A Project Scheduling Method Based on Fuzzy Theory

Document Type : Research Paper


1 Sharif University of Technology and Engineering Research Institute, Ministry of Agricultural Jahad, P. O. Box: 13445-754, Tehran, Iran

2 Department of Industrial Engineering, Sharif University of Technology, P. O Box: 11365-9414, Tehran, Iran


In this paper a new method based on fuzzy theory is developed to solve the project scheduling problem under fuzzy environment. Assuming that the duration of activities are trapezoidal fuzzy numbers (TFN), in this method we compute several project characteristics such as earliest times, latest times, and, slack times in term of TFN. In this method, we introduce a new approach which we call modified backward pass (MBP). This approach, based on a linear programming (LP) problem, removes negative and infeasible solutions which can be generated by other methods in the backward pass calculation. We drive the general form of the optimal solution of the LP problem which enables practitioners to obtain the optimal solution by a simple recursive relation without solving any LP problem. Through a numerical example, calculation steps in this method and the results are illustrated.


Main Subjects

[1] Chanas S., Kamburowski J. (1981), The use of fuzzy variables in PERT; Fuzzy Sets and Systems 5(1);
[2] Chanas S., Zielinski P. (2001), Critical path analysis in the network with fuzzy activity times; Fuzzy
Sets and Systems 122; 195-204.
[3] Chang S., Tsujimura Y., Tazawa T. (1995), An efficient approach for large scale project planning
based on fuzzy delphi method; Fuzzy Sets and Systems 76; 277-288.
[4] Chen S. J., Hwang C. L. (1992), Fuzzy multiple attribute decision making: methods and applications;
Lecture notes in economics and mathematical systems, Springer-Verlag; Berlin, Germany.
[5] Dubois D., Prade H. (1988), Possibility theory: an approach to computerized processing of uncertainly;
Plenum Press; New York.
[6] Gazdik I. (1983), Fuzzy-network planning-FNET; IEEE Transactions Reliability 32(2); 304–313.
[7] Kaufmann A., Gupta M. (1985), Introduction to fuzzy arithmetic theory and applications; Van
Nostrand Reinhold; New York.
[8] Kuchta D. (2001), Use of fuzzy numbers in project risk (criticality) assessment; International Journal
of Project Management 19; 305-310.
[9] Lin F.T., Yao J.S. (2003), Fuzzy critical path method based on signed-distance ranking and statistical
confidence-interval estimates; Journal of Supercomputing 24(3); 305-325.
[10] Lorterapong P., Moselhi O. (1996), Project-network analysis using fuzzy sets theory; Journal of
Construction Engineering and Management 122(4); 308-318.
[11] McCahon C.S. (1993), Using PERT as an approximation of fuzzy project-network analysis; IEEE
Transactions on Engineering Management 40(2); 146-153.
[12] Nasution S.H. (1994), Fuzzy critical path method; IEEE Transactions on Systems, MAN, AND
Cybernetics 41(1); 48-57.
[13] Oliveros A., Robinson A. (2005), Fuzzy logic approach for activity delay analysis and schedule
updating; J. Constr. Engrg. and Mgmt. 131(1); 42-51.
[14] Yao J.S., Lin F.T. (2000), Fuzzy critical path method based on signed distance ranking of fuzzy
numbers; IEEE Transactions on Systems, MAN, AND Cybernetics 30(1); 76-82.
[15] Zimermann H.J. (1996), Fuzzy set theory-and its applications; Third Edition, Kluwer Academic
Publishers; Boston.