caa a22 4500 445359773 CHVBK 20180317142911.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10100-010-0151-x doi (NATIONALLICENCE)springer-10.1007/s10100-010-0151-x Monhor Davaadorjin Faculty of Geoinformatics, University of West Hungary, Pirosalma u.1-3, Szekesfehervar, Hungary aut A new probabilistic approach to the path criticality in stochastic PERT [Elektronische Daten] [Davaadorjin Monhor] The notion of critical path is a key issue in the temporal analysis of project scheduling in deterministic setting. The very essence of the CPM consists in identifying the critical path, i.e., the longest path in a project network, because this path conveys information on how long it should take to complete the project to the project manager. The problem how can a stochastic counterpart of the deterministic critical path be defined is an important question in stochastic PERT. However, in the literature of stochastic PERT this question has so far almost been ignored, and the research into the random nature of a project duration has mainly been concentrated on the completion time in stochastic PERT in which any concrete special path is not specified. In the present paper we attempt to take first steps to fill this gap. We first developed a probabilistic background theory for univariate and bivariate marginal distributions of path durations of stochastic PERT whose joint path durations are modelled by multivariate normal distribution. Then, a new probabilistic approach to the comparison of path durations is introduced, and based on this comparison we define the concept of probabilistically critical path as a stochastic counterpart of the deterministic critical path. Also, an illustrative simple example of PCP and numerical results on the established probability bounds are presented. Springer-Verlag, 2010 Bounding bivariate normal probabilities nationallicence Critical path nationallicence Completion time in stochastic PERT nationallicence Probabilistically critical path nationallicence Stochastic PERT nationallicence Central European Journal of Operations Research Springer-Verlag 19/4(2011-12-01), 615-633 1435-246X 19:4<615 2011 19 10100 https://doi.org/10.1007/s10100-010-0151-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10100-010-0151-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Monhor Davaadorjin Faculty of Geoinformatics, University of West Hungary, Pirosalma u.1-3, Szekesfehervar, Hungary aut NATIONALLICENCE 773 0- Central European Journal of Operations Research Springer-Verlag 19/4(2011-12-01), 615-633 1435-246X 19:4<615 2011 19 10100 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer