A hybrid lexicographic and VIKOR approach for prioritizing construction projects by considering sustainable development criteria

Article history: Received: November 5, 2017 Received in revised format: February 20, 2017 Accepted: March 10, 2018 Available online: March 10, 2018 Nowadays, one of the challenges in the organizations according to budget limitations in the companies, is how to prioritize their project portfolios in the events of their strategies. In other words, organizations are seeking to allocate resources in order to gain the maximum profit according to budget limitations. In this article, a hybrid decision making method is used to prioritize construction project portfolio by considering sustainability criteria. First, Lexicographic method is applied to weight the sustainability criteria. Then, by considering the weights derived from the Lexicographic and sustainability criteria, projects are prioritized based on VIKOR method. The proposed method of this study is applied for a case study of projects in the refinery scope. © 2018 by the authors; licensee Growing Science, Canada.


Introduction
Nowadays, one of the major challenges of the organizations in regard to their budget limitations is to decide how to prioritize the project portfolio according to strategies.In other words, the organizations are seeking to determine the ways to allocate resources to their plans and projects to receive the maximum profit according to the budget limitations.The necessity of a management system that incorporates different dimensions of the organization has made the project portfolio management to be of great interest for many managers.The portfolio management, in contrast to the project management, is not started with the beginning of the project and not terminated with the end of the project and it is endless.In such a viewpoint, the projects are regularly monitored and revised.One of the main advantages of the portfolio management is that it shifts the monitoring parameters towards macro scale.Although all selected plans and projects take steps in line with the organization strategies and are aligned with the business of the organizations, their importance is not equal.Hence, the selected plans and projects are required to be prioritized so that their relative importance is identified.Usually, after the selection of the plans and projects of the organization, they are prioritized.
To evaluate the projects, the ranking methods are usually used or the relative weight of each project is identified according to the organization's criteria using multi-criteria decision making techniques.These methods provide the manager with an ordered list in which the priority of the projects has been determined.These methods are easily understood and can be applied by the managers.But, one of the major deficiencies of these methods is that they provide the managers with no alarm about the irrelevancy of the projects with the organizational strategies.To tackle this problem, the selection process must first be accomplished on the portfolio and then the selected projects are prioritized.Jabbarzadeh (2018) presented a multi-criteria method for contractor selection.The criteria used are namely; Experience, Financial stability, Quality performance, Manpower resources, Equipment resources and Current workload for evaluating different contractors.Analytical hierarchy process (AHP) (Saaty, 1989) with TOPSIS (Hwang & Yoon, 1981) were used in the study to rank the contractors as alternatives according to proposed criteria.Sadjadi and Sadi-nezhad (2017) used TOPSIS as a multicriteria decision making method to rank different oil and gas projects in Canada in the field of investment.They considered different criteria such as net present value, rate of return, benefit-cost analysis and payback period along with the intensity of green gas effects for ranking the abovementioned projects.
Using the fuzzy multi-criteria decision making methods Rathi et al. (2016) prioritized and selected the six sigma projects.They used a hybrid method of the TOPSIS and VIKOR (Opricovic & Tzeng, 2007) in a fuzzy context, investigated 7 critical criteria for selecting the projects and applied the proposed method for a case study to evaluate its efficiency.Yousefi and Hadi-Vencheh (2016) prioritized and selected the six sigma projects using a combination of hierarchical analysis, TOPSIS, and data envelopment analysis (DEA) (Charnes et al., 1984) and assigned the weights to all the proposed criteria and projects as their priority.Finally, they selected the projects of high priority.Rahmani et al. (2012) used analytic network process (ANP) (Saaty, 2013) and TOPSIS in a fuzzy environment for selecting and prioritizing of oil and gas projects.First, their considered criteria were weighted by the analytic network process and then, the projects were prioritized by the fuzzy TOPSIS.Abdollahi et al. (2015) used three methods of the DEA, DEMATEL (Yu, 1973;Duckstein & Opricovic, 1980), and ANP to select and prioritize the supplier portfolio.First, using the analytic network process, the criteria were weighted and then, to select and prioritize the projects, the DEA method was applied and finally, to identify the dependency existed among the criteria, the DEMATEL technique was used.
To validate their proposed model, they implemented it in a case study.Baynal et al. (2016) used a combined method of two multi-criteria decision making methods (the hierarchical analysis and PROMETHE method) for prioritizing the studied cases of Turkish projects.First, using the hierarchical process analysis, they weighted the considered criteria and then, using the PROMETHE method, they prioritized the projects and selected ones with more priority.Salehi (2015) used a combination of multicriteria decision making including the VIKOR and hierarchical analysis to prioritize the project portfolio and then selected the projects with a higher priority.Using three methods of MCDM methods including Delphi, hierarchical analysis, and TOPSIS, Pangsri (2015) selected and prioritized the projects.They first weighted the criteria by the hierarchical analysis and prioritized the projects by the TOPSIS method, and considering the acquired weights, selected the projects of high priority.Taylan et al. (2014) prioritized the construction projects by means of a combined method of fuzzy hierarchical analysis and fuzzy TOPSIS.They used five criteria of the cost, time, quality, environmental sustainability and security in prioritizing the projects.They applied their model to 30 construction projects.Wang et al. (2013) addressed the problem of prioritizing six sigma projects with the aim of maximizing financial profit and considering other impacts on the organization.They used a combination of the analytic network process and VIKOR methods for prioritizing the projects.Also, they used the DEMATEL technique to identify the precise relationships of the proposed criteria.Khalili-Damghani et al. (2013) utilized a combination of the TOPSIS, goal programming, and hierarchical analysis process to select and prioritize the optimized project portfolio.Their study was carried out in two phases.In the first phase, the importance of the criteria provided by experts was identified using the goal programming and in the second phase, the TOPSIS and the hierarchical methods were used to prioritize the projects according to the priority score.Amiri et al. (2010) proposed a combined method of the hierarchical analysis process and TOPSIS for prioritizing and finally selecting the oil and gas portfolio projects.
In this paper, a combination of two decision making models has been used for prioritizing different projects.For this purpose, first, the factors that affect the success of the projects prioritization problem, which are sustainability criteria are studied.Then, using the lexicographic method, for each sustainability criteria, some weights are assigned and these weights are considered as the input of the VIKOR method which its outcome will be a rank for each project that represents the organization projects prioritization.Finally, the proposed method is applied for a case study.An obvious innovation of this paper is to consider the sustainability criteria that has not been considered before in the prioritization problem of the project portfolio.Also, applying the lexicographic method is another innovation of this model that considers the pair-wise comparisons in an interval form and somehow incorporates the uncertainty in the decision making and its combination with the VIKOR method (Yu, 1973) is a new hybrid method.
The rest of the paper is organized as follows.Section 2 explores the sustainability criteria that are important for the prioritization process.Section 3 introduces the proposed methodology and section 4 analyzes the data and research findings.Section 5 concludes the paper.

