Letter to the Editor—Monte Carlo Methods and the PERT Problem

Abstract

Many planning problems can be represented as a network in which the arcs represent “activities” with lengths equal to the time required for the activities performance and the nodes represent “events,” marking the beginning and ending in time of activities. For fixed activity durations, a very simple algorithm gives the length of time required for the total project as well as indicating the activities which are particularly obstructive, those on the “critical path” “PERT” generalizes the above model to recognize uncertainty in the activity durations by allowing them to be random variables. A relatively crude solution to this problem is obtained by reducing the problem back to the first case, by means of appropriate approximation. In this paper the results of a Monte Carlo simulation of PERT networks are given. First the concept of using Monte Carlo methods to give solutions to PERT problems under less restrictive assumptions is discussed. Results are given for the accuracy obtainable, for the computing time required and devices for reducing computation are developed. Finally a “critically” index is defined for each activity. This index is simply the probability that the activity will be on the critical path. The ramifications and uses of this parameter, which is not available using current techniques, are developed.