Risk-Taking in Critical Path Analysis

In most PERT scheduling problems, uncertainties in job duration are handeled by a “wait-and-see” formulation in which it is assumed that the samples of job duration are known at the moment of scheduling; much attention has been devoted to the distribution of minimal project time under these assumptions. In this paper, a “here-and-now” formulation is proposed in which the manager takes a risk by fixing the project event times before the job durations are known; based on the allotted time interval, and the actual duration of the job, additional effort may have to be expended to stay on schedule. Under general assumptions, it is shown that minimizing the average total additional effort needed to stay on schedule will result in a cost-time scheduling problem of the CPM type.