Identification of the prioritization criteria
Regarding the reviews that have been accomplished in the literature of sustainable development criteria in the context of the project portfolio (Siew, 2016;Wang et al., 2013;Xing et al., 2009), especially the construction projects, a set of sustainability criteria can be considered regarding the organization's objectives, which fall in three categories of the economic, environmental, and social criteria (Tables 1, 2, 3).Finally, in Table 4, all sustainability criteria have been gathered.

The Methodology
In this section, a brief description of the proposed methods is given.

The Lexicographic Method
The preference of criterion over the criterion j may fall between and that are non-negative real numbers and .Hence, , where According to the Arbel and Vargas researches (1993), the matrix ( ) A a   is a comparison matrix of consistent intervals if and only if it satisfies the following inequality: max( .) min( .) (2) The preference degree of interval a over b (or a > b) is defined as follows: . are the interval weights, the possible relations are shown in the following figure: It's possible that the interval judgments be considered as a limitation on the weights.Therefore, The following inequality is only for the consistent judgments.In case of inconsistency, the deviation variables .can be defined as the following inequality: . 1. … .
(5) in which . are both nonnegative real numbers but they cannot be simultaneously positive, that is .=0.It's desirable that these deviation variables be small values as long as it's possible.To achieve this, the lexicographic goal programming model has been used:

