Modeling activity times by the Parkinson distribution with a lognormal core: Theory and validation

• Published in: European journal of operational research Vol. 216; no. 2; pp. 386 - 396
• Main Authors: Trietsch, Dan, Mazmanyan, Lilit, Gevorgyan, Lilit, Baker, Kenneth R.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.01.2012; Elsevier; Elsevier Sequoia S.A
• Subjects: Applied sciences; Exact sciences and technology; Linear association; Linear programming; Lognormal scheduling; Operational research and scientific management; Operational research. Management science; Parkinson distribution; PERT; Probability distribution; Project scheduling; Random variables; Scheduling, sequencing; Stochastic models; Stochastic scheduling; Validation studies; Lognormal scheduling; Project scheduling; Stochastic scheduling; PERT; Parkinson distribution; Linear association; Project management; Empirical method; Rounding error; Censorship; Scheduling; Modeling; Lognormal distribution; Linear model; Stochastic programming; Statistical test; Dependence; Earliness
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2011.07.054

► We validate the lognormal distribution for project activity times. ► We introduce a new version of the Parkinson distribution (hidden earliness). ► We show how use it to diagnose and estimate the Parkinson effect. ► We demonstrate that activity times are usually correlated and often uncalibrated. ► We show how to account for correlation and calibration by a linear association model. Based on theoretical arguments and empirical evidence we advocate the use of the lognormal distribution as a model for activity times. However, raw data on activity times are often subject to rounding and to the Parkinson effect. We address those factors in our statistical tests by using a generalized version of the Parkinson distribution with random censoring of earliness, ultimately validating our model with field data from several sources. We also confirm that project activities exhibit stochastic dependence that can be modeled by linear association.