Project scheduling with stochastic activity durations and opportunity costs

The PERT approach to project scheduling with stochastic activity durations has been criticised due to activity-based and network-based inaccuracies. The approximate mean and variance in combination with range and mode do not always lead to a feasible parameter set (p,q) for the Beta-distribution. It can also be questioned whether using the mean as certainty equivalent is an appropriate choice. When a cost concept is introduced, other candidates appear as certainty equivalents. It can be observed that the cost of underestimation is different from the cost of overestimation. A point estimate based on both costs can be realised by defining a loss function and making a Bayesian estimate. When using a linear cost function, cost optimal estimates can be obtained numerically. It is shown which is the range of the optimal estimate, given user input on optimistic, most likely and pessimistic estimates.