The VIKOR Method
In decision making problems with m criteria and n alternatives, the VIKOR method is used for prioritizing the alternatives and selecting the best one.The steps of this method are as follows: Step 1: Preparing the decision making matrix (the decision matrix X whose elements are xij.) Step 2: Normalizing the decision making matrix and identifying the weighted decision making matrix The normalization is carried out by the following formula: Then, to calculate the weighted decision matrix, the weight of each criterion is multiplied by the normalized decision matrix.
Step 3: Identifying the best and the worst value of each criterion from the weighted decision making matrix In this step, the maximum and the minimum values of each column are identified.That is, the two elements that have the greatest positive value and the greatest negative value, respectively.Accordingly, if the criterion is a negative one, the maximum value will be the lowest value and the minimum value will be the greatest one, and vice versa.
Step 4: Calculating the utility index Sj and the regret index Rj 1 .
i f  : the maximum value of the weighted normalized matrix for each column ij f : the score of the corresponding alternative for each criterion in the weighted normalized matrix f  : the smallest number of the weighted normalized matrix for each column In this method, for each alternative, a utility index is obtained for each criterion where the sum of these scores identifies the final index Sj.The biggest Sj of each alternative for each criterion is the regret index (R) of that alternative.
Step 5: Calculating the value Q .
( 1 v ) .Step 6: The final ranking In the last step of the VIKOR technique, according to the values of S, R, and Q, the alternatives are ascendingly sorted in three groups.The best alternative is the one has the smallest value of Q provided that the two following propositions.
Proposition 1: if the alternatives A1 and A2 have the first and second ranks, the following relation must be satisfied: Proposition 2: the alternative A1 must be known as the best rank at least in one of the R and S groups.
If the first condition is not satisfied, both alternatives are the best one.If the second condition is not satisfied, then both alternatives A1 and A2 are selected as the best one.

The Analysis of Research Data and Findings
To prioritize the project portfolio, a hybrid optimization method of the lexicographic and VIKOR methods has been used.First, the factors that are effective in prioritizing the project portfolio are selected using the lexicographic method.Then, the weights of these factors are identified.The decision making matrix in this method is an interval based matrix and can be seen in Tables 5 and 6.These tables respectively present the lower and upper limits of the decision makers' preferences.The proposed method has been applied to a case study of 19 construction projects in the field of the refinery.Due to the security concerns, we are not allowed to mention full information about the projects.

Table 5
Lower bound of lexicographic decision matrix After applying the lexicographic method, the weights obtained for each factor are given in Table 7.

Results of the VIKOR method
Based on the results of the lexicographic method and the weights obtained for each factor, we apply the VIKOR method to prioritize the 19 projects of the organization.In Table 8, the initial decision making matrix has been shown.

Table 8
The initial decision matrix of the VIKOR method In the next step, the values of the VIKOR index (Q) have been calculated and, along with the other utility and satisfaction indicators, shown in Table 12.Also, the final ranking of the alternatives is given in this table.As it can be seen in Table 12, the final results of prioritizing the selected projects have been shown in the form of a ranking.It is observed that the project 17 has the highest priority and the project 18 has the lowest priority.Considering the prioritization results, the chief managers of the organization can decide about the implementation and allocation of financial and non-financial resources to each project.

Conclusion
Nowadays, the problem of how to institutionalize the project management in project-based organizations and utilizing its advantages in the long term has been a main concern of the project portfolio and special techniques of project management have been usually neglected.In this regard, the project portfolio management can be an extremely useful tool in improving the efficiency and effectiveness of the organization's projects.Many organizations have defined and started a large set of projects that need a budget more than 10 times of what has been previously set.Here, the role of the high-level management was highlighted.Considering the organizational strategic requirements, they select and prioritize the suitable projects in each time period and allocate them the resources.In this paper, a hybrid decision making method has been proposed for prioritizing the projects by considering the factors of the sustainable development.This is a comprehensive and applicable method especially for prioritizing the construction projects.Also, using the lexicographic method that considers the pairwise comparisons in an interval form, the uncertainty has been incorporated into the decision making model that in turn minimizes the pairwise comparison errors.Finally, the prioritization of the construction projects is carried out in such a way that incorporates the environmental requirements that are from the essential concerns.
Sj= The sum of values S for each alternative S -=The minimum value of index S for each alternative S + =The maximum value of index S for each alternative Rj= The sum of values R for each alternative R -= The minimum value of index R for each alternative R + = The maximum value of index R for each alternative

Table 6
Upper bound of lexicographic decision matrix

Table 7
Weight of criterion derived from lexicographic method

Table 12
Final ranking of the alternatives