Applying fuzzy method for measuring criticality in project network. (English) Zbl 1124.90013

Chen, Chen-Tung; Huang, Sue-Fen

Inf. Sci. 177, No. 12, 2448-2458 (2007).

Summary: Program evaluation and review technique (PERT) is widely used as a tool for managing large-scale projects. In the traditional PERT model, the durations of activities (tasks) are either represented as crisp numbers or drawn from the beta distribution to estimate the task durations such as pessimistic, most likely and optimistic times. However, the operation time for each activity is usually difficult to define and estimate precisely in a real situation. The aim of this paper is to present an analytical method for measuring the criticality in a project network with fuzzy activity times. Triangular fuzzy numbers are used to express the operation times for all activities in a project network. A new model that combines fuzzy set theory with the PERT technique is proposed to determine the critical degrees of activities (tasks) and paths. In the proposed model, a possibility index is defined to identify the likelihood of meeting a specified required time for a project network. At the end of the paper, an example is presented to compare with those obtained using the proposed method as well as other methods. The comparisons reveal that the method proposed in this paper is more effective in determining the activity criticalities and finding the critical path.

MSC:

90B50

Management decision making, including multiple objectives

Keywords:

project management; fuzzy set; program evaluation and review technique (PERT); fuzzy PERT

References:

[1]	Avraham, S., Project segmentation – a tool for project management, International journal of project management, 15, 15-19, (1997)
[2]	Azaron, A.; Perkgoz, C.; Sakawa, M., A genetic algorithm approach for the time-cost trade-off in PERT networks, Applied mathematics and computation, 168, 1317-1339, (2005) · Zbl 1082.65543
[3]	Azaron, A.; Katagiri, H.; Sakawa, M.; Kato, K.; Memariani, A., A multi-objective resource allocation problem in PERT networks, European journal of operational research, 172, 838-854, (2006) · Zbl 1111.90051
[4]	Chanas, S.; Kamburowski, J., The use of fuzzy variables in PERT, Fuzzy sets and systems, 5, 11-19, (1981) · Zbl 0451.90076
[5]	Chanas, S.; Zielinski, P., Critical path analysis in the network with fuzzy task times, Fuzzy sets and systems, 122, 195-204, (2001) · Zbl 1015.90096
[6]	Chen, S.M.; Chang, T.H., Finding multiple possible critical paths using fuzzy PERT, IEEE transactions on systems, man and cybernetics – part B: cybernetics, 31, 930-937, (2001)
[7]	Chen, S.J.; Hwang, C.L., Fuzzy multiple attribute decision making-methods and applications, (1992), Springer-Verlag Berlin Heidelberg
[8]	Chiu, C.W.; Ping, H.L.; Yingn, C.T., Resource-constrained project management using enhanced theory of constraint, International journal of project management, 20, 561-567, (2002)
[9]	Dawson, C.W.; Dawson, R.J., Generalised task-on-the-node networks for managing uncertainty in projects, International journal of project management, 13, 353-362, (1995)
[10]	Dawson, R.J.; Dawson, R.J., Practical proposals for managing uncertainty and risk in project planning, International journal of project management, 16, 299-310, (1998)
[11]	Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academy Press · Zbl 0444.94049
[12]	Dubois, D.; Fargier, H.; Galvagonon, V., On latest starting times and floats in task networks with ill-known durations, European journal of operational research, 147, 266-280, (2003) · Zbl 1037.90004
[13]	H. Fargier, V. Galvagnon, Fuzzy PERT in series-parallel graphs, in: Prooceedings of Nineth International Conference on Fuzzy Systems, 2000, pp. 717-722.
[14]	Fatemi Ghomi, S.M.T.; Teimouri, E., Path critical index and task critical index in PERT networks, European journal of operational research, 141, 147-152, (2002) · Zbl 0998.90009
[15]	Fatemi Ghomi, S.M.T.; Rabbani, M., A new structural mechanism for reducibility of stochastic PERT networks, European journal of operational research, 145, 394-402, (2003) · Zbl 1012.90004
[16]	Graham, K.R., Critical chain: the theory of constraints applied to project management, International journal of project management, 18, 173-177, (2000)
[17]	Giovanni, M., Measuring uncertainty and criticality in network planning by PERT-path technique, International journal of project management, 15, 377-387, (1997)
[18]	Hapke, M.; Slowinski, R., Fuzzy project scheduling system for software development, Fuzzy sets and systems, 67, 101-107, (1994)
[19]	Hapke, M.; Slowinski, R., Fuzzy priority heuristics for project scheduling, Fuzzy sets and systems, 83, 291-299, (1996)
[20]	Heizer, J.; Render, B., Principles of operations management, (1999), Prentice-Hall
[21]	Jha, K.N.; Iyer, K.C., Critical determinants of project coordination, International journal of project management, 24, 314-322, (2006)
[22]	Kaufmann, A.; Gupta, M.M., Introduction to fuzzy arithmetic: theory and applications, (1991), International Thomson Computer Press London · Zbl 0754.26012
[23]	Klir, G.J.; Yuan, B., Fuzzy sets and fuzzy logic: theory and applications, (1995), Prentice-Hall International Inc. · Zbl 0915.03001
[24]	Kuchta, D., Use of fuzzy numbers in project risk (criticality) assessment, International journal of project management, 19, 305-310, (2001)
[25]	Lee, E.S.; Li, R.J., Comparison of fuzzy numbers based on the probability measure of fuzzy events, Computers and mathematics with applications, 15, 887-896, (1988) · Zbl 0654.60008
[26]	Mon, D.L.; Cheng, C.H.; Lu, H.C., Application of fuzzy distributions on project management, Fuzzy sets systems, 73, 227-234, (1995) · Zbl 0855.90056
[27]	Neil, H., The prediction and control of project duration: a recursive model, International journal of project management, 19, 401-409, (2001)
[28]	Premachandrak, I.M., An approximation of the task duration distribution in PERT, Computers and operations research, 28, 443-452, (2001) · Zbl 1080.90531
[29]	Roy, G.; Nava, P.; Israel, S., Integrating system analysis and project management tools, International journal of project management, 20, 461-468, (2002)
[30]	Stevenson, W.J., Operation management, (2002), McGraw-Hill
[31]	Wang, W.C., Impact of soft logic on the probabilistic duration of construction projects, International journal of project management, 23, 600-610, (2005)
[32]	Zadeh, L.A., Fuzzy sets, Information and control, 8, 338-353, (1965) · Zbl 0139.24606
[33]	Zadeh, L.A., Toward a generalized theory of uncertainty (GTU) - an outline, Information sciences, 17, 1-40, (2005) · Zbl 1074.94021
[34]	Zimmerman, H.J., Fuzzy set theory and its applications, (1991), Kluwer Academic Publishers Boston