Linear preselective policies for stochastic project scheduling

We introduce a new class of policies for stochastic project scheduling with resource constraints, the linear preselective policies. They combine the benefits of two known classes of scheduling policies for stochastic and deterministic scheduling, viz. priority policies and preselective policies. Priority policies solve resource conflicts by means of a priority list (list scheduling). They have several computational benefits but suffer from the well-known Graham anomalies. On the other hand, preselective policies possess favorable properties such as continuity and monotonicity and thus avoid these anomalies, but computing optimal such policies requires excessive computation time. The new class of linear preselective policies is a subclass of the class of preselective policies. Like priority policies, linear preselective policies use priority lists for their definition. They thus inherit all favorable properties of preselective policies but are far better computationally tractable. We study several properties of this new class and compare it with other classes of policies which have been stated in the literature. It particularly turns out that this class properly dominates the class of activity-based priority rules known from deterministic scheduling.