Using the ordinal priority approach for selecting the contractor in construction projects

The contractor can be defined as a person or firm who handles the construction project, and ensures the execution of tasks planned for implementation at the construction site by directly communicating with other staff in the site, and involving them in the needed day-to-day activities whose performance is needed for the project’s ultimate fulfilment. The conventional roles of a contractor are known – such as responsibility for preparing and handling the subcontractor’s work with other personnel in a construction project (CITB 2015). Before a construction project commences, the contractor and the client are bounded through contracts that have been signed by both parties; and thus, to fulfil the client’s requirements, the contractor needs to use his experience and knowledge pertaining to construction activity and organise all the necessary resources (Yongtao 2008). There are many crucial factors that must be considered during the contractor’s evaluation and selection process, and these exercise a significant influence on project implementation. Fong and Choi (2000) identified eight ‘uncorrelated’ criteria for contractor selection, namely the following: tender price; financial capability; past performance; past experience; resources; current workload; past relationship; and safety performance. These are intended for application in contractor selection. According to numerous studies comprised in the literature (Cheng and Li 2004; Lam et al. 2005; Elazouni 2006; Brauers et al. 2008; Mitkus and Trinkūnienė 2008; El-Sayeg 2009; Mohamed and Majeed 2016), there are several criteria commonly used for contractor evaluation in the construction industry, namely the following: financial standing, technical ability, management capability, health and safety, and reputation.

Many researches (e.g. Zavadskas and Kaklauskas 1996; Ginevičius and Vaitkūnaitė 2006; Zavadskas and Vilutiene 2006) have pointed out that in construction it is essential to be able to consider the impacts of cultural, social, moral, legislative, demographic, economic, environmental, governmental and technological change, as well as impacts of changes in the business world on international, national, regional and local real estate markets, when selecting a contractor. The evaluation of contractors based on multi-attributes is becoming more popular and is, in essence, largely dependent on the uncertainty inherent in the nature of construction projects and subjective judgement of decision-makers. As we have identified through our literature review, there are many methods and techniques that have been used in contractor selection processes, as illustrated and summarised in Table 1; some of these methods are based on a pairwise comparison, decision matrix, averaging and normalisation procedures, and ideal solutions.

The OPA is a new method of objective decision-making that can be used to handle situations involving numerous attributes. It is a cutting-edge method for solving MCDM issues using a linear mathematical model. OPA uses an easy method to determine the weights of alternatives, experts and attributes all at once. Ataei et al. (2020) suggested OPA as a solution for the tackling of MCDM issues that may be constructed using ordinal relationships while also addressing the shortcomings of some MCDM approaches. Ataei et al. (2020) demonstrated the effectiveness of OPA over similar decision-making approaches by using various arguments, as presented below:

Instead of a pairwise comparison or a decision matrix, the OPA method requires the order of attributes and alternatives.

OPA was used to resolve project selection issues in the context of project management with huge and partial data sets (Mahmoudi et al. 2020). Additionally, to address the uncertainty in practical situations, OPA was expanded in fuzzy and grey settings (Mahmoudi et al. 2021a, 2021b). There are several studies (e.g. Mahmoudi and Javed 2021; Quartey-Papafio et al. 2021; Sadeghi et al. 2021; Shajedul 2021) offering a confirmation of the soundness of OPA for solving MCDM problems objectively, flexibly and effectively, as well as in the absence of there needing to be concerns with regard to pairwise comparisons and normalisation and completeness of data.

The core idea of the OPA technique is to build a comprehensive model that accounts for all aspects of decision-making challenges, including experts, criteria and alternatives. The experts offer an unbiased opinion based on the importance of the criteria and alternatives. As a result, (I * j) rankings are produced for each of the (k) current choices. The sets, parameters and variables employed in the OPA method’s mathematical model are listed in Table 2.

where k alternatives will be based on the stages below:

Experts rank the attributes.

