1 Construction Management and Economics (December 2004) 22, Contractor selection using the analytic network process EDDIE W. L. CHENG and HENG LI* Department of Building and Real Estate, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong Received 30 January 2003; accepted 9 January 2004 Contractor selection is one of the main activities of clients. Without a proper and accurate method for selecting the most appropriate contractor, the performance of the project will be affected. The multi-criteria decisionmaking (MCDM) is suggested to be a viable method for contractor selection. The analytic hierarchy process (AHP) has been used as a tool for MCDM. However, AHP can only be employed in hierarchical decision models. For complicated decision problems, the analytic network process (ANP) is highly recommended since ANP allows interdependent influences specified in the model. An example is demonstrated to illustrate how this method is conducted, including the formation of supermatrix and the limit matrix. Keywords: Analytic network process, analytic hierarchy process, multi-criteria decision making, contractor selection Introduction Contractor selection is one of the main decisions made by the clients. In order to ensure that the project can be completed successfully, the client must select the most appropriate contractor. This involves a procurement system that comprises five common process elements: project packaging, invitation, pre-qualification, shortlisting and bid evaluation (Hatush, 1996; Hatush and Skitmore, 1997). Moreover, there are methods attempting to estimate the values of contractors by using various selection criteria (e.g. Samuelson and Levitt, 1982; Jaselskis and Russell, 1990). These methods include multi-criteria decision-making (MCDM), multiattribute analysis (MAA), multi-attribute utility theory (MAUT), multiple regression (MR), cluster analysis (CA), bespoke approaches (BA), fuzzy set theory (FST) and multivariate discriminant analysis (MDA) (Hatush and Skitmore, 1997; Holt, 1998; Mahdi et al., 2002). Selection criteria on the other hand can be classified as pre-qualification and project-specific (Alarcon and Mourgues, 2002). Among those well-known methods, MCDM is relatively new to be employed to select contractors. *Author for correspondence. MCDM aims at using a set of criteria for a decision problem. Since these criteria may vary in the degree of importance, the analytic hierarchy process (AHP) technique is employed to prioritize the selection criteria (i.e. assign weights to the criteria). In the existing literature of contractor selection, studies have utilized AHP to set up a hierarchical skeleton within which multi-attribute decision problems can be structured (e.g. Fong and Choi, 2000; Mahdi et al., 2002). Conceptually, AHP is only applicable to a hierarchy that assumes a unidirectional relation between decision levels. The top level of the hierarchy (apex) is the overall goal for the decision model, which decomposes to a more specific level of elements until a level of manageable decision criteria is met (Meade and Sarkis, 1999). Yet, the strict hierarchical structure may need to be relaxed when modelling a more complicated decision problem that involves interdependencies between elements of the same cluster or different clusters. This requires the generic analytic method the analytic network process (ANP) that can evaluate multidirectional relationship among decision elements (Saaty, 1988; Meade and Sarkis, 1998). In most studies of contractor selection, selection criteria are assumed to be independent of each other. Construction Management and Economics ISSN print/issn X online 2004 Taylor & Francis Ltd DOI: /
2 1022 Cheng and Li Apparently, these criteria are likely to affect each other. For example, Fong and Choi (2000) used a sample of 13 respondents to identify and prioritize eight uncorrelated criteria (tender price, financial capability, past performance, past experience, resources, current workload, past relationship and safety performance) for contractor selection. In fact, the eight criteria are interrelated to a certain extent. For example, good past experience may lead to good safety performance if the past experience includes good safety records. Good past performance and experience are good evidence of successful projects, which in turn results in strong financial capability. Resources and financial capability may be positively correlated. Tender price may be negatively related to other criteria. Therefore, ANP is more favourable to be employed in this interdependent relationship framework. Since ANP is new to the construction field, this study will demonstrate how to apply ANP to improve the prioritization of contractor selection criteria. It is expected that by using ANP, clients are able to establish a complete decision model without sacrificing the validity due to limitations of the analytical tool. Contractor selection Existing literature on contractor selection mainly deals with how to identify and assess the criteria to make the most appropriate decisions (Holt, 1997). A more promising approach to classifying the contractor selection criteria has been provided by Hatush and Skitmore (1997), who focused on two of the five-stage process of contractor selection: (1) pre-qualification, and (2) bid evaluation. Holt (1998) and Valentine (1995) referred to this as a two-stage procedure: (1) pre-qualification, and (2) evaluation of tenderers. Figure 