On scheduling influential stochastic tasks on a single machine

A single machine is available to process a collection of stochastic tasks in a manner consistent with precedence constraint ¦). The degree of success encountered in the processing of a task influences the returns from task processed later. Two different modes of influence (called sequence and predecessor) are considered, but influence is always expressed via a multiplicative contribution to the appropriate returns. Developments of Gittins index theory yield optimal policies in the class of preemptive/nonpreemptive/permutation policies for a variety of assumptions about ¦).