A New Technique for Estimating the Distribution of a Stochastic Project Makespan

A critical success dimension in projects is the ability to complete a project within an estimated duration. In that regard, effective project scheduling techniques in an uncertain environment is of interest in many organizations. In this paper, the authors use an analytic approach to analyze the behavior of time duration distributions of projects in stochastic activity networks, and propose a simple computation scheme for approximating their distribution. The findings offer an understanding of the large gap between PERT and simulation results, and the deviation of projects from their intended schedules. In addition to providing theoretical framework, the proposed approach also recommends a simple practical pragmatic technique that computes the time distribution of project duration. This is a simple and handy tool for the project manager that may replace simulation. As a byproduct, the earliest start time distribution for each activity is also estimated.

[1]  Terry R. Adler,et al.  How organisational cost reporting practices affect project management: the issues of project review and evaluation , 2009 .

[2]  Jane N. Hagstrom,et al.  Computing the probability distribution of project duration in a PERT network , 1990, Networks.

[3]  Salah E. Elmaghraby,et al.  On the fallacy of averages in project risk management , 2005, Eur. J. Oper. Res..

[4]  Konstantinos Kirytopoulos,et al.  PERT vs. Monte Carlo Simulation along with the suitable distribution effect , 2008 .

[5]  Ofer Zwikael,et al.  Non-delay scheduling as a managerial approach for managing projects , 2006 .

[6]  John M. Burt,et al.  Conditional Monte Carlo: A Simulation Technique for Stochastic Network Analysis , 1971 .

[7]  Vamsi Salaka,et al.  Project management and scheduling for enterprise integration , 2008 .

[8]  Richard M. Van Slyke,et al.  Letter to the Editor---Monte Carlo Methods and the PERT Problem , 1963 .

[9]  Janice M. Burn,et al.  Knowledge Management Strategies for Virtual Organisations , 2000, Inf. Resour. Manag. J..

[10]  Eugene David Hahn,et al.  Mixture densities for project management activity times: A robust approach to PERT , 2008, Eur. J. Oper. Res..

[11]  George B. Kleindorfer,et al.  Bounding Distributions for a Stochastic Acyclic Network , 1971, Oper. Res..

[12]  S. Elmaghraby.  On the Expected Duration of PERT Type Networks , 1967 .

[13]  Mehdi Khosrow-pour,et al.  Advanced topics in information resources management , 2003 .

[14]  Robert C. Ash,et al.  Towards holistic project scheduling using critical chain methodology enhanced with PERT buffering , 2008 .

[15]  Gideon Weiss,et al.  Stochastic bounds on distributions of optimal value functions with applications to pert, network flows and reliability , 1984, Oper. Res..

[16]  Andrew W. Shogan.  Bounding distributions for a stochastic pert network , 1977, Networks.

[17]  H. N. Nagaraja,et al.  Order Statistics, Third Edition , 2005, Wiley Series in Probability and Statistics.

[18]  Vidyadhar G. Kulkarni,et al.  A classified bibliography of research on stochastic PERT networks: 1966-1987 , 1989 .

[19]  Malik Ranasinghe,et al.  Quantification and management of uncertainty in activity duration networks , 1994 .

[20]  Richard J. Schonberger,et al.  Why Projects Are “Always” Late: A Rationale Based on Manual Simulation of a PERT/CPM Network , 1981 .

[21]  Terry Williams,et al.  Practical Use of Distributions in Network Analysis , 1992 .

[22]  Mehdi Khosrow-Pour,et al.  Printed at: , 2011 .

[23]  Bajis M. Dodin,et al.  Approximating the Criticality Indices of the Activities in PERT Networks , 1985 .

[24]  Shih-Pin Chen,et al.  Analysis of critical paths in a project network with fuzzy activity times , 2007, Eur. J. Oper. Res..

[25]  R. A. Bowman.  Efficient estimation of arc criticalities in stochastic activity networks , 1995 .

[26]  A. R. Klingel,et al.  Bias in Pert Project Completion Time Calculations for a Real Network , 1966 .

[27]  R. Alan Bowman.  Due Date-Based Metrics for Activity Importance in Stochastic Activity Networks , 2001, Ann. Oper. Res..

[28]  Jack C. Hayya,et al.  Efficiency of the Antithetic Variate Method for Simulating Stochastic Networks , 1982 .

[29]  Ofer Zwikael,et al.  Modelling and scheduling projects using Petri nets , 2008 .

[30]  Tetsuo Iida,et al.  Computing bounds on project duration distributions for stochastic PERT networks , 2000 .

[31]  Helen Richardson,et al.  Directing Equal Pay in the UK ICT Labour Market , 2006 .

[32]  B. Yum,et al.  An uncertainty importance measure of activities in PERT networks , 1997 .

[33]  G. Kelley.  Selected Readings on Information Technology Management: Contemporary Issues , 2008 .

[34]  José Francisco Aldana Montes,et al.  Database Technologies on the Web , 2005, Encyclopedia of Information Science and Technology.

[35]  Mete Sirvanci,et al.  Stochastic networks and the extreme value distribution , 1990, Comput. Oper. Res..

[36]  Bajis M. Dodin,et al.  Bounding the Project Completion Time Distribution in PERT Networks , 1985, Oper. Res..

[37]  Mehdi Khosrowpour,et al.  Dictionary of Information Science and Technology , 2006 .

[38]  J. Michael Pearson,et al.  An Empirical Examination of the Impact Organizational Culture Has on Employees' Computer Self-Efficacy , 2004 .

[39]  Bajis Dodin,et al.  A Practical and Accurate Alternative to PERT , 2006 .

[40]  Erik Demeulemeester,et al.  Project scheduling : a research handbook , 2002 .

[41]  Rolf H. Möhring,et al.  A Computational Study on Bounding the Makespan Distribution in Stochastic Project Networks , 2001, Ann. Oper. Res..

[42]  D. Malcolm,et al.  Application of a Technique for Research and Development Program Evaluation , 1959 .

[43]  Bajis M. Dodin.  Determining the K Most Critical Paths in PERT Networks , 1984, Oper. Res..

[44]  Ned Kock,et al.  Compensatory Adaptation to Media Obstacles: An Experimental Study of Process Redesign Dyads , 2005, Inf. Resour. Manag. J..

[45]  Alfredo Cuzzocrea.  Models and Techniques for Approximate Queries in OLAP , 2009 .

[46]  Salah E. Elmaghraby.  On criticality and sensitivity in activity networks , 2000, Eur. J. Oper. Res..

[47]  Ignacio E. Grossmann,et al.  The exact overall time distribution of a project with uncertain task durations , 2000, Eur. J. Oper. Res..

[48]  E. Turban,et al.  Usage of and support for information centers: an exploratory survey , 1990, Twenty-Third Annual Hawaii International Conference on System Sciences.