A study of approximating the moments of the job completion time in PERT networks

Kishan Mehrotra, John Chai, Sharma Pillutla

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


The importance of proper management of projects has not gone unrecognized in industry and academia. Consequently, tools like the Critical Path Method (CPM) and the Program Evaluation Review Technique (PERT) for project planning have been the focus of attention of both practitioners and researchers. Determination of the Time to Complete the Job (TCJ) in PERT networks is important for planning and bidding purposes. The complexity involved in accurately determining the TCJ has led to the development of many approximating procedures. Most of them ignore the dependence between paths in the network. We propose an approximation to determine the TCJ which explicitly recognizes this dependency. Dependency in networks arises due to commonality of activities among various paths in the network. We develop an approximation which is simple to use and makes use of readily available tables. Also, the approximation employs the traditional concept of the critical path which is easy to understand and to operationalize. The activities on the critical paths are divided into an independent portion and a dependent portion. The dependent portion comprises activities common to various critical paths. Order statistics are used in computing the time for the dependent portion of the critical path. We present the theoretical underpinnings of our approach and illustrate its application via an example. In the absence of other measures, we use simulation results as a proxy for the TCJ and as a benchmark to measure the accuracy of our approximation. Empirical results are obtained for a variety of networks in the literature. We show that the distribution of the TCJ is better approximated by a mixture of distributions. Comparison with other approaches from the literature indicates that our approximation yields estimates for the TCJ which are closer to the simulation results.

Original languageEnglish (US)
Pages (from-to)277-289
Number of pages13
JournalJournal of Operations Management
Issue number3
StatePublished - Sep 1996


  • AOA (Activity-on-Arrow)
  • Activity criticality index
  • Arc
  • CPM (Critical Path Method)
  • Critical path
  • Deterministic
  • Node
  • PERT (Program Evaluation Review Technique)
  • Path activity index
  • Stochastic
  • Subcritical path
  • TCJ (Time to Complete the Job)

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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