Improving AHP for construction with an adaptive AHP approach (A3)
Chun-Chang Lina, , Wei-Chih Wanga, , and Wen-Der Yub,
Department of Civil Engineering, National Chiao Tung University, 1001, Ta-Hsueh Road, Hsinchu 300, Taiwan
Abstract
The Analytic Hierarchy Process (AHP) approach is widely used for multiple criteria decision-making in construction management. However, the traditional AHP requires that decision makers remain consistent in making pairwise comparisons among numerous decision criteria. Accurate expression of relative preferences on the criteria is difficult for decision makers due to the limitations of the 9-value scale of Saaty. Although Saaty proposed a method to assess the consistency of pairwise comparisons, no automatic mechanism exists for improving the consistency for AHP. This work proposes an adaptive AHP approach (A3) that uses a soft computing scheme, Genetic Algorithms, to recover the real number weightings of the various criteria in AHP and provides a function for automatically improving the consistency ratio of pairwise comparisons. A real world construction management example for determining the weightings of the multiple criteria for a best-value bid is chosen as a case study to demonstrate the applicability of the proposed A3. The application results show that the proposed A3 is superior to the traditional AHP in terms of cost effectiveness, timeliness, and improved decision quality.
Keywords: Multiple criteria analysis; Analytic hierarchy process; Soft computing; Genetic Algorithms; Construction
Article Outline
1. Introduction
2. The traditional AHP approach for MCDM problems
3. Proposed adaptive AHP approach (A3)
3.1. Selection of soft computing scheme
3.2. Definition of objective functions
3.3. Determination of coding scheme
3.4. Formulation of GA for A3
3.5. GA operations in A3
4. Demonstrated case study
4.1. Description of case background
4.2. Weighting approaches
4.2.1. Traditional AHP weightings (AHP weightings)
4.2.2. Proposed A3 weightings (A3 weightings)
4.3. Evaluation results
5. Benefits and limitations
5.1. Benefits
5.1.1. Cost effectiveness
5.1.2. Timeliness
5.1.3. Improved decision quality
5.2. Limitations
6. Conclusion
Acknowledgements
References
1. Introduction
Construction management involves numerous multi-criteria decision-making (MCDM) problems. Correctly weighting various criteria is the key issue in a MCDM problem. The use of the Analytic Hierarchy Process (AHP) approach [1] and [2] to assess the criterion weightings in MCDM recently has become popular in different areas of construction management, such as project management [3] and [4], contractor selection [5], [6], [7] and [8], procurement [9], facility location determination [10], construction safety management [11], project/proposal evaluation [12] and [13], green building evaluation [14], and technology/equipment/material selection [15], [16] and [17].
The AHP method can be used to construct the additive value functions for preferentially independent MCDM problems [18] and [19] and to determine the membership values of the elements in a fuzzy set [20]. However, several researchers, including Triantaphyllou and Mann [21] and Lakoff [22], have pointed out the weakness of AHP in assessing the relative importance weights of various criteria. This weakness results primarily from two limitations: (1) the difficulty of using Saaty's discrete 9-value scale to reflect the belief of decision makers in the relative importance relationship among the various criteria; (2) the difficulty of identifying the in-between numbers of fuzzy sets. Saaty's discrete 9-value scale method forces decision makers (DMs) to select numbers from the finite set {1/9, 1/8, 1/7, …, 1, 2, 3, …, 7, 8, 9}, contradicting the real world fuzzy memberships of elements in a fuzzy set. In most real world problems, the membership values in a fuzzy set take on continuous values (namely real numbers) rather than discrete numbers [21]. Triantaphyllou and Mann [21] found that this limitation can cause extremely high failure rates for AHP. Furthermore, the ability of humans to accurately express their knowledge decreases with increasing problem complexity. Thus, as the number of criteria in AHP increases, DMs are likely to make inconsistent judgments during pairwise comparison. The above two limitations are sources of the high Consistency Ratio (CR), that is the high inconsistency, when adopting the AHP method.
Saaty devised a method of measuring CR (see Saaty [2]). If CR exceeds 0.10, the pairwise comparison needs to be reassessed. The reassessment process is tedious and does not guarantee the consistency of pairwise comparisons. Thus, another reassessment is necessary if the resulting CR remains unsatisfactory. The reassessment process is impractical in situations where time is crucial for DMs who are top managers of a company or for urgent MCDM problems that must be solved rapidly. Reassessment is simply too expensive for sorting out inconsistencies [23]. Tam et al. [23] proposed a tool that aids AHP decision-making that changes the consistency checking from a 1–9 value scale to a 1–3 value scale, thereby reducing the time required to handle inconsistency in decision-making for construction problems. Alternatively, the development of a method that automatically improves the CR of pairwise comparisons and recovers the continuous relative importance weights of various criteria is extremely attractive.
This investigation develops an Adaptive AHP Approach (in brief A3) using Genetic Algorithm (GA) to recover the continuous relative importance weights of the various criteria based on two objective values: (1) CR, and (2) the difference of the derived pairwise weighting matrix (PWM) from the initial PWM. Since the search process of GA is guided by minimizing CR, it results in an adapted PWM with lower CR, which is acceptable in terms of the consistency requirements of AHP. The search process is also guided by minimizing the difference from the initial PWM. Thus, the resulting PWM reserves the original beliefs of the DM regarding the relative importance relationship among the criteria. The proposed A3 also provides an automatic mechanism for improving CR, and thus eliminates the reassessment process of AHP.
The remainder of this paper is organized as follows: Section 2 reviews the traditional AHP approach and its application in determining the fuzzy weightings of the various criteria in the MCDM; Section 3 then presents the proposed A3; next, Section 4 analyzes the proposed A3 for a real world best-value-bid MCDM problem to demonstrate the applicability of the proposed A3; finally, advantages, limitations, and future research directions are discussed and conclusions presented.
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