Risk taking in stochastic PERT networks

Abstract

This paper studies a PERT problem which incorporates project managers' risk taking behavior in stochastic environments. In this stochastic PERT network, which we refer to as RISKPERT, activity durations are nonnegative random variables, and a project manager uses a disutility function to evaluate each path and chooses that path which maximizes his expected disutility as an ‘optimal’ (or critical) path. This path, as opposed to the classical critical path, is used as a basis to analyze the PERT network and to estimate the probability of completion time. The general RISKPERT is difficult to solve; however, special cases when activity durations are statistically independent and disutility functions are linear, exponential, quadratic, or linear-exponential, are solvable exactly. The illustrative examples demonstrate that RISKPERT captures managers' risk taking behavior and provides results that are more realistic than those of the classical PERT models. Furthermore, this paper extends some of the RISKPERT models to include multi-dimensional PERT networks.