Table 7: Indirect influence matrix ID for the factors
Factors US OB PM DM Sum
Step D4: Deriving total influence matrix
The total influence matrix T is defined as follows:
T = +D ID (4)
Table 8 presents the total influence matrix for the factors. Additionally, suppose di denotes the row sum of the i-th row of matrix T. Then d can represent the sum of direct and indirect i influences of factor i on the other factors. If rj denotes the column sum of the j-th column of matrix T, then rj indicates the sum of direct and indirect influences that factor j has received from the other factors. Furthermore, when j = i, di+ri provides an index of the strength of influences given and received. If di-ri is positive, then factor i influences other factors more than it is influenced. Conversely, if di-ri is negative, then factor i is influenced by other factors (Tzeng et al., 2007). Table 9 shows the results of d+r and d-r for the factors.
Table 8: Total influence matrix T for the factors
Factors US OB PM DM Sum
27th International Symposium on Automation and Robotics in Construction (ISARC 2010)
Table 9: Degree of total influence for the factors
Factors
Sum of columns (d)
Sum of rows (r)
Sum of (columns + rows) (d+r)
Sum of (columns – rows) (d-r) 1. US 13.654 12.795 26.449 0.859 2. OB 13.700 12.302 26.002 1.398 3. PM 12.154 13.474 25.627 -1.320 4. DM 12.164 13.101 25.266 -0.937
Step D5: Obtaining the influence-relations map
An influence-relations map can be developed using the values of d+r and d-r to be the x axis and y axis, respectively. Figure 2 presents the IR map for the case project. Additionally, a net influence matrix N can also be calculated as follows:
ij ij ji
N=nt = −t t (7) For example, based on the total influence matrix T for the factors (Table 8), the net influence of the OB factor on the US factor is calculated to be 0.137 (=3.468-3.331).
Figure 2: Influence-relations map of the factors
Integration of SIA and DEMATEL
Figure 3 integrates the evaluation results of applying the SIA and DEMATEL methods. The left of the figure (SIA) shows that the “organization’s decision makings and budget constraints (OB)” factor has a positive value of importance (i.e., a high influence on the performance of design duration) and a negative value of satisfaction (i.e., unfavorable performance of design duration). That is, the performance of the OB factor requires to be improved immediately. Management then should trace which factor dominates the OB factor from the right of the figure (DEMATEL). The DEMATAL suggests that improving the performance of the OB factor must improve itself because the performance of the OB factor is only dominated by itself.
27th International Symposium on Automation and Robotics in Construction (ISARC 2010)
Figure 3: Integration of SIA and DEMATEL for the factors
Tracing to the second-level sub-factors
The next step is to further find out which sub-factors under the OB factor are the most influential factors that cause the design delays. Using the similar steps of SIA and DEMATEL methods, the results found that sub-factors OB1 (DM’s decision makings) and OB2 (DM’s supervision ability) need to be improved immediately under the OB factor.
Figure 4 displays the IR map for the sub-factors under the OB factor.
Figure 4: IR map for the sub-factors under the OB factor
CONCLUSIONS
Based on a real design project, this work proposes a methodology to support analyze and solve design delay problems. In the case study, the SIA analysis indicates that the OB factor is the key delay factor. Additionally, suggested by the DEMATEL analysis, improving the performance of the OB factor is to improve itself. Next, using the similar steps of SIA and DEMATEL, the results found that the OB1 and OB2 sub-factors of the OB1 factor must be improved immediately. Top management of the case project appreciates the application results. Future research is to computerize the proposed methodology for expediting the
-2 -1.5 -1 -0.5 0 0.5 1 1.5
Standardized satisfaction value (SS) 1. User needs and
specification requirements (US) 2. Organization’s
decision makings and
budget constraints (OB) 3. Project control and review management
(PM)
4. Design execution and interface management (DM) 4. Design exe.
& interface manage. (DM)
3. Project control and review management (PM) 2. Organization’s decision makings
and budget constraints (OB)
1. User needs and Budget availability
(OB3)
DM’s supervision ability
(OB2) DM’s decision-makings (OB1)
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 DM’s supervision
ability (OB2)
DM’s resource allocation (OB4) DM’s
decision-makings (OB1)
Budget availability (OB3)
27th International Symposium on Automation and Robotics in Construction (ISARC 2010)
evaluations such that proper actions can be taken in time for supporting design duration management.
ACKNOWLEDGEMENT
The authors would like to thank the National Science Council of Taiwan for financially supporting this research under Contract No. NSC98-2221-E-009-169. Those respondents and experts involved in the case study are appreciated for their collaboration.
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