Indirect parameter elicitation procedures for some distributions with bounded support - with applications in Program Evaluation and Review Technique (PERT)

摘要

The introduction of the Program Evaluation and Review Technique (PERT) dates back to the 1960s and has found wide application since then in the planning of construction projects. Difficulties with the interpretation of the parameters of the beta distribution let Malcolm et al. (Malcolm, D.G., et al., 1959. Application of a technique for research and development program evaluation. Operations Research, 7, 646-649) to elicit them indirectly via the classical expressions for the PERT mean and variance for an activity's completion time. These expressions are specified, given a lower and upper bound estimates a and b and a most likely estimate θ for the activity's duration. Despite a by now 50 -year controversy exemplified by current articles still questioning the PERT mean and variance elicitation approach, their use is still prevalent in current operations research and industrial engineering college text books. In this article an overview is presented of some alternative approaches that have been suggested, including a recent approach that allows for a direct modal range estimation combined with an indirect elicitation of bound and tail parameters of generalised trapezoidal uniform distributions describing activity uncertainty. The potential effect of eliciting a modal range, rather than the narrower point estimate of a single most likely value, shall be demonstrated in an illustrative Monte Carlo analysis for the completion time of an 18-node activity network.