Notes on Combinatorial Mathematics

An Estimate of Expected Critical Path Length in PERT Networks

by J. H. Lindsey

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PERT (Program Evaluation and Review Technique), a much-used management control technique for scheduling and administering large projects, has been applied to numerous defense programs in which the problem of treating schedule uncertainties during the development phase is troublesome. This report supplies a new estimate of the expected time required to complete an entire project, assuming that the times required to carry out the various subprojects are uncertain. A method is described for obtaining an approximation of the expected duration time of a project whose individual job times are discrete random variables. The approximation should be more accurate than a previous one by D. R. Fulkerson (RM-3075), but has the disadvantage that it may lie on either side of the expected duration time. (See also RM-3408, RM-4137, RM-4697.)

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