On computing the latest starting times and floats of activities in a network with imprecise durations

The paper deals with the problems of computing the intervals of possible values of the latest starting times and floats of activities in networks with imprecise durations, represented by means of interval or fuzzy numbers. So far, these problems have been completely solved when the networks are series parallel. We propose new polynomial algorithms for determining the intervals of the latest starting times in general networks. We also present some complexity results for floats (the computation of floats is probably intractable) and describe some polynomially solvable cases. Then we extend the results to networks with fuzzy durations.

[1]  S. H. Nasution.  Fuzzy Critical Path Method , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[2]  Madan M. Gupta,et al.  Fuzzy mathematical models in engineering and management science , 1988 .

[3]  Andrzej Jaszkiewicz,et al.  Fuzzy project scheduling system for software development , 1994 .

[4]  Heinrich Rommelfanger.  Network analysis and information flow in fuzzy environment , 1994 .

[5]  Giorgio Ausiello,et al.  Theoretical Computer Science Approximate Solution of Np Optimization Problems * , 2022 .

[6]  Pawel Zielinski,et al.  The computational complexity of the criticality problems in a network with interval activity times , 2002, Eur. J. Oper. Res..

[7]  S. Chanas,et al.  THE USE OF FUZZY VARIABLES IN PERT , 1981 .

[8]  H. Prade.  Using fuzzy set theory in a scheduling problem: A case study , 1979 .

[9]  Stefan Chanas,et al.  On the hardness of evaluating criticality of activities in a planar network with duration intervals , 2003, Oper. Res. Lett..

[10]  F. Lootsma.  Fuzzy Logic for Planning and Decision Making , 1997 .

[11]  Didier Dubois,et al.  On the sure criticality of tasks in activity networks with imprecise durations , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[12]  Janet Efstathiou,et al.  Applications of fuzzy set methodologies in industrial engineering , 1990 .

[13]  Ronald R. Yager,et al.  The personalization of security selection: An application of fuzzy set theory , 1981 .

[14]  Igor Gazdik.  Fuzzy-Network Planning - FNET , 1983, IEEE Transactions on Reliability.

[15]  Didier Dubois,et al.  Fuzzy scheduling: Modelling flexible constraints vs. coping with incomplete knowledge , 2003, Eur. J. Oper. Res..

[16]  E. Lee,et al.  Project network analysis with fuzzy activity times , 1988 .

[17]  C. McCahon.  Using PERT as an approximation of fuzzy project-network analysis , 1993 .

[18]  Hélène Fargier,et al.  Fuzzy PERT in series-parallel graphs , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[19]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

[20]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[21]  Pawel Zielinski,et al.  Critical path analysis in the network with fuzzy activity times , 2001, Fuzzy Sets Syst..

[22]  Didier Dubois,et al.  On latest starting times and floats in activity networks with ill-known durations , 2003, Eur. J. Oper. Res..

[23]  James E. Kelley,et al.  Critical-path planning and scheduling , 1899, IRE-AIEE-ACM '59 (Eastern).