Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2008.4061.4069GhoseiriK.MoghadamA.R.J.122008822In order to specify the critical path in project networks
in the traditional models, the durations of activities (tasks) are represented
as crisp numbers. However, the operation time for each activity is usually
difficult to define and estimate precisely in a real situation. The aim
of this study is to present an analytical method to determine the critical
path in a project network with continuous fuzzy activity durations by
use of the longest path algorithm. In this study, we will propose fuzzy
program evaluation review technique Bellman algorithm by the use of fuzzy
sets, program evaluation review technique and Bellman algorithm to specify
the critical path and the fuzzy earliest/latest starting time and fuzzy
floats of activities in the continuous fuzzy network. Inputs and outputs
of the proposed algorithms are fuzzy numbers and this algorithm is able
to compute the fuzzy error time and occurrence probability of this error
time. The complexity of this algorithm is the indicator its excellent
performance. An example is presented to illustrate the proposed algorithm
as well as to compare the results with those obtained using the crisp
models. The comparisons reveal that the use of fuzzy models is more effective
in determining the critical path and floats.]]>Chanas, S. and J. Kamburowski,1981Chanas, S. and P. Zielinski,2001Chanas, S. and P. Zielinski,2002Chanas, S., D. Dubois and P. Zielinski,2002Chen, S.P., 2006Chen, C.T. and S.F. Huang,2007Cheng, C.H.,1980Delgado, M., J.L. Verdegay and M.A. Vila,1988Dubois, D., H. Fargier and V. Galvagnon,2003Dubois, D. and H. Prade,1980GarcĂa, M.S. and M.T. Lamata, 2005Hernandes, F., M.T. Lamata, J.L. Verdegay and A. Yamakami,2007Ishibuchi, H. and H. Tanaka,1990Kaufmann, A. and M.M. Gupta,1991Klir, G.J. and B. Yuan,1995Liou, T.S. and M.J.J. Wang,1992Liberatore, M.J. and J.F. Connelly,2001Mon, D.L., C.H. Cheng and H.C. Lu,1995Nayeem, S.M.A. and M. Pal,2005Seda,2006Sengupta, A. and T.K. Pal,2000Shipley, M.F., A. De Korvin and K. Omer,1997Zielinski, P.,2005Zimmerman, H.J.,1991Wang, X. and E. Kerre,2001Wang, X. and E. Kerre,2001