Possibilistic Moments for the Task Duration in Fuzzy PERT

AbstractProgram (or project) evaluation review technique (PERT) has remained a modern method in project scheduling for decades. Since its invention, numerous authors have tried modifications to its basic method in an attempt to overcome its intrinsic drawbacks. In this paper, the authors research improvements to the Fuzzy version of PERT. The initial motivation is the avoidance of the backward recursion problem in Fuzzy PERT, with fuzzy input data for the task durations through an alternative approach. Furthermore, the authors propose various membership functions for the representation of the fuzzy task duration in accordance with the nature of each task. This approach is intended to give more realistic results. The tools for this operation are the possibilistic mean and the possibilistic variance of fuzzy numbers. The possibilistic method acts as a defuzzification method that results in a crisp value as an outcome both for the task times (earliest/latest start - earliest/latest finish) and for the floats...

[1]  D. Malcolm,et al.  Application of a Technique for Research and Development Program Evaluation , 1959 .

[2]  Chengdong Wu,et al.  The rough set theory and applications , 2004 .

[3]  Albert P.C. Chan,et al.  Fuzzy set theory approach for measuring the performance of relationship-based construction projects in Australia , 2012 .

[4]  Jiuping Xu,et al.  Control Risk for Multimode Resource-Constrained Project Scheduling Problems under Hybrid Uncertainty , 2015 .

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

[6]  Aerambamoorthy Thavaneswaran,et al.  Fuzzy random‐coefficient volatility models with financial applications , 2006 .

[7]  Basil K. Papadopoulos,et al.  Approaching activity duration in PERT by means of fuzzy sets theory and statistics , 2014, J. Intell. Fuzzy Syst..

[8]  D. Dubois,et al.  The mean value of a fuzzy number , 1987 .

[9]  T. Ross.  Fuzzy Logic with Engineering Applications , 1994 .

[10]  Murat Gunduz,et al.  Fuzzy Assessment Model to Estimate the Probability of Delay in Turkish Construction Projects , 2015 .

[11]  Ming Lu.  Enhancing Project Evaluation and Review Technique Simulation through Artificial Neural Network-based Input Modeling , 2002 .

[12]  Qiming Li,et al.  Performance Objectives Selection Model in Public-Private Partnership Projects Based on the Perspective of Stakeholders , 2010 .

[13]  Basil K. Papadopoulos,et al.  Hybrid (fuzzy-stochastic) modelling in construction operations management , 2013, Int. J. Mach. Learn. Cybern..

[14]  A. Thavaneswaran,et al.  Option valuation model with adaptive fuzzy numbers , 2007, Comput. Math. Appl..

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

[16]  Konstantinos A. Chrysafis,et al.  On theoretical pricing of options with fuzzy estimators , 2009 .

[17]  Christer Carlsson,et al.  On Possibilistic Mean Value and Variance of Fuzzy Numbers , 1999, Fuzzy Sets Syst..

[18]  Margaret F. Shipley,et al.  BIFPET methodology versus PERT in project management: fuzzy probability instead of the beta distribution , 1997 .

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

[20]  Michael Hanss,et al.  Applied Fuzzy Arithmetic: An Introduction with Engineering Applications , 2004 .

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

[22]  Ronald R. Yager,et al.  Operations on fuzzy numbers via fuzzy reasoning , 1997, Fuzzy Sets Syst..

[23]  M. Shimura.  Fuzzy sets concept in rank-ordering objects , 1973 .

[24]  José Ramón,et al.  Critical Path Definition Using Multicriteria Decision Making: PROMETHEE Method , 2013 .

[25]  James T. O'Connor,et al.  Characteristics for Leveraging Value Management Processes on Capital Facility Projects , 2006 .

[26]  R. Goetschel,et al.  Elementary fuzzy calculus , 1986 .

[27]  Garyfalos Papaschinopoulos,et al.  On the fuzzy difference equations of finance , 2008, Fuzzy Sets Syst..

[28]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .

[29]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[30]  Erik Demeulemeester,et al.  Project scheduling : a research handbook , 2002 .

[31]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[32]  Konstantinos A. Chrysafis,et al.  Corporate investment appraisal with possibilistic CAPM , 2012, Mathematical and computer modelling.

[33]  Chen-Tung Chen,et al.  Applying fuzzy method for measuring criticality in project network , 2007, Inf. Sci..

[34]  Simaan M. AbouRizk,et al.  FITTING BETA DISTRIBUTIONS BASED ON SAMPLE DATA , 1994 .