As a result, the following are the main steps of the OPA method (Ataei et al. 2020):

Specification of the criteria

Ataei et al. (2020) stated that the linear model (Eq. [1]) should be created based on the data acquired in the previous steps. 1 Objectivefunction=MaxZ \[\text{Objective}\,\text{function}=\text{Max}\,Z\]

S.t., z≤i(j(r(wijkr−wijkr+1)))∀i,j,kandrz≤ijmwijkm∀i,jandk∑i=1p∑j=1n∑k=1mwijk=1wijk≥0∀i,jandk \[\begin{matrix} z\le i\left( j\left( r\left( {{w}_{ijk}}^{r}-{{w}_{ijk}}^{r+1} \right) \right) \right)\,\forall i,j,k\,and\,r \\ z\le ijm{{w}_{ijk}}^{m}\,\forall i,j\,and\,k \\ \sum\limits_{i=1}^{p}{\sum\limits_{j=1}^{n}{\sum\limits_{k=1}^{m}{{{w}_{ijk}}=1}}} \\ {{w}_{ijk}}\ge 0\,\forall i,j\,and\,k \\ \end{matrix}\]

where Z is unrestricted in sign.

Eqs, (2)–(4) can be used to solve the model and determine the expert(s), criterion and alternative weights. Eq. (2) will be applied to obtain the weights of the alternatives. 2 WK=∑i=1p∑j=1nWijk∀k \[{{W}_{K}}=\sum\limits_{i=1}^{p}{\sum\limits_{j=1}^{n}{{{W}_{ijk}}\,\forall k}}\]

In order to determine the weights of criteria, Eq. (3) will be employed. 3 Wj=∑i=1P∑k=1mWijk∀j \[{{W}_{j}}=\sum\limits_{i=1}^{P}{\sum\limits_{k=1}^{m}{{{W}_{ijk}}\,\forall j}}\]

In order to calculate the weights of experts, Eq. (4) will be utilised. 4 Wi=∑j=1n∑k=1mWijk∀j \[{{W}_{i}}=\sum\limits_{j=1}^{n}{\sum\limits_{k=1}^{m}{{{W}_{ijk}}\,\forall j}}\]

As a research method, the Delphi survey tries to generate a ‘consensus opinion of a panel of specialists through a recurrent exercise in which participants have the option to adjust their opinions without being forced through the appropriate management of controlled feedback from the coordinator’ (Hasson and Keeney 2011). Even when the participants know each other, without fear of collusion or coercion, the Delphi method is an excellent research instrument for tackling difficult problems in the engineering sector (Ogbeifun et al. 2016). Practically, the Delphi approach is the only study method that allows participants to react with one other’s viewpoints without being forced to do so, alter their positions as needed and maintain anonymity. Three or four rounds are commonly involved in a Delphi study (Welding 2013). The approach has various advantages, including the following (Ralitsa et al. 2005):

It offers the ability to carry out research in a geographically distant setting without physically bringing the participants together.

There is no consensus on panel size for Delphi investigations, nor is there a clear definition of ‘small’ or ‘big’ samples. There could be as few as 3 people on a Delphi panel or as many as 80. It is rare to find a Delphi research with less than 10 participants (Malone et al. 2005). It is important to select people who are knowledgeable in the field of study and are willing to commit themselves to multiple rounds of questions or interactions on the same topic (Grisham 2009). Wainwright et al. (2010) and Crane et al. (2017) stated that in Delphi exercises, a minimum of 12 respondents is generally considered to be sufficient to enable consensus to be achieved; larger sample sizes can provide diminishing returns regarding the validity of the findings.

PCA is the most widely used multivariate analysis technique, with applications in practically every scientific field. One of the main uses of PCA, which has been widely used by academics in a range of domains, is dimensionality reduction (Preetha and Vinila 2020). As its name implies, instead of studying every aspect of a problem, the PCA can help with some of the most crucial aspects and identify key components. In fact, the PCA extracts the attributes with a factor pattern coefficient greater than 0.3 that are the most valuable (Ringnér 2008; Lever et al. 2017).

