined using the typical criteria of material selection. Then, using Monte Carlo simulation and the statistical property at 95% confidence, the criteria weight will be integrated.

• Using integrated criteria weighting on major MCDM methodologies, the uncorrelated MCDM was chosen.

4.4.2 Phase 2: formwork selection

• The subjective–objective criteria weighting of Monte Carlo simulation criteria weighting will be generated utilizing all the criteria used in the formwork section.

• The subjective–objective criteria weighting of the Monte Carlo simulation will be used to determine the performance ratings of all uncorrelated MCDM.

• Using the statistical property at 95% confidence, 100,000 random numbers will be generated using the performance score.

• Formwork selection will be ranked using the weighted average of the randomized performance score.

This method solves decision of mathematically complex problems, risk aversion, gain or loss function seeking, uncertain, vague, and subjective decision-making of limited information and objective MCDM problem. The monte Carlo simulation bond the unique MCDM performance score and criteria weighting of formwork quantity of high-rise building under statistical theory at certain confidence. However, this model output is limited to the existing MCDM and criteria weight assumption and the long computation process will limit the application on the most critical decision-making problems.

4.5 Combined subjective–objective formwork selection criteria weighting

The pairwise comparisons and Delphi subjective weighting method is selected due to the point allocation method is applied for less than 6 criteria, Ranking method is limited to small criteria weighting. Ratio, Swing, Nominal Group Technique and SMART weighting method based on the decision of researcher and stakeholder like Delphi method [42, 58]. The Bayesian method is excluded from this criterion weighting due to the nature of decision maker in ranking [44]. Pairwise comparison of AHP verified by AHP consistency index, which use simple order adjustment to solve the inadequacy consistency criterion weighting. The criteria weighting combination discarded the induvial objective criteria weighting using SPSS highly correlated (< 95%) with each other. Even if the SD and SVP are 99.1% correlation, in addition SD is highly correlated with entropy, CRITIC, and LOPCOW, the SVP and SD is selected in the model to increase the contribution on objective criteria weighting in the model. Therefore, the combination Entropy, CRITIC, LOPCOW, SVP, SD, and MEREC by bondage of linear Monte Carlo simulation will be the objective criteria weighting of the formwork selection.

However, the criteria weighting of the subjective is the value of Delphi summer for LFN and pairwise compassion for AHP MCDM method. The Delphi summary are given in Table 7, and the pairwise comparison (AHP) weighted value was examined as follows: Initially, by multiplying all the matrix's row entries together to obtain the n^th root of that product, the criterion weight for pairwise comparison is identified. The total would be 1 once this product is divided by the sum of the n^th roots of each row and normalized. The other criteria weighting is summarized and stated on the Table 4. Then the consistency Ratio (CR) is calculation by dividing consistency index (CI) by random index (RI) taken from Table 2 [23, 42], if CR is less than 0.1, it is acceptable [42, 58]. Otherwise the pairwise comparison shall be done again [89] or adjusted by simple order. \(CI = \frac{{\uplambda }_{\text{max}}-n}{n-1}\), \({\uplambda }_{\text{max}}\) is the average of the dividend of weight sum by criteria weight and n is number criteria.

Thus, the researcher improve consistency by rank the activities through a simple order as state on Table 3. It used the weights of the first run to develop another pair-wise comparison matrix [96].

Entropy, CRITIC, LOPCOW, SVP, and MEREC are the chosen objective criteria. Table 12 displays the analysis of the result using the formula found in Table 10. By randomizing the weights of Delphi, pairwise comparison, entropy, CRITIC, LOPCOW, SVP, and MEREC listed in Table 12, the combined subjective and objective criterion weighting model is created. As seen in Fig. 3, the 100,000 random weights were produced using @RISK based on the statistical characteristic of each weight. Table 12 and Fig. 4 provide the value of the subjective–objective criteria weighted by Monte Carlo methods. By generating higher and lower weight in an integrated Monte Carlo weighting, this weight aggregation will strengthen the critical criteria and weaken the weak criteria. The elimination of the deficit of the subjective or objective weight and reducing the mistake in a single criterion weighting that would smoothen the criteria weight, it will combine and lessen the potential bias of a single weighting [49] (Tables 4, 5, 6, 7).

