Efficient Estimation of Arc Criticalities in Stochastic Activity Networks

Abstract

An algorithm is described for estimating arc and path criticalities in stochastic activity networks by combining Monte Carlo simulation with exact analysis conditioned on node release times. These estimators are proved to be unbiased and to have lower variance than the corresponding standard Monte Carlo estimators. The algorithm is applied to a variety of standard and randomly generated test networks to establish that the estimators are significantly and robustly more efficient than the standard estimators when run time and statistical efficiency are properly combined.project management, simulation, conditional estimators

Modeling and Simulation of Project Management through the PMBOK® Standard Using Complex Networks

“…To illustrate the above, the subprocess "develop the project charter" is taken as an example, using a numerical identifier to simplify the simulation process, as follows: source nodes: exogenous (1) and qualitative analysis of risk (4), plan scope management (9), collect requirements (10), define scope (11), plan schedule management (15), plan cost management (22), plan risk management (36), and identify stakeholders (46).…”

“…This included criticism of PERT and the beta-distribution [29][30][31], and the treatment of project management as being not only deterministic [32]. The modeling of the uncertainty of project phenomena began to be considered as assumptions about attributes considered static broadened [33][34][35][36][37][38][39]. System dynamics began to be used for modeling the nonlinear effects of feedback loops in projects [40][41][42][43] and the modeling of projects under diffuse or probabilistic assumptions [44][45][46][47][48].…”

Digital Circuit Optimization via Geometric Programming

“…Statistical (static) timing analysis of a digital circuit is closely related to the stochastic PERT problem for the associated stochastic project network, a well-researched topic (Anklesaria and Drezner 1986, Bowman 1995, Devroye 1979, Hartley and Wortham 1966, Robillard and Trahan 1976, Van Slyke 1963. Indeed, many techniques for statistical timing analysis are based on those developed in the operations research and management science literature, e.g., criticality analysis (Bowman 1995) and distribution bounding (Kleindorfer 1971, Ludwig et al 2001).…”

“…Indeed, many techniques for statistical timing analysis are based on those developed in the operations research and management science literature, e.g., criticality analysis (Bowman 1995) and distribution bounding (Kleindorfer 1971, Ludwig et al 2001). …”

A Dynamic Model F Or Pert Risk Evaluating In Fuzzy Environment

“…Most of these approaches are based on the CPM with formulas for the forward and the backward recursions, in which the deterministic activity times are replaced with the fuzzy activity times.Fatemi and Teimouri [27] presented a exact formula to compute the path critical index and activity critical index for the PERT network by assuming that each activity duration time is a discrete random variable. Bowman [28] described an algorithm for estimating arc and path criticalities in stochastic activity network by combining Mont Carlo simulation with exact analysis conditioned on node release times. Other researchers also done similar cases, but investigating the criticality of a set of activities that are simultaneous progress in project network do not much.…”