The Influence of Beta Shape Parameters in Project Planning
Networks can be utilized to represent project planning problems, using nodes for activities and arcs to indicate precedence relationship between them. For fixed activity duration, a simple algorithm calculates the amount of time required to complete a project, followed by the activities that comprise the critical path. Program Evaluation and Review Technique (PERT) generalizes the above model by incorporating uncertainty, allowing activity durations to be random variables, producing nevertheless a relatively crude solution in planning problems. In this paper, based on the findings of the relevant literature, which strongly suggests that a Beta distribution can be employed to model earthmoving activities, we utilize Monte Carlo simulation, to estimate the project completion time distribution and measure the influence of skewness, an element inherent in activities of modern technical projects. We also extract the activity criticality index, with an ultimate goal to produce more accurate planning estimations.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.2643634Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 463
 AbouRizk, S. M. and Halpin, D. W. (1992), “Statistical properties of construction duration data”, Journal of Constr. Eng. and Management 118(3), 525–544.
 Azaron, A. and Fatemi Ghomi, S. (2007), “Expected duration of dynamic Markov PERT networks”, Int. J. of Industrial Engineering & Production Research 18(3), 1–5.
 Elmaghraby, S. (1997), Markov activity networks, Technical report, North Carolina State University.
 Farnum, N. R. and Stanton, L. W. (1987), “Some results concerning the estimation of beta distribution parameters in PERT”, Journal of the Operations Research Society 38(3), 287–290.
 Golenko-Ginzburg, D. (1988), “On the distribution of activity time in PERT”, Journal of the Operations Research Society 39(8), 767-771.
 Kamburowski, J. (1997), “New validations of PERT times”, Omega, 25(3), 323-328.
 Keefer, D. L. and Verdini, W. A. (1993), “Better estimation of PERT activity time parameters”, Management Science 39(9), 1086–1091.
 Kulkarni, V. and Adlakha, V. (1986), “Markov and Markov-regenerative PERT networks”, Operations Research 34(5), 769–781.
 Littlefield, T. and Randolph, P. (1991), “PERT duration times: mathematics or MBO”, Interfaces 21(6), 92–95.
 Malcolm, D. G., Roseboom, J. H., Clark, C. E. and Fazar, W. (1959), “Application of a technique for research and development program evaluation”, Operations Research 7(5), 646-669.
 Mehrotra, K., Chai, J. and Pillutla, S. (1996), “A study of approximating the moments of the job completion time in PERT networks”, J. of Op. Management 14(3), 277.
 Milian, Z. (2008), “Monte Carlo simulation with exact analysis for stochastic PERT networks”, ISARC-2008, pp. 598–603.
 Norris, J. R. (1998), Markov chains, Cambridge University Press.
 Premachandra, I. (2001), “An approximation of the activity duration distribution in PERT”, Computers & Operations Research 28(5), 443–452.
 Shankar, N. R., Babu, S. S., Thorani, Y. and Raghuram, D. (2011), “Right skewed distribution of activity times in PERT”, Int. Journal of Eng. Science 3(4), 2932–2938.
 Shankar, N. R. and Sireesha, V. (2009), “An approximation for the activity duration distribution, supporting original PERT”, Ap. Math. Sciences 3(57), 2823–2834.
 Tattoni, S., Laura, L. and Schiraldi, M. (2008), “Estimating projects duration in Uncertain environments: Monte Carlo simulations strike back”, 22nd IPMA World Congress, Roma, Italy.
 Van Slyke, R. M. (1963), “Letter to the editor-Monte Carlo methods and the PERT problem”, Operations Research 11(5), 839–860.
 Wyrozebski, P. and Wyrozebska, A. (2013), “Benefits of Monte Carlo simulation as the extension to the PERT technique”, 2nd EIIC.
 Xiangxing, K., Xuan, Z. and Zhenting, H. (2010), “Markov skeleton process in PERT networks”, Acta Mathematica Scientia 30(5), 1440–1448.