Selecting Appropriate Structural System: Application of PROMETHEE Decision Making Method V. Balali1, B. Zahraie2, A. Hosseini3, A. Roozbahani4 1
Graduate Student, School of Civil Engineering, University of Tehran, (
[email protected]) Associate Professor, School of Civil Engineering, University of Tehran, (
[email protected]) 3 Assistant Professor, School of Civil Engineering, University of Tehran, (
[email protected]) 4 Ph.D. Student, School of Civil Engineering, University of Tehran, (
[email protected]) 2
ABSTRACT Recent advancements in various structural systems have made the selection of the appropriate structural system for a specific project a challenging decision making process. This process involves different economic and technical criteria representing the availability of experienced technicians and engineers and necessary machinery and construction materials. Economic life cycle, environmental protection related issues, safety of the project site, and vulnerability to natural disasters such as earthquakes are also issues related to the country and location in which the project will be constructed and they should also be addressed in the decision making process. In this paper, “PROMETHEE” multicriteria decision making technique has been used to consider these criteria in selection of the most appropriate structural system for multi-housing projects. A questioner has been designed to gather engineering judgments and experts opinions about PROMETHEE parameters such as weights of different criteria. The team of experts who has cooperated in this research includes engineers and managers of consulting firms and general contractors who have been involved in the same type of the projects. The results of this study have shown that the proposed methodology can be effectively used in selection of the appropriate structural systems for the case study of this research. This method can also be used for other industrial or commercial building projects while the criteria should be revised with respect to the influencing parameters in those projects. Keywords: Structural Systems, Multi Criteria Decision Making (MCDM), Construction Management, PROMETHEE. ranking of different alternatives based on multiple conflicting criteria. The PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) family of outranking methods is among the recently developed MCDM methods which are also used in this study for structural system selection has attracted much attention.
1. INTRODUCTION Selection of structural systems is characterized by several features, which make it suitable for Multiple Criteria Decision Making (MCDM) approach. It is a highly interactive procedure, requiring a great deal of coordination of information from various sources. The selection of structural system is an initial task in the overall process of the structural design, where the result is a proposed general arrangement of the structure, incorporating the overall form, geometry and nomination of the principal structural elements. Over a period of time, experienced designers build up some procedures for this task; these procedures can be embraced in MCDM. Selection of the structural systems is complicated due to the uncertainties in the decision making procedure. Structural systems knowledge is vast and weak structured, and contains a variety of expertise. Designers require a wide range of knowledge and experiences about the behavior of different structures and structural requirements. Thus the selection of structural systems seems to be a suitable candidate for a MCDM application. In the past decade, a great deal of attention has been given to the MCDM applications in construction engineering and management. MCDM often deals with
As an example, two MCDM approaches, the AHP and Analytic Network Process (ANP), were employed by Wong et al. (2008) to evaluate the intelligence level of the intelligent building systems. A total of 69 key intelligence criteria were identified for eight major intelligent building systems [1]. Tabarak et al. (2003) utilized Artificial Neural Network (ANN) to assist in incorporating buildability during the preliminary design of buildings. The back-propagation learning algorithm is adopted to train the networks. This training involves capturing the relationships embedded in buildable designs collected from previously completed design projects [2]. Goletsis et al. (2003) used an especially developed MCDM method namely MURAME (MUlti criteria
1
methods for multi-criteria analysis (Brans et al., 1986) [6].
RAnking MEthod) for project ranking. The method is based on the construction of an outranking relationship. In MURAME method pair-wise comparison between alternatives results in the degree of dominance of the one over the other. MURAME is implemented in two main phases combining two of the most popular outranking methods, namely ELECTRE III and PROMETHEE [3].
The following family of methods has been used in this paper [5]: • PROMETHEE I establishes a partial preorder among the alternatives and can be used for choice problems. • PROMETHEE II establishes a complete preorder among the alternatives, and can be used for ranking problems. • PROMETHEE-GAIA (Geometrical Analysis for Interactive Aid) extension of the results of PROMETHEE, through a visual and interactive procedure.
