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This paper presents the ways of quantification of flow time qualifications that can be used for planning or other stochastic processes by employing Clark’s methods, central limit theorem and Monte Carlo simulation. The results of theoretical researches on superponed flow time quantification for complex activities and events flow in PERT network for project management are also presented. | Yugoslav Journal of Operations Research Vol 19 (2009), Number 1, 195-207 DOI:10.2298/YUJOR0901195L THE DISTRIBUTION OF TIME FOR CLARK’S FLOW AND RISK ASSESSMENT FOR THE ACTIVITIES OF PERT NETWORK STRUCTURE Duško LETIĆ Technical Faculty “Mihajlo Pupin”, Zrenjanin, Serbia dletic@tf.zr.ac.yu Vesna JEVTIĆ Technical Faculty “Mihajlo Pupin”, Zrenjanin, Serbia vesna@tf.zr.ac.yu Received: December 2007 / Accepted: May 2009 Abstract: This paper presents the ways of quantification of flow time qualifications that can be used for planning or other stochastic processes by employing Clark’s methods, central limit theorem and Monte Carlo simulation. The results of theoretical researches on superponed flow time quantification for complex activities and events flow in PERT network for project management are also presented. By extending Clark's research we have made a generalization of flow models for parallel and ordinal activities and events and specifically for their critical and subcritical paths. This can prevent planning errors and decrease the project realization risk. The software solution is based on Clark's equations and Monte Carlo simulation. The numerical experiment is conducted using Mathcad Professional. Keywords: Simulation, mathematical model, risk assessment. 1. INTRODUCTION Figure 1 represents the basic submodel of network diagram for activities and events for which Clark’s equation of resulting activity is defined. It consists of an oriented graph with two parallel activities with a common start (r) and a terminal event D. Letić, V. Jevtić / The Distribution of Time 196 (k). Complex network with parallel-ordinal activities like this one, for the sake of further analysis must be divided into sub networks with only ordinal or parallel activities. Parallel activities may be independent (locally autonomous) until their realization (e.g. in k moment). However, there can exist dependencies between them, in case of which we have Clark’s equations [1]. In this .