Probability distribution of criteria weight of safety (S₁₂) and performance score of Plastic Formwork

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Graphical representation of criteria weight

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4.6 Formwork selection using compressive integrated MCDM model

The formwork selection criteria of quality and surface finish, safety, behavior, maturity, life cycle cost, load-carrying capacity, project time, lifespan, payback period, and structural dimension were analyzed to choose the uncorrelated MCDM and criteria approach. The relative relevance index gives this criterion a score of more than 5% and more than 50% overall. Initially, the model uses TODIM as a reference because of its capacity to examine both qualitative and quantitative data about risk seeking or aversion in connection to gain/loss functions [66, 122]. Consequently, TODIM has a strong connection (> 90%) with CoCoSo, WSM, WPM, and EDAS. GRA and PROMETHEE. Additionally, substantially associated were MOORA with EDAS, COPRAS with CODAS, and COPRAS with TOPSIS. For objective MCDM, the model employed the extremely uncorrelated TODIM, VIKOR, MOORA, COPRAS, and CODAS. Subjective MCDM analysis makes use of Consistency-AHP and the LFN. The AHN, Best Worst approach, and Graph-Theory-Matrix Approach are excluded from this model due to data limitations and irregular data conversion.

To summarize, the MCDM approach for Monte Carlo simulation is designed with the weight of objective (Entropy, CRITIC, LOPCOW, SD, SVP, and MEREC) and subjective (Delphi and pairwise comparison) criteria at a 95% confidence level. The performance score for the LFN, consistency-AHP, TODIM, COPRAS, MOORA, CODAS, and VIKOR MCDM is then generated using 100,000 random numbers. Then the formwork selection based on the rank of the 100,000 random numbers generated performance score. Thus, formwork selection as examined via the lens of LFN is demonstrated. Table 5 is used to analyze the consistency-AHP, TODIM, COPRAS, MOORA, CODAS, and VIKOR. Thus, to fix the optimal formwork, Monte Carlo simulation unites them all. The value indicated in Table 9 is the criteria value of the formwork system used for performance analysis and objective criteria.

The Delphi fuzzy weightings of formwork selection criteria importance and candidate were determined using the five LFN. It converted triangular fuzzy number of (0.75, 1.0, 1.0), (0.5, 0.75, 1.0), (0.25, 0.5, 0.75), (0, 0.25, 0.5), and (0, 0, 0.25) to the linguistic fuzzy expression of Very Important (VI), Important (I), Fair (F), Unimportant (U), and Very Unimportant (VU). Like this, the triangular fuzzy numbers for the linguistic variables (0.75, 1.0, 1.0), (0.5, 0.75, 1.0), (0.25, 0.5, 0.75), and (0, 0, 0.25) for Very Good (VG), Good (G), Fair (F), Poor (P), and Very Poor (VP). The Delphi method are used to aggregate fuzzy weights and aggregated fuzzy ratings on the Table 7. For a positive triangular fuzzy number (X₁, Y₁, Z₁); the Crisp values of fuzzy weighting and fuzzy ratings is calculated by ref. [56]:

Fuzzy rating/weighting = \(\frac{\text{d}}{\text{d}*\text{dt}}\), where d = [(X² + Y² + Z²)/3]^1/2 and dt = [(1−X)² + (1−Y)² + (1−Z)²)/3]^1/2; and the value is summarized in Table 8.

The transformation values of fuzzy ratings, as shown in Table 9, are then the average of the product of fuzzy rating and fuzzy weight. To determine the SAW utility values, the Transformation values of fuzzy ratings for each formwork type are first divided by the maximum value of the corresponding formwork sub criteria. The average of the product of the criteria weight and the corresponding Transformation values of fuzzy ratings for each formwork type is then determined. In the end, arrange it in ascending order as shown in Table 10.

From the LFN analysis using Monte Carlo simulation criteria weight, the order of the formwork system is SF > AL > P_oF > PF > TF. Similarly, the performance score and the rank of the formwork system by the uncorrelated MCDM method of the Monte Carlo simulation MCDM model are shown in Table 11 and Fig. 5. The average value of the 95% confidence interval of the comprehensive integrate MCDM model performance score is 0.10, 0.14, 0.22, 0.33 and 0.20 for timber (TF), plywood (P_oF), steel (SF), aluminum (AF), and plastic (PF) formwork using the uncorrelated MCDM model stated and summarized on Table 11. Then, the order of formwork system is AL > SF > PF > P_oF > TF.

Performance score of component and proposed MCDM performance

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To maximize the overall advantages of the formwork selection system, it is linearly programmed using the performance score of the integrated comprehensive state of art MCDM model, as illustrated in Table 12. This table displays the per-building profit formwork system selected performance score of a Monte Carlo simulation of MCDM.

FSj: Binary decision variable for formwork system selection j, j = 1, if Formwork system j is selected, 0 otherwise, n: Number of Formwork system, j: Formwork system, j = 1−n, T_b = Total Benefits, O_Bj: Overall benefit on the ranking of formwork system j from the performance score of an integrated Monte Carlo simulation of subjective and objective MCDM methods under an integrated subjective and objective criteria weight under a Monte Carlo simulation. C_ij: Average profit of formwork under Monte Carlo simulation per building in the high-rise building of i required when the project constructed by formwork system j, and D_i: Total capital available.

4.6.1 Constraint

• Total formwork profit per building, 0.418TF₁ + 0.317P_oF₂ + 0.303SF₃ + 0.288AF₄ + 0.293PF₅ ≤ 1.618

• To use the formwork in all structural condition, timber and plywood shall be combined with aluminum, steel and plastic as follow. TF₁ + AF₄ ≤ 1, TF₁ + SF₃ ≤ 1, TF₁ + PF₅ ≤ 1, P_oF₁ + AF₄ ≤ 1, P_oF₁ + SF₃ ≤ 1 and P_oF₂ + PF₅ ≤ 1.

• To the worst, the false structure can be constructed by combination of 3 formworks at a floor to substitute nonstandard shape of concrete structure, TF₁ + P_oF₂ + SF₃ + AF₄ + PF₅ ≤ 3.

• The decision variable; FS_j ≥ 0 for FS_j = 0—1; TF₁, P_oF₂, SF₃, AF₄ and PF₅ ≥ 0

The optimization formwork system has a coefficient of 1, PF, SF, and AF. PoF is roughly 0, and TF is 0. The best choice, with a maximum benefit of 75.45% under 13 constraints, is the formwork made of plastic, steel, and aluminum. According to the linear optimization, the investor should fund the construction of high-rise structures using a combined formwork system. A combination of aluminum, steel, and plastic formwork will be necessary to effectively finish projects on time and under budget. Thus, construction speed per floor of aluminum, steel, and plastic formwork is about 1.38 and 3.89 times better than plywood and timber formwork, respectively. In addition, the life cycle costs of the combined AL, SF, and PF can save about 10% and 45% of the extra per cycle costs incurred by PoF and TF, respectively.

Similarly, the combined AL, PL, and SF quality and surface finish are about 12.65 and 16.66 times more effective than TF and PoF, respectively. This indicated the project was more effective in the current formwork technology. In addition, this model summarized various orders of the model element LFN (SF > AL > PoF > PF > TF), consistency and TODIM of AF > PL > SF > PoF > TF, COPRAS and MOORA of AF > SL > PF > PoF > TF, and AF > PL > SF > PoF > TF of CODAS and VIKOR. This improves the performance and cost savings of selecting formwork material by a single MCDM method.

4.7 Model validation by previous studies

Malesia hosted the cradle-to-cradle life cycle assessment of formwork [7]. Even if the inclusion of subjective decision with extra criteria deviates the plastic formwork, the ranking of the formwork system is PF > SF > PoF > TF, which proves the comprehensive integrated subjective–objective MCDM model when AF is eliminated. Furthermore, aluminum is the least expensive formwork material when compared to steel and timber [101]. Thus, in the absence of aluminum formwork, steel formwork is the most effective. In general, in the consideration of all major formwork system, aluminum formwork is the best type of formwork available. However, both the current and previous study prove [7] that to reduce impurities, the material-intensive manufacturing industry's environmental effect must be addressed through the treatment and recycling of western material [102,103,104,105]. But in the current study, formwork's environmental impact was examined and chosen based on the quantity of harmful chemicals like CO₂, SO₂, NOx, and human non-carcinogenic toxicity [7] that were emitted unlike treating, processing and recycling of western material [102,103,104,105]. In terms of the quantity of harmful material released into the environment, the formwork system does not, however, have a final ranking [7]. Therefore, formwork production critically needs toxic material degradation methods like wastewater degradation by electrochemical in the textile industry [102,103,104,105]. In conclusion, the ranking of formwork systems is based the general effect of all formwork property agree with previous study, even if the previous study exclude aluminum formwork, so that it proves the comprehensive integrated subjective–objective criteria weighting MCDM model.

Selecting a formwork system can save costs while improving environmental protection. In this work, a new Comprehensive integrated subjective–objective criterion weighting MCDM model was created, which incorporates LFN, Consistency-AHP, TODIUM, MOORA, VIKOR, COPRAS, and CODAS. It is integrated objective (Entropy, CRITIC, LOPCOW, SD, SVP, and MEREC) and subjective (Delphi and pairwise comparison) criteria weighting. The findings showed that aluminum is the best formwork system for high-rise building construction followed by steel, plastic, plywood and timber. Furthermore, even though the initial cost increased, the formwork system's per cycle cost fell as reuse increased. Moreover, the overall cost and construction time of a high-rise structure are determined by its aluminum design. Aluminum, Steel, and Plastic constitute the optimum combination formwork system to optimize the benefit. Altogether, using aluminum formwork for building construction would result in lower startup costs, shorter project completion times, and higher formwork rental profits.

A comprehensive integrated subjective–objective criterion weighting MCDM model is an essential tool for dynamically choosing model components to enable reliable, accurate, and well-informed decision-making. The most difficult combination of mathematically complex, subjective and objective MCDM problems it can handle is risk aversion or seeking a gain or loss function, as well as hazy, subjective, and uncertain decision-making with little information. It is a useful technique for making decisions for important decision-making problems that may be applied to important MCDM problems, despite its laborious and complicated data collecting, analysis, and validation processes. Since the uncorrelated TODIM, VIKOR, MOORA, COPRAS, and CODAS are included in the model, it considers the assumption, benefit, and drawback of the highly correlated CoCoSo, WSM, WPM, EDAS, PROMETHEE, CODAS, and TOPSIS. The main advantage of this model’s result is the direct counterbalancing of criteria weighting and MCDM models.

This model fills the gap of MCDM and weighting approach selection. Overall, the comprehensive integrated subjective–objective criteria weighting MCDM model of LFN, Consistency-AHP, TODIUM, MOORA, VIKOR, COPRAS, CODAS and linear programming cemented by statistical theory and Monte Carlo simulation are dynamic, significant, and useful tools for identifying, to some extent, the most important multi-criteria decision problem of unknown condition. It includes all the important MCDM and criteria weighting assumptions by reducing the individual MCDM and criteria weighting methods' strengths, weaknesses, and uniqueness in terms of approach selection, objective scaling, parameter management, and economic significance analysis of multi-criteria problem.

Recommendation: The future researchers shall conduct the sensitivity of this model dynamic nature through changing the variable and study area. In addition, the environmental impact of formwork should be conducted based on the amount of adverse effect the individual pollutant.