A review of the literature and field visits to the related government directorates in Iraq (e.g. The Housing Directorate, Buildings Directorate, National Center for Engineering Consultancy and Al-Mansour General Engineering Company) were conducted to collect the related data about the criteria that will be used in the decision-making process for selecting the contractor of the construction project. The Delphi survey with 12 experts was performed to identify the selection criteria/attributes. All the selected experts are working in the planning and management of construction projects and possess an experience of more than 15 years; additionally, they also have a willingness to participate in this process. Figures 2–4 show the working sector, the academic degrees and the specialisation for the selected sample; and Table 3 lists occupational information pertaining to the experts’ sample in the Delphi survey.

Fig. 2:

Fig. 3:

Fig. 4:

The form’s questions of the first round of the Delphi were formulated. Similar to the approach adopted in the studies of Al-Agele and Al-Kaabi (2016) and Mohammed and Jasim (2018), and as indicated in Table 4, the Likert 5-scale with weighted value (WV) was utilised.

The 12 experts were asked to rank the importance of the 40 selection criteria included in the questionnaire form; the participants had the option to add more criteria if they felt the need to do so. Face-to-face interviews were conducted with each participant in the first round to ensure that the format of the round’s questions was clear. After Delphi’s first round, the responses and recommendations of the selected experts were thoroughly examined and statistically analysed using XLSTAT software, using which were computed the mean (M), the standard deviation (SD) and the Cronbach’s alpha (α). The mathematical formula for determining the Cronbach’s alpha (α) is shown in Eq. (5) (Al-farra 2009): 5 α=KK−1(1−∑ si2st2) \[\alpha =\frac{K}{K-1}\left( 1-\frac{\sum{s{{i}^{2}}}}{s{{t}^{2}}} \right)\] where K represents the number of elements in the group, si the element variance and st the variance of the total score of the elements.

The results of the analyses showed that the mean of Cronbach’s alpha (α) for all questions was more than (0.7). In the second round of the Delphi survey, the criterion with an average value less than (3.4) will be excluded. In addition, a number of criteria were incorporated or cancelled based on the opinions of the participants. Therefore, the list of criteria/attributes used in the decision to select the best bidder or contractor in the implementation of a construction project include 23 criteria at the end of the first round. These selection criteria/attributes that resulted from the first round will be used in the second round of the Delphi survey. In the second Delphi round, experts were asked to rank a list of 23 selection criteria that resulted from the first round of Delphi. Statistical analysis of expert responses in the second Delphi round showed an average Cronbach’s alpha (a) value equal to (0.97), and there were 20 criteria having an average value above (3.4); accordingly, only three criteria will be excluded.

In the third round of the Delphi procedure, the selection criteria from the second round will be applied. The same appointed experts were asked to re-evaluate the relative weight of the selection criteria that had passed from the second Delphi round. The results of the statistical analysis of the third round showed that all criteria/attributes of the selection process for the best bidder/contractor for the implementation of the construction project obtained an average value of more than (3.4) (high–very high, an important degree in the decision-making process), with a Cronbach’s alpha (a) of (0.959), as illustrated in Figure 5. Therefore, the results of the third round, as presented in Table 5, demonstrate lack of need for a fourth round, because the responses of the experts were consistent.

Fig. 5:

It is necessary to complete the Kaiser–Meyer–Olkin (KMO) test before performing the PCA. KMO is capable of determining whether the data are appropriate for performing the PCA. It is not acceptable to conduct the PCA if the KMO is smaller than (0.5) (Mahmoudi et al. 2020). Kaiser (1974) developed the equation of the KMO calculation, as shown in Eq. (6): 6 KMO=∑i∑j≠irij2∑i∑j≠irij2+∑i∑j≠imij2 \[KMO=\frac{\sum\nolimits_{i}{\sum\nolimits_{j\ne i}{r_{ij}^{2}}}}{\sum\nolimits_{i}{\sum\nolimits_{j\ne i}{r_{ij}^{2}}}+\sum\nolimits_{i}{\sum\nolimits_{j\ne i}{\text{m}_{ij}^{2}}}}\] (Kaiser 1974)

where R =rij is the correlation matrix and U = [uij] is the partial covariance matrix.