Shamrani et al. (2009) proposed procedures and guidelines for the selection of optimum structural systems and materials in two stages. Stage one is based on a list of criteria, including architectural considerations. Stage two is dedicated to evaluation of the selected systems and materials. The selection of structural system and material is often done according to personal experiences or perceptions without being evaluated as it should be for optimum performance. Their proposed selection process provided a methodology for selection of the optimum structural system [4].
2.1. PROMETHEE II The basic principle of PROMETHEE II is based on a pair-wise comparison of alternatives. Alternatives are evaluated according to different criteria, which have to be maximized or minimized. The implementation of the PROMETHEE II requires the following two additional types of information [6]:
In this study, a multi criteria model for group decisionmaking based on PROMETHEE method has been presented in order to select the appropriate structural system through the selection of an optimal set of alternatives.
The Weights of Criteria: determination of the weights is an important step in most multi-criteria methods. PROMETHEE II assumes that the decision-maker is able to weight the criteria appropriately, at least when the number of criteria is not too large (Macharis et al., 2004).
2. METHODOLOGY The relevance of MCDM methodology stems from the fact that, in most decision-making situations, there are many objectives to be taken into consideration. As it was mentioned before, the case study of this research is to select the appropriate structural system taking into account the interests of the various decision-makers. In this case, an outranking approach is more appropriate. Le T´eno and Mareschal (1998) have concluded that the basic principle of outranking is that if alternative a performs better than alternative b on the majority of criteria and if there is no criterion in which b is strongly better than a, then a will be preferred over b (democratic principle of majority without strong minority) [5].
The preference functions: for each criterion, the preference function translates the difference between the evaluations obtained by two alternatives into a preference degree ranging from zero to one. In order to facilitate the selection of a specific preference function, Vincke and Brans (1985) proposed six basic types of criteria: (1) usual, (2) U-shape, (3) V-shape, (4) level, (5) V-shape with indifference and (6) Gaussian. These six types are particularly easy to define. For each criterion, the value of an indifference threshold, q, the value of a strict preference threshold, p, and the value of an intermediate value between p and q, s, has to be defined (Brans and Mareschal, 1992) [6].
The PROMETHEE outranking method was adopted for this study. This method is software driven, user-friendly, provides direct interpretation of parameters, and a sensitivity analysis of results.
The first stage in MCDM problems is to determine the following three important aspects: • Identification of decision makers and stakeholders. • Selection of the criteria and their relative weights. • Selection of alternatives.
The PROMETHEE family of outranking methods is one of the most recent MCDM methods that was developed by Brans (1982) and further extended by Vincke and Brans (1985). PROMETHEE is an outranking method for a finite set of alternative actions to be ranked and selected among criteria, which are often conflicting. PROMETHEE is also a quite simple ranking method in concept and application compared with the other
Figure 1 presents stepwise procedure for implementing PROMETHEE II. The procedure starts with determining deviations based on pair-wise comparisons. It is followed by using a relevant preference function for each criterion
2
in Step 2, calculating global preference index in Step 3, and calculating positive and negative outranking flows for each alternative and partial ranking in Step 4. The procedure comes to an end in step 5 by calculating net outranking flow for each alternative and completes ranking. The maximum amount of net flow denotes the best alternative [6].
rankings can be obtained. In the indifference situation (aIb), two alternatives a and b have the same leaving and entering flows: (2) aIb if: φ+(a) = φ+(b) and φ−(a) = φ−(b). Two alternatives are considered incomparable, aRb, if alternative a is better than alternative b in terms of leaving flow, while the entering flows indicate the reverse: aRb if: φ+(a) > φ+(b) and φ−(a) > φ−(b); or φ+(a) < φ+(b) and φ−(a) < φ−(b). (3)
Step1: Determination of deviations based on pair-wise comparison
PROMETHEE I ensure creation of indifferent and incomparable alternatives. In some ranking problems, PROMETHEE I can give a complete ranking depending on the evaluation matrix values. This ranking cannot be different from the ranking made by PROMETHEE II [7].