1 illustrates a typical bespoke approach that shows where these stages are located. Pre-qualification is the process that compares the key contractor-organizational criteria among a group of contractors desirous to tender. Such criteria can be past performance, past experience, and financial stability. In order to identify the contractor-organizational criteria, researchers have proposed useful methods, such as MAA (e.g. Russell and Skibniewski, 1987; Russell et al., 1992; Holt et al., 1994). Evaluation of contractors on the other hand considers specific criteria that can measure the suitability of contractor for the proposed project (Holt, 1998). Contractor evaluation is not equivalent to contractor selection. Specifically, contractor evaluation is the process of investigating or measuring project-specific attributes, while contractor selection refers to as the process of aggregating the results of evaluation to identify Figure 1 A simplified bespoke approach (note: this simplified bespoke approach (BA) is typically run in a large client in Hong Kong. It may be different from other BAs (e.g. Holt, 1998) optimum choice. In practice, these two processes are always grouped together to represent a single procedure to prioritize the contractors according to the project specific criteria, which can be office location with respect to the project, experience in the geographical region, and experience of the proposed construction methods. There are methods apt to identify project-specific criteria. For example, MAUT is one of the current available techniques (Alarcon and Mourgues, 2002). MAA, MAUT and AHP are comparable methods that assign weights to selection criteria (Holt, 1998; Alarcon and Mourgues 2002). Table 1 illustrates their respective formula to show why their functions are alike (Holt, 1998). As shown in Table 1, these contractor evaluation methods are known to calculate an aggregate (or composite) score for each criterion. The differences between these methods are that: (1) MAA and AHP use
3 Contractor selection using analytic network process 1023 Table 1 Comparison of MAA, MAUT and AHP Method Formula Description Multi-attribute n ACr j is the aggregate score for contractor j; analysis (MAA) ACr j = SV ij W i V ij is the attribute i score with respect to contractor j; i = 1 n is the number of attributes considered in the analysis; W i is the weighting indices to V i Multi-attribute utility n ACr j is the aggregate score for contractor j; theory (MAUT) ACr j = SU ij W i U ij is the attribute i score with respect to contractor j; i = 1 n is the number of attributes considered in the analysis; W i is the weighting indices to U i Analytic hierarchy n Cr i is the composite score for contractor i; process (AHP) Cr i = Sc i V ij c i is the relative weight for V i with respect to contractor j; i = 1 and V ij is the selection criterion i with respect to contractor j Note: Partially adapted from Holt (1998). simple scoring for rating the criteria, while MAUT makes use of utility value; and (2) AHP employs pairwise comparison for determining the weights, while MAA and MAUT use simple scoring. Yet, Mahdi et al. (2002) suggested that AHP could be the weighting method incorporated into MAA or MAUT. When considering that the criteria are somewhat related and what Holt (1997) mentioned about the rationalization, resource saving and objectivity, ANP (analytic network process) would be a more reliable method to assign weights to correlated attributes. This paper is not intended to compare existing contractor evaluation methods. Those who are interested in knowing more about other methods may refer to Holt (1998). hierarchy and uncorrelated elements within each cluster as well as between clusters. It is not appropriate for models that specify interdependent relationships in AHP. ANP is then developed to enhance the tool s analytical power. ANP is a generic form of AHP and allows for more complex interdependent relationships among elements (Saaty, 1996). It is also known as the systems-withfeedback approach (Meade and Sarkis, 1998). Interdependence can occur in several ways: (1) uncorrelated elements are connected, (2) uncorrelated levels are connected and (3) dependence of two levels is two-way (i.e. bi-directional). Figure 2 illustrates examples of these interdependencies. By incorporating interdependencies AHP and ANP AHP and ANP are two separate concepts introduced by Saaty (1980, 1996). Saaty (1980) first developed the AHP, which helps to establish decision models through a process that contains both qualitative and quantitative components. Qualitatively, it helps to decompose a decision problem from the top overall goal to a set of manageable clusters, sub-clusters, and so on down to the final level that usually contains scenarios or alternatives. The clusters or sub-clusters can be forces, attributes, criteria, activities, objectives, etc. Quantitatively, it uses pair-wise comparison to assign weights to the elements at the cluster and sub-cluster levels and finally calculates global weights for assessment taking place at the final level. Each pair-wise comparison measures the relative importance or strength of the elements within a cluster by using a ratio scale. One of the main functions of AHP is to calculate the consistency ratio to ascertain that the matrices are appropriate for analysis (Saaty, 1980). Nevertheless, AHP models assume that there are unidirectional relationships between clusters of different decision levels along the Figure 2 Examples of interdependence (notes: (1) uncorrelated elements are connected; (2) uncorrelated levels are connected; (3) dependence of two levels is two-way (i.e. bi-directional)
4 1024 Cheng and Li Figure 3 Hierarchical structure of contractor selection (source: Fong and Choi, 2000)
5 Contractor selection using analytic network process (i.e. addition of the feedback loops in the model), a supermatrix will be developed. The supermatrix adjusts the relative importance weights in individual matrices to form a new overall matrix with the eigenvectors of the adjusted relative importance weights (Meade and Sarkis, 1998). According to Sarkis (1999), ANP comprises four main steps: (1) Conducting pair-wise comparisons on the elements at the cluster and sub-cluster levels; (2) Placing the resulting relative importance weights (eigenvectors) in submatrices within the supermatrix; (3) Adjusting the values in the supermatrix so that the supermatrix can achieve column stochastic; and (4) Raising the supermatrix to limiting powers until the weights have converged and remain stable. Methodology The current study revises the hierarchical model of Fong and Choi (2000) by adding interdependent influences at the selection criteria level. Figure 3 illustrates the original model being composed of four levels. At the top level is the decision problem itself, while the bottom level comprises the three decision alternatives (i.e. contractor candidates). The criteria and sub-criteria represent the middle two levels. Figure 4 illustrates a general view of the new decision network model. In this model, the main difference from the original model is that there 1025 is a feedback loop in the selection criteria level. It is assumed that the eight selection criteria are interdependent. Figure 4 also illustrates a clearer view of the interrelationship structure by the callout box. Moreover, only four of the eight criteria have sub-criteria (see Figure 3). It is worth noting that sub-criteria decomposed from their respective criterion are not assumed to be interdependent. Pair-wise comparisons The normal procedure of a pair-wise comparison is to invite experts to compare two sub-cluster s elements with respect to their respective cluster s element. Saaty (1980) has developed a 9-point priority scale of measurement, with a score of 1 representing equal importance of the two compared elements and 9 being overwhelming dominance of one element (row element) over another element (column element). When there is overwhelming dominance of a column element over a row element, a score of 1/9 is given. Figures 5 and 6 provide an illustration of the use of the scale to represent the judgments generated in this study. After having consulted with five construction professionals, the pair-wise comparisons in this paper are of three bases. First, this paper adopts the original pair-wise comparison results in Fong and Choi (2000) who compared the criteria and sub-criteria for the three candidates, which had fifteen sets of judgment matrices. Second, this paper adjusted part of the original relative weights of the criteria with respect to the top goal and Figure 4 The ANP network component
6 1026 Cheng and Li Figure 5 Relative weights of criteria and sub-criteria those of the sub-criteria with respect to their respective criteria. Figure 5 presents these five sets of judgment matrices. Third, for synthesizing the relative weights among the criteria, other pair-wise comparisons have to be made for this study. This is to compare two criteria with respect to a selected criterion. This requires establishing eight additional sets of judgment matrices for analysis. Figure 6 presents these eight paired comparison matrices. For example, with respect to the criterion tender price, financial capability is relatively more important than safety performance. Noteworthy, clients should develop their own set of scores for the criteria and sub-criteria matching their project requirements. Relative weights of elements and consistency ratio of matrices After the pair-wise comparison matrices are developed, a vector of priorities (i.e. a proper or eigen vector) in
7 Contractor selection using analytic network process 1027 Figure 6 Criteria interdependency comparisons
8 1028 Cheng and Li Figure 6 Continued
9 Contractor selection using analytic network process each matrix is calculated and is then normalized to sum to 1.0 or 100 per cent. This is done by dividing the elements of each column of the matrix by the sum of that column (i.e. normalizing the column); then, obtaining the eigen vector (evector) by adding the elements in each resulting row (to obtain a row sum ) and dividing this sum by the number of elements in the row (to obtain priority or relative weight ) (Cheng and Li, 2002). Moreover, for ascertaining the consistency of the judgment matrices, Saaty (1994) suggested three threshold levels: (1) 0.05 for 3-by-3 matrix; (2) 0.08 for 4-by-4 matrix; and (3) 0.1 for all other matrices. Those who want to know the algorithm for computing consistency ratio may refer to Saaty (1980) and Cheng and Li (2001). Figures 5 and 6 present the relative weights (priorities) and the CR values for the comparison matrices. Supermatrix and the limit matrix With interdependent influences, the system that consists of cluster and sub-cluster matrices must translate to a supermatrix. This can be achieved by entering the local priority vectors in the supermatrix, which in turn obtains global priorities. Table 2 shows the supermatrix for the ANP decision model. It contains the weights (or priorities) for the judgment matrices. After entering the sub-matrices into the supermatrix and completing the column stochastic, the supermatrix is then raised to sufficient large power until convergence occurs (Saaty, 1996; Meade and Sarkis, 1998). Table 3 presents the final limit matrix. Each column is the same and provides the local relative weights of individual sets of elements. Discussions The limit matrix shows the local relative weights for all the elements in the supermatrix. In order to ascertain the value of ANP, results of the normalized relative weights of the candidates obtained from ANP and AHP are compared. Table 4 presents the local relative weights of the three candidates based on the results from ANP, as well as the local relative weights from AHP. In the demonstrated example, candidate A should be chosen because it has the largest relative weights (= 0.473, from ANP in Table 4). However, if the decision model does not specify the interdependent relationships (i.e. only AHP model), candidate B should have been selected since it had the largest relative weights (= 0.448, from AHP in Table 4). Candidate A was even the worst among all candidates. It is because the ANP decision model has taken into account the interdependencies among selection criteria that exert extra influences on the model AHP has its limitation because it can only be applied in simple hierarchical structures, while ANP provides powerful capability in solving nowadays construction management issues that involve more complicated decision problems. It is not to say that results from AHP would be different from those of ANP. It depends on the subjective and/or objective ratings given to the judgment matrices. However, when there are interdependent influences, ANP is a viable method for prioritization. In this study, the ANP method is applied in contractor selection, and ANP enhances the increasingly popular multi-criteria decisionmaking (MCDM) approach to criteria prioritization. When researchers and practitioners have realized that lowest-price is not the promising approach to attain the overall lowest project cost upon project completion, multi-criteria selection becomes more popular (Wong et al., 2001). There are various methods used for multicriteria contractor evaluation. Multivariate statistical analytic methods are more quantitative in nature. Wong et al. (2001) refer to them as the objective tender evaluation methods. Yet, these methods need a sufficiently large amount of respondents in order to ensure the objective quality. Although researchers tend to believe the need for identifying a set of general selection criteria using empirical surveys (Holt et al., 1995; Fong and Choi, 2000; Wong et al., 2001), assigning weights to these general criteria is however the internal business decisions made by individual clients. In other words, the clients evaluate contractors according to the requirements of individual projects. Basically, there are two types of projects: public and private. There may be necessary to develop individual sets of criteria for these project types. For example, there is an expanding view that long-term or strategic partnering becomes more appropriate in private projects procurement. Hence, the relationship between the client and the bidding contractors may be an important selection criterion. On the other hand, the competitive tendering process is still the current practice for public projects although some may argue that it is becoming less popular. The private relationship criterion would be inappropriate when selecting contractors in the process of public tendering. In normal practices of contractor selection, only a small group of experts (mainly the top management of the client) is responsible for evaluating the contractor candidates. In such circumstances, using the MCDM approach to contractor selection is more plausible (Mahdi et al., 2002). ANP and AHP can help assign weights to selection criteria so as to increase the accuracy of judgments made by experts. They are not only the decision tools appropriate for contractor evaluation at both the pre-qualification and project-specific stages but can also act as the quantitative tools for assigning weights to criteria in other methods (e.g. MAA and MAUT). These decision tools set the new horizon for contractor selection by raising key processes of
10 1030 Cheng and Li Table 2 Supermatrix (major components) Goal Selection criteria Selection sub-criteria F.C. P.P. P.E. R. T.P. F.C. P.P. P.E. R. C.W. C.R. S.P. F.S. F.R. C.C. C.O. D. A.Q. S.C. T.C. E.A. P.R. H.R. Goal Selection T.P criteria F.C P.P P.E R C.W C.R S.P Selection F.C. F.S sub-criteria F.R P.P. C.C C.O D A.Q P.E. S.C T.C E.A R. P.R H.R Contractor A candidates B C Note: All figures are rounded to two decimal places.
11 Contractor selection using analytic network process 1031 Table 3 The limit matrix (local priorities for major components) Goal Selection criteria Selection sub-criteria F.C. P.P. P.E. R. T.P. F.C. P.P. P.E. R. C.W. C.R. S.P. F.S. F.R. C.C. C.O. D. A.Q. S.C. T.C. E.A. P.R. H.R. Selection T.P criteria F.C P.P P.E R C.W C.R S.P Selection F.C. F.S sub-criteria F.R P.P. C.C C.O D A.Q P.E. S.C T.C E.A R. P.R H.R Contractor A candidates B C Notes: (1) Each column is the same. (2) All figures are rounded to two decimal places.
12 1032 Cheng and Li Table 4 decomposing a complex problem to a manageable network or hierarchical structure, eliciting accurate rating by employing pair-wise comparison and consistency measure, and obtaining overall priority vector by dependent and/or interdependent matrix computations. Conclusions ANP extends the function of AHP and is a viable method for multi-criteria decision problems that involve interdependent relationships. In order to highlight the possible difference between the use of AHP and ANP, the results obtained from both supermatrix and limit matrix are compared. The mathematics performed in this research may not be familiar to every reader. Yet, Saaty is now developing a software tool for conducting ANP. Once the software tool is available for sale, a much faster growing use of ANP can be anticipated. Acknowledgement This paper was financially supported by The Hong Kong Polytechnic University under grant number G-YW72. References Comparing the results from ANP and AHP Candidate ANP AHP A B C Alarcon, L.F. and Mourgues, C. (2002) Performance modelling for contractor selection. Journal of Management in Engineering, 18(2), Cheng, E.W.L. and Li, H. (2001) Analytic hierarchy process: an approach to determine measures for business performance. Measuring Business Excellence, 5(3), Cheng, E.W.L. and Li, H. (2002) Construction partnering process and associated critical success factors: a quantitative investigation. Journal of Management in Engineering, 18(4), Fong, S.P. and Choi, S.K. (2000) Final contractor selection using the analytical hierarchy process. Construction Management and Economics, 18, Hatush, Z. (1996) Contractor selection: using multiattribute utility theory, unpublished thesis, Department of Surveying, University of Salford, Salford. Hatush, Z. and Skitmore, M. (1997) Criteria for contractor selection. Construction Management and Economics, 15, Holt, G.D. (1997) Classifying construction contractors: a case study using cluster analysis. Building Research and Information, 25(6), Holt, G.D. (1998) Which contractor selection methodology? International Journal of Project Management, 16(3), Holt, G.D., Olomolaiye, P.O. and Harris, F.C. (1994) Evaluating prequalification criteria in contractor selection. Building and Environment, 29(4), Holt, G.D., Olomolaiye, P.O. and Harris, F.C. (1995) A review of contractor selection practice in the U.K. construction industry. Building and Environment, 30(4), Jaselskis, E. and Russell, J. (1990) Risk analysis approach to selection of contractor evaluation method. Journal of Construction Engineering and Management, 118, Mahdi, I.M., Riley, M.J., Fereig, S.M. and Alex, A.P. (2002) A multi-criteria approach to contractor selection. Engineering, Construction and Architectural Management, 9(1), Meade, L. and Sarkis, J. (1998) Strategic analysis of logistics and supply chain management systems using the analytic network process. Transportation Research Part E: Logistics and Transportation Review, 34(3), Meade, L. and Sarkis, J. (1999) Analyzing organizational project alternatives for agile manufacturing processes: an analytic network approach. International Journal of Production Research, 37(2), Russell, J.S. and Skibniewski, M.J. (1988) Decision criteria in contractor prequalification. Journal of Management in Engineering, 4(2), Russell, J.S., Hancher, D.E. and Skibniewski, M.J. (1992) Contractor prequalification data for construction owners. Construction Management and Economics, 10, Saaty, T.L. (1980) The Analytic Hierarchy Process, McGraw- Hill, New York. Saaty, T.L. (1994) How to make a decision: the analytic hierarchy process. Interfaces, 24(6), Saaty, T.L. (1996) Decision Making with Dependence and Feedback: The Analytic Network Process, RWS Publications, Pittsburgh, PA. Samuelson, N.M. and Levitt, R.E. (1982) Owner s guidelines for selecting safe contractors. Journal of the Construction Division, 108(CO4), Sarkis, J. (1999) A methodological framework for evaluating environmentally conscious manufacturing programs. Computers & Industrial Engineering, 36, Sarkis, J. and Sundarraj, R.P. (2002) Hub location at Digital Equipment Corporation: a comprehensive analysis of qualitative and quantitative factors. European Journal of Operational Research, 137, Valentine, R. (1995) Effective Contract Administration: For Road, Bridge and General Civil Engineering Works, Ecat Publications, Tuscon, AZ, pp Wong, C.H., Holt, G.D. and Cooper, P.A. (2000) Lowest price or value? Investigation of UK construction clients tender selection process. Construction Management and Economics, 18,