Theoretical Article


, Volume 48, Issue 4, pp 355-370

First online:

Solution of interval PERT/CPM network problems by a simplified tabular method

  • Sathi MukherjeeAffiliated withDepartment of Mathematics, Bengal College of Engineering & Technology Email author 
  • , Kajla BasuAffiliated withDepartment of Mathematics, National Institute of Technology

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In conventional project scheduling problem like PERT/CPM, the activity times are determined by experts as crisp numbers. But in an uncertain environment, the representation of an expert may be imprecise. Several factors can affect the schedule. In this paper, a method of solving an interval PERT/CPM problem has been proposed. We have considered interval numbers to represent the activity times which is more realistic in nature. This method is based on interval analysis and provides all the parameters involved in the traditional PERT/CPM technique including interval latest starting and finishing times in the network. It involves a tabular method that is very simple and easy to understand, both for technical and non-technical persons. As the data of the problem are interval numbers, the results are also in terms of interval numbers. Interval total completion time and the critical path can be found by this method even without finding the total float or free float of the activities. A notion of the criticality degree of the activities has been introduced here. A numerical example illustrates the method.


Network flows Project management PERT/CPM Interval numbers Critical path Float Interval activity time