The KMO value was calculated using XLSTAT software. The results showed that the specific criteria/attrib- utes that were used to select the best bidder/contractor for the implementation of the construction project had a KMO value of (0.672). Also, the PCA value showed that 20 criteria/attributes are the most valuable, and there is no way to reduce them because they all have factor pattern parameter values of more than (0.3). Table 5 shows the final results of the selection criteria/attributes of the best provider/contractor for the implementation of the construction project.

The decision-maker/expert plays a valuable role in the success of construction projects. The process of selecting a decision-maker needs to be helmed by a person or a team themselves having the requisite qualifications, because, otherwise, the result would be the choice of an unsuitable person to play the role of the decision-maker. So, in identifying this problem and establishing a means for its prevention or rectification, we are able to suitably address one of the main reasons underlying the failure of construction projects. It is proposed that the experts’ evaluation system can be implemented to overcome this problem, and the following steps were performed in that regard:

Identifying the main criteria and sub-criteria of selection of the decision-makers/experts in the construction projects by conducting face-to-face interviews with a group of experts;

Information about the criteria to be employed for selection of experts/decision-makers in construction projects was gathered by reviewing the related literature and visiting the related government directorates, as well as private and public construction companies. Then, to identify the main criteria and sub-criteria that would need to be applied for the selection and evaluation of the experts/ decision-makers, face-to-face interviews were conducted with a group of experts possessing more than 15 years of experience in construction projects’ management. After analysing the experts’ opinions, a list of the main criteria and sub-criteria has been formulated. The arithmetic mean was used to rank and calculate the weight value of each main criterion, while using the expert- suggested weights values for the sub-criteria as presented in Table 6. Depending on the results presented in Table 6, the flowchart of the proposed experts’ evaluation system was developed as shown in Figure 6. Then, the proposed evaluation system program was created by using Visual basic software; and, to enable the obtaining of the engineer’s acceptance for taking on the role of an expert/ decision-maker in construction projects, the final output degree of the proposed experts’ evaluation system must be not less than a score of 50.

Fig. 6:

Finally, the present study stated that the sub-criterion for each expert should be evaluated by the company’s top management based on the recorded history of the expert under consideration.

The multi-criteria attribute is regarded as a defining characteristic of the decision-making involved in the selection of a bidder/contractor for implementing the construction project; accordingly, the present study uses the developed proposed model to enhance decision-making with regard to the process involved in the selection of a contractor in the construction project, as illustrated in Figure 7.

Fig. 7:

A rest house construction project in Dhi Qar Governorate was selected as a case study for the proposed model’s application, so as to ascertain its efficacy in enhancing the decision-making process involved in construction projects. This project is one of the projects of the Iraqi Ministry of Construction and Housing, which is subject to the instructions for implementing Iraqi government contracts. The owner aims to select the best contractor to implement this project from among four bidders. Three experts were assigned to participate in the model application in collaboration with the owner’s crew. In order to rank, and ascertain the degree of suitability of, the selected experts concerning participation in the decision-making process, the proposed expert evaluation system was applied. According to the qualifications of each expert, shown in Table 7, the results of the proposed expert evaluation system showed that the rank and degree of each expert’s evaluation are as follows:

Exp. 1 with a score of (75.12)

Based on the evaluation results, all the appointed experts have been found suitable concerning the assumption of a role in the decision-making process, and the rank of each of them will be used when applying the OPA model. The bidder/contractor selection criteria that resulted from the Delphi survey and PCA were adopted in this case study. The appointed experts were then asked to rank these selection criteria for the best bidder/contractor. The final ranking of the selection criteria was collected, as shown in Table 8, and will used in applying the OPA model. The qualifications of the four competing contractors were collected, the experts were asked to rank the four contractors according to their criteria. The results of the competing contractors’ ranking are summarised in Table 9. As for formulation of the OPA mathematical model, MATLAB software was used for the realisation of the present study’s proposal of a computerised program for formulating the OPA mathematical model; Figure 8 shows the interface of this computerised program. So, the research applied the proposed computerised program to formulate the OPA mathematical model for selecting the best bidder/contractor. Once the OPA mathematical model for selecting the best bidder/contractor was formulated, the research used the LINGO software to solve the mathematical model of this problem. Based on the results from the LINGO software, the research calculated the weight of each alternative, the weight of each criterion and the weight of each expert by solving Eqs (2), (3) and (4), respectively. The results showed that the weights of Exp. 1, Exp. 2 and Exp. 3 are (0.589), (0.262) and (0.148), respectively, as shown in Table 10; and the weight of each criterion has been calculated as illustrated in Table 11. Finally, the weights of the contractors ‘R’, ‘F’, ‘A’ and ‘B’ are (0.234803), (0.312379), (0.249111) and (0.203858), respectively, as shown in Table 12. Further, all weights of alternatives are more than the Z value (0.0249) that resulted from solving the OPA mathematical model. According to the mentioned results, the best contractor for implementing the rest house building in Thi-Qar Governorate is the contractor ‘F’, followed by ‘A’, ‘R’ and ‘B’.

Fig. 8:

For comparison, when the principle of the lowest bid was applied in the selection of the best contractor for the project of construction of the rest house building in Thi-Qar Governorate, together with the applicability of the bid amounts for each contractor as illustrated in Table 13, the results showed that the contractor ‘B’ was the best alternative, followed by ‘A’, ‘F’ and ‘R’.

In the real world, the traditional method, involving the usage of the weighting form that is based on an averaging method (stated in the instructions for implementing Iraqi government contracts), was applied to select the best contractor for the project of construction of the rest house building in Thi-Qar Governorate, by a new group of the experts (not the same experts of the case study; and these experts were chosen without making an assessment of their attributes); the results showed that the contractor ‘F’ was the best alternative, followed by ‘R’, ‘A’ and ‘B’, and the scores of alternatives in this application are illustrated in Table 14. For this case study, the final rank of contractors from using the proposed framework for enhancing the decision-making process differs in the second rank from using the traditional method and differs in all ranks from using the principle of the lowest bid. The validity and usefulness of the proposed framework for enhancing the decision-making process are thus well indicated by these results.

Every decision-making process can benefit from a sensitivity analysis. The consequences of any modifications to the input data are often of interest to project managers and decision-makers. So, another approach to assess the effectiveness of the OPA model will be executed using a sensitivity analysis, by adjusting the priority of experts, criteria and alternatives. Three scenarios for sensitivity analysis will be applied as follows:

First scenario: The ranks of experts that are used in this scenario are the same ranks that are obtained from applying the proposed experts’ evaluation system, as mentioned in the case study, and as follow: (Exp.1 > Exp.2 > Exp.3); this scenario is called ‘Basic or Original’.

After formulation of the OPA mathematical model for each scenario in the construction project under study and solving them with the use of LINGO software, the results showed that the weight of each alternative was affected in each scenario as shown in Figure 9. Moreover, the weight of alternative ‘F’ is the highest and followed by the weight of alternative ‘A’ in the first and second scenarios, while in the third scenario the weight of alternative ‘F’ stayed the highest but was followed by the weight of alternative ‘R’. The sensitivity analysis result indicates a possibility for there being an effect on the final decision resultant to changes taking place in the rank of experts. Also, the weight of each criterion was affected in each scenario, as shown in Figure 10, where the weight of criterion ‘C12’ was the highest weight and followed by the weight of criterion ‘C2’ in the first and second scenarios, while in the third scenario the weight of criterion ‘C2’ was the highest and followed by the weight of criterion ‘C1’. So, this result indicates the possibility for there being an effect on the final decision resultant to changes taking place in the rank of experts.

Fig. 9:

Fig. 10:

Finally, the proposed computerised programs were sent to experts with the questionnaire form and the flowchart of the proposed framework, to evaluate their performance. The evaluation process was conducted through 14 experts, all of them possessing greater than 20 years’ experience in planning, consulting and construction management. According to the experts’ answers, as shown in Table 15, the research concluded that the proposed framework and the computerised program have a high applicability in construction projects and provide a high contribution in enhancing the decision-making process. Moreover, it has a high degree in the organisation, suitability and easily in use, and accuracy in outputs.