Step2: Application of the preference function
Step 3: Calculation of an overall or global preference index
2.3. PROMETHEE GAIA Graphical geometrical analysis for interactive aid (GAIA) displays the relative position of the alternatives, in terms of contributions to the various criteria (Brans and Vincke 1985; Brans and Mareschall 1994). Principal components analysis is applied to the matrix of ‘‘normed flows’’, defined for alternative a and criterion j by:
Where of a over b (from 0 to 1) as defined as the of for each criterion and is the weight weighted sum associated with jth criterion. Step 4: Calculation of outranking flows/ The PROMETHEE I partial ranking
Where n is the number of alternatives, and this is used to generate a two-dimensional plot in which the alternatives and criteria are represented in the same plot (Belton and Stewart 2002) [7].
Where and denote the positive outranking flow and negative outranking flow for each alternative.
3. CASE STUDY OF STRUCTURAL SYSTEM SELECTION
Step 5: Calculation of net outranking flow/ The PROMETHEE II complete ranking Where alternative.
The new technologies in construction can be classified in four groups: (1) production and application of materials,(2) building components, (3) structural systems such as LSF, 3D Wall, ICF, RCSF and (4) mechanical and electrical equipment technologies. In this paper, the third category is examined. In the case study, through new architectural technologies and structural systems five systems which are approved by the Iranian Building and House Research Center (BHRC) are selected. The most important features of these systems are light weight, ease of construction, high construction speed, high structural system stability, environmental friendliness and ease of industrial production. These five systems are [8]: • LSF(Light Gauge Steel Frames) • 3D Wall • ICF(Insulating Concrete Formwork) • Tunnel Formwork Systems(Reinforced Concrete Continuous Frames)
denotes the net outranking flow for each
Figure1. Stepwise Procedure for PROMETHEE II [6]. 2.2. PROMETHEE I The PROMETHEE I partial ranking provides a ranking for alternatives. In PROMETHEE I, alternative a is preferred over alternative b, aPb, if alternative a has a greater leaving flow than that of alternative b and a smaller entering flow than the entering flow of alternative b: aPb if : φ+(a) > φ+(b) and φ−(a) < φ−(b); or φ+(a) > φ+(b) and φ−(a) = φ−(b); or (1) φ+(a) = φ+(b) and φ−(a) < φ−(b). PROMETHEE I evaluation allows indifference and incomparability situations. Therefore, sometimes partial
3
•
Tronco System
Before using the PROMETHEE method to rank the alternatives, for each criterion, a specific preference function, with its thresholds is defined. Preference functions and threshold values have been defined by the decision-making team. Decision-making team has set these values by taking into consideration the features of alternative structural systems and the project conditions. The preference functions and thresholds defined are provided in Table 2.
In this study, the appropriate systems are selected based on the following criteria [9]: 1) Cost: The cost criterion include production line establishment, expenses per square meter of building, material, transportation and operation and maintenance costs. 2) Ease of Construction: Access to some specific equipment and necessity of special expertise and also simple and safe assemble are some of important aspects affecting this criterion. 3) Energy Saving: Energy indicators and parameters in outside walls, grouping within building codes and the application ability of existent energies in ventilation, chilling and heating are the important indexes in energy evaluation of these structural systems. 4) Dead load: For decreasing the damages and victim in earthquake, buildings must be designed and constructed based on seismic provisions, latest codes and minimum weight. 5) Number of Stories: Number of stories and maximum height of the buildings is usually an important factor in mass construction projects. 6) Age and durability: Permanency of content materials, resistance to decay and corrosion and also structure durability are the most important component of this evaluation.
Table2. Criteria Weights and Preference Functions
Positive indexes Negative indexes
Average
High
Very High
1
3
5
7`
9
9
7
5
3
1
Preference Function
Preference Threshold
Indifference Threshold
Cost
0.25
Linear
280
30
Ease of Construction
0.20
V-Shape
6
-
0.18
V-Shape
5
-
0.15
Linear
7
2
0.12
Linear
300
100
0.10
Linear
15
5
3.1. Results After evaluation matrix and preference functions are determined, alternatives are evaluated by using Decision Lab software (developed in collaboration with the Canadian company Visual Decision 1999). The positive flow (φ+), negative flow (φ−) and net flow (φ) values obtained from the evaluation process are shown in Table 3. Table3. PROMETHEE Flows LSF 3D Wall ICF Tunneling Tronco
Table1. Bipolar Scale For Positive Indexes [10]. Low
Weight
Energy Saving Number of Stories Max. Dead Load Age & Durability
Some of these criteria are qualitative and should be transformed to quantitative criteria. The general method in evaluation of qualitative criteria is application of bipolar scale which is denoted in Table 1 for positive and negative indexes [10]. Very Low
Criteria
Φ+
Φ-
Φ
0.1955 0.2565 0.2387 0.2000 0.2430
0.1910 0.1158 0.1508 0.4800 0.1960
0.0045 0.1407 0.0878 -0.2800 0.0470
By using the flow values in Table 3, firstly the partial ranking is determined via PROMETHEE I (Fig. 02). PROMETHEE I used positive and negative flow values to find the partial ranking. It is based on strongly established preferences only. As a consequence, not all alternatives can be compared one-to-one with the others and some alternatives are simply incomparable. Highlighting incomparable alternatives is interesting for decision makers because it usually emphasizes alternatives with quite different profiles.
Based on a preliminary study, the decision making team determined five possible new structural systems suitable for the needs of the mass construction. The decision making team consisted of engineers and managers of consultant firms and general contractors. The six criteria, namely cost, ease of construction, energy saving, number of stories, maximum dead load and age and durability which have been taken into account in the selection process, were determined. Then the weights of criteria and preference functions were determined by the decision makers.
Tunnel Formwork system is determined as the worst alternative according to the PROMETHEE I partial ranking. LSF, 3D Wall, ICF and Tronco systems are
4
preferred to Tunnel Formwork system, and Tronco system is preferred to LSF system. On the other hand ICF, LSF and Tronco systems are incomparable alternatives. As it is shown in Figure 2, PROMETHEE I provide 3D wall as the best alternative.
This plane is the result of principal component analysis (PCA), projecting the 6-dimensional space of criteria onto a two-dimensional plane. By applying the PCA related criteria are handled by these combinations and double counting never occurs (Metin Da˘gdeviren 2008). As it is shown in the Figure 04, the Delta-parameter is 96.65%; this means only 3.35% of the total information is lost by the projection. It can be seen from Figure 4 that pi vector is in the direction of energy saving, maximum dead load, cost and the closest alternative to the pi vector is 3D Wall. This result is consistent with the complete ranking of PROMETHEE II.
The net flow values given in the last column of Table 3 , are used in PROMETHEE II complete ranking to identify the best alternative (Fig. 3). All the alternatives are ranked, leaving no incomparable pair of alternatives. This information is most straightforward and is easier to use than the PROMETHEE I partial ranking, but it could be a reflection of less reliable preferences.
Figure2. PROMETHEE I Partial Ranking.
Figure4. GAIA Plane. 3.2. Sensitive Analysis
Figure3. PROMETHEE II Complete Ranking.
For each criterion, a stability interval is computed. It indicates the range in which the weights of that criterion can be modified without affecting the PROMETHEE II complete ranking, provided that the relative weights of the other criteria are not modified. This information is interesting for assessing the general robustness of the ranking. For example it shows that if the weight of number of stories criterion is changed in range of 8.18% to 21.39% the ranking doesn’t change.
The 3D Wall is selected as the best alternative based on the information PROMETHEE II provides, and the other ranked alternatives are ICF, Tronco, LSF, Tunnel formwork system, respectively. Both PROMETHEE I and II help the decision maker to finally select the best alternative. The GAIA plane provides the decision maker with comprehensive graphical image of the decision problem and is thus a descriptive complement to PROMETHEE rankings. The decision problem can be represented in the GAIA plane (see Fig. 4) where structural systems are represented by points and criteria by vectors. In this way, conflicting criteria may appear clearly. Criteria vectors expressing similar preferences on the data are oriented in the same direction, while conflicting criteria are pointing in opposite directions. The length of each vector is a measure of its power in structural systems differentiation.
Table4. Stability Intervals. Weight Cost Ease of Construction Energy Saving Number of Stories Max. Dead Load Age&Durability
5
Interval
0.25
Min 0.1788
Max 0.3111
0.20
0.0838
0.2374
0.18 0.15 0.12 0.10
0.1071 0.0818 0.0000 0.0748
1.0000 0.2139 0.4762 0.1705
4. CONCLUSIONS
used. Integration of the two decision making methods and also fuzzy approach for handling uncertainties are the directions in our future research.
In this paper, a decision approach is provided for structural system selection. Application of new architectural technologies and structural systems can accelerate the construction speed in some developed countries such as Iran especially in mass construction projects. Thus, selecting the appropriate structural system plays a significant role in designing and also construction.
5. ACKNOWLEDGEMENT This study is partially supported by the Pars Special Economic Energy Zone Organization (PSEEZ) and is hereby acknowledged. 6. REFERENCES
This selection problem is based on the comparisons of new architectural technologies and structural systems according to the selected criteria. PROMETHEE I, II and GAIA decision making methods have been used in the proposed approach. The weights obtained from experts are included in the decision making process by using them in PROMETHEE computations and the alternative priorities are determined based on these weights. By this way, weighting of the criteria considered during decision making and evaluation of these criteria via preference functions are performed simultaneously. Additionally, in the application, it is shown that the criteria weights are important in PROMETHEE method and they could change the ranking. PROMETHEE method takes into account the preference function of each criterion, determined by the decision-makers. By this way, each criterion is evaluated on a different basis and it is possible to make better decisions. PROMETHEE I identifies the alternatives which cannot be compared and the alternatives which are indifferent, by making a partial ranking, while PROMETHEE II provides a complete ranking for alternatives. The GAIA plane is a useful analytical tool that some remarks can be detected from the alternatives and criteria sets. For example, in structural system evaluation, LSF and Tronco system receive the same ranking with respect to ease of construction criterion. In addition, differentiation of the criteria, similar criteria, independent criteria, and opposite criteria can be determined from the GAIA analysis. By sensitivity analysis of the result, the most effective criteria in decision making are determined. These opportunities are not available in other decision making methods such as AHP, fuzzy AHP, ELECTRE and TOPSIS.
[1] Wong, J., Li, H., Lai, J., “Evaluating the system intelligence of the intelligent building systems Part 1: Development of key intelligent indicators and conceptual analytical framework”, Automation in Construction, Vol.17, pp. 284 – 302, 2008. [2] Tabarak, M.A., William, D., “Artificial neural network for the selection of buildable structural systems”, Engineering, Construction and Architectural Management Journal, Vol. 10, No.4, pp. 263-271, 2003. [3] GOLETSIS, Y., PSARRAS, J., SAMOUILIDIS, J.E., “Project Ranking in the Armenian Energy Sector Using a Multicriteria Method for Groups”, Annals of Operations Research, No. 120, pp. 135–157, 2003. [4] Al Shamrani, O.S., Schierle, G.G., “Selection of optimum structural systems and materials”, Art in Science & Engineering publications, Vol.13, pp.91103, 2009. [5] Danielle, C.M., Adiel, T., ‘‘Group decision-making for leakage management strategy of water network”, Resources, Conservation and Recycling, Vol. 52, pp. 441-459, 2007. [6] Behzadian, M., Kazemzadeh, R.B., Albadvi, A., Aghdasi, M., “PROMETHEE: A comprehensive literature review on methodologies and applications”, European Journal of Operational Research 2009. [7] Metin, D., “Decision making in equipment selection: an integrated approach with AHP and PROMETHEE”, Springer, No. 19, pp. 397-406, 2008. [8] Golabchi, M. and Mazaherian, H., New Architectural Technologies, University of Tehran press, Tehran, 2010. [9] Edward, A., and Joseph, I., The Architect’s Studio Companion, John Wiley & Sons, Inc., New York, 2002. Asgharpour, M.J., Multi Criteria Decision [10] Making, University of Tehran Press, Tehran, 2008.
The proposed model has only been implemented on an structural system selection problem in the mass construction projects. It can be used also in other aspects of construction engineering and management decision making problems such as equipment management, project delivery systems selection and etc. The PROMETHEE ranking family methods do not have veto threshold. This threshold means that if a criterion overflow the veto threshold, its dependant alternative will be omitted. In such cases the ELECTRE